Patent Publication Number: US-11646045-B2

Title: Robust short-time fourier transform acoustic echo cancellation during audio playback

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority under 35 U.S.C. § 120 to, and is a continuation of, U.S. non-provisional patent application Ser. No. 16/600,644, filed on Oct. 14, 2019, entitled “Robust Short-Time Fourier Transform Acoustic Echo Cancellation During Audio Playback,” which is incorporated herein by reference in its entirety. 
     U.S. non-provisional patent application Ser. No. 16/600,644 claims priority under 35 U.S.C. § 120 to, and is a continuation of, U.S. non-provisional patent application Ser. No. 15/717,621, filed on Sep. 27, 2017, entitled “Robust Short-Time Fourier Transform Acoustic Echo Cancellation During Audio Playback,” and issued as U.S. Pat. No. 10,466,165 on Oct. 15, 2019, which is incorporated herein by reference in its entirety. 
    
    
     FIELD OF THE DISCLOSURE 
     The disclosure is related to consumer goods and, more particularly, to methods, systems, products, features, services, and other elements directed to media playback or some aspect thereof. 
     BACKGROUND 
     Options for accessing and listening to digital audio in an out-loud setting were limited until in 2003, when SONOS, Inc. filed for one of its first patent applications, entitled “Method for Synchronizing Audio Playback between Multiple Networked Devices,” and began offering a media playback system for sale in 2005. The Sonos Wireless HiFi System enables people to experience music from many sources via one or more networked playback devices. Through a software control application installed on a smartphone, tablet, or computer, one can play what he or she wants in any room that has a networked playback device. Additionally, using the controller, for example, different songs can be streamed to each room with a playback device, rooms can be grouped together for synchronous playback, or the same song can be heard in all rooms synchronously. 
     Given the ever-growing interest in digital media, there continues to be a need to develop consumer-accessible technologies to further enhance the listening experience. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Features, aspects, and advantages of the presently disclosed technology may be better understood with regard to the following description, appended claims, and accompanying drawings where: 
         FIG.  1    shows a media playback system configuration in which certain embodiments may be practiced; 
         FIG.  2    is a functional block diagram of an example playback device; 
         FIG.  3    is a functional block diagram of an example controller device; 
         FIGS.  4 A and  4 B  are controller interfaces; 
         FIG.  5 A  is a functional block diagram of an example network microphone device in accordance with aspects of the disclosure; 
         FIG.  5 B  is a diagram of an example voice input in accordance with aspects of the disclosure; 
         FIG.  6    is a functional block diagram of example remote computing device(s) in accordance with aspects of the disclosure; 
         FIG.  7    is a schematic diagram of an example network system in accordance with aspects of the disclosure; 
         FIG.  8 A  is a functional block diagram of an example acoustic echo cancellation pipeline; 
         FIG.  8 B  is a functional block diagram of an example acoustic echo cancellation pipeline; 
         FIG.  9    is a flow diagram of a method of performing acoustic echo cancellation. 
     
    
    
     The drawings are for purposes of illustrating example embodiments, but it is understood that the inventions are not limited to the arrangements and instrumentality shown in the drawings. In the drawings, identical reference numbers identify at least generally similar elements. To facilitate the discussion of any particular element, the most significant digit or digits of any reference number refers to the Figure in which that element is first introduced. For example, element  110  is first introduced and discussed with reference to  FIG.  1   . 
     DETAILED DESCRIPTION 
     I. Overview 
     Networked microphone devices may be used to control a household using voice control. Voice control can be beneficial for a “smart” home having a system of smart devices, such as playback devices, wireless illumination devices, thermostats, door locks, home-automation devices, as well as other examples. In some implementations, the system of smart devices includes a networked microphone device configured to detect voice inputs. A voice assistant service facilitates processing of the voice inputs. Traditionally, the voice assistant service includes remote servers that receive and process voice inputs. The voice service may return responses to voice inputs, which might include control of various smart devices or audio or video information (e.g., a weather report), among other examples. 
     A voice input typically includes an utterance with a wake word followed by an utterance containing a user request. A wake word, when uttered, may invoke a particular voice assistance service. For instance, in querying the AMAZON® voice assistant service, a user might speak a wake word “Alexa.” Other examples include “Ok, Google” for invoking the GOOGLE® voice assistant service and “Hey, Siri” for invoking the APPLE® voice assistant service. 
     Upon detecting a wake word, a networked microphone device may listen for the user request in the voice utterance following the wake word. In some instances, the user request may include a command to control a third party device, such as a smart illumination device (e.g., a PHILIPS HUE® lighting device), a thermostat (e.g., NEST® thermostat), or a media playback device (e.g., a Sonos® playback device). For example, a user might speak the wake word “Alexa” followed by the utterance “turn on the living room” to turn on illumination devices. A user might speak the same wake word followed by the utterance “set the thermostat to 68 degrees.” The user may also utter a request for a playback device to play a particular song, an album, or a playlist of music. 
     When a playback device is playing audio in the same acoustic environment as a networked microphone device, sound captured by the microphone(s) of the networked microphone device might include the sound of the audio playback as well as an uttered voice input. Since the sound of the audio playback might interfere with processing of the voice input by a voice assistant service (e.g., if the audio playback drowns out the voice input), an Acoustic Echo Canceller (“AEC”) may be used to remove the sound of the audio playback from the signal captured by microphone(s) of the networked microphone device. This removal is intended to improve the signal-to-noise ratio of a voice input to other sound within the acoustic environment, which includes the sound produced by the one or more speakers in playing back the audio content, so as to provide a less noisy signal to the voice assistant service. 
     In example implementations, an AEC is implemented within the audio processing pipeline of an audio playback device or a networked microphone device. Inputs to an AEC may include the signal captured by the microphone(s) of a networked microphone device, and a reference signal. To represent the audio playback as closely as practical, the reference signal may be taken from a point in the audio playback pipeline that closely represents the analog audio expected to be output by the transducers. Given these inputs, the AEC attempts to find a transfer function (i.e., a ‘filter’) that transforms the reference signal into the captured microphone signal with minimal error. Inverting the resulting AEC output and mixing it with the microphone signal causes a redaction of the audio output signal from the signal captured by the microphone(s). 
     As those of ordinary skill in the art will appreciate, one issue with conventional AEC techniques is ‘double-talk’. Double-talk can occur, for example, when two people talk concurrently in the same acoustic environment being captured by the microphones. A conventional AEC may treat one ‘voice’ as an input while the other voice is treated as changing room effect. In this condition, the conventional AEC may attempt to adapt to the changing “room effect” but cannot keep up with the pace of advancement of the speech. In such conditions, the AEC may de-stabilize and introduce more noise into the system than it was supposed to remove. Yet, the capture of multiple concurrent voices is expected to be a common condition in many environments, such as a home with multiple users and possibly multiple networked microphone devices. 
     To avoid this condition, some systems have implemented a double-talk detector, which is designed to detect when two or more users are talking in the same acoustic environment and suspending the AEC during the double-talk condition. Using a double-talk detector may help to avoid destabilization of the AEC during double-talk conditions. But by suspending the AEC during the double-talk condition, the AEC no longer cancels echoes within the acoustic environment, which ultimately results in a “noisier” voice input to the voice assistant service. Moreover, utilizing a double-talk detector requires additional processing capability. 
     Example implementations described herein may improve acoustic echo cancellation though a combination of techniques. Such techniques may include processing in the Short-Time Fourier Transform (“STFT”) instead of the Frequency-Dependent Adaptive Filter (“FDAF”) domain). The techniques may also include using a mathematical processing model that keeps the AEC robust in face of double-talk conditions and in noisy environments. The techniques can further include applying a sparsity criterion that improves converge rate of the adaptive filter by focusing adaptation of the filter on only those areas of the impulse response which are in greatest error. Inactive portions of the filter are deactivated, so as to allow use of a high order multi delay filter where only the partitions that correspond to the actual model are active, thereby increasing stability and hastening convergence. 
     These techniques can result in tolerance for frequent double-talk conditions without compromising AEC performance during audio playback. 
     Example techniques described herein may involve acoustic echo cancellation. An example implementation may involve causing, via an audio stage, the one or more speakers to play back audio content and while the audio content is playing back via the one or more speakers, capturing, via the one or more microphones, audio within an acoustic environment, wherein the captured audio comprises audio signals representing sound produced by the one or more speakers in playing back the audio content. The example implementation may further involve receiving an output signal from the audio stage representing the audio content being played back by the one or more speakers, determining a measured signal comprising a series of frames representing the captured audio within the acoustic environment by transforming into a short time Fourier transform (STFT) domain the captured audio within the acoustic environment, and determining a reference signal comprising a series of frames representing the audio content being played back via the one or more speakers by transforming into the STFT domain the received output signal from the audio stage. 
     During each n th  iteration of an acoustic echo canceller (AEC), the implementation may involve determining an n th  frame of an output signal. Determining the n th  frame of the output signal may involve generating an n th  frame of a model signal by passing an n th  frame of the reference signal through an n th  instance of an adaptive filter, wherein the first instance of the adaptive filter is an initial filter; and generating the n th  frame of the output signal by redacting the n th  frame of the model signal from an n th  frame of the measured signal. The example implementation may also involve sending the output signal as a voice input to one or more voice services for processing of the voice input 
     The implementation may further involve, during each n th  iteration of the acoustic echo canceller (AEC), determining a n+1 th  instance of the adaptive filter for a next iteration of the AEC. Determining the n+1 th  instance of the adaptive filter for the next iteration of the AEC may involve determining an n th  frame of an error signal, the n th  frame of the error signal representing a difference between the n th  frame of the model signal and the n th  frame of the reference signal less audio signals representing sound from sources other than an n th  frame of the audio signals representing sound produced by the one or more speakers in playing back the n th  frame of the reference signal, determining a normalized least mean square (NMLS) of the n th  frame of the error signal, determining a sparse NMLS of the n th  frame of the error signal by applying to the NMLS of the n th  frame of the error signal, a sparse partition criterion that zeroes out frequency bands of the NMLS having less than a threshold energy, converting the sparse NMLS of the n th  frame of the error signal to an n th  update filter, and generating the n+1 th  instance of the adaptive filter for the next iteration of the AEC by summing the n th  instance of the adaptive filter with the n th  update filter. 
     This example implementation may be embodied as a method, a device configured to carry out the implementation, a system of devices configured to carry out the implementation, or a non-transitory computer-readable medium containing instructions that are executable by one or more processors to carry out the implementation, among other examples. It will be understood by one of ordinary skill in the art that this disclosure includes numerous other embodiments, including combinations of the example features described herein. Further, any example operation described as being performed by a given device to illustrate a technique may be performed by any suitable devices, including the devices described herein. Yet further, any device may cause another device to perform any of the operations described herein. 
     While some examples described herein may refer to functions performed by given actors such as “users” and/or other entities, it should be understood that this description is for purposes of explanation only. The claims should not be interpreted to require action by any such example actor unless explicitly required by the language of the claims themselves. 
     II. Example Operating Environment 
       FIG.  1    illustrates an example configuration of a media playback system  100  in which one or more embodiments disclosed herein may be implemented. The media playback system  100  as shown is associated with an example home environment having several rooms and spaces, such as for example, an office, a dining room, and a living room. Within these rooms and spaces, the media playback system  100  includes playback devices  102  (identified individually as playback devices  102   a - 1021 ), network microphone devices  103  (identified individually as “NMD(s)”  103   a - 103   g ), and controller devices  104   a  and  104   b  (collectively “controller devices  104 ”). The home environment may include other network devices, such as one or more smart illumination devices  108  and a smart thermostat  110 . 
     The various playback, network microphone, and controller devices  102 - 104  and/or other network devices of the media playback system  100  may be coupled to one another via point-to-point and/or over other connections, which may be wired and/or wireless, via a local area network (LAN) via a network router  106 . For example, the playback device  102   j  (designated as “LEFT”) may have a point-to-point connection with the playback device  102   a  (designated as “RIGHT”). In one embodiment, the LEFT playback device  102   j  may communicate over the point-to-point connection with the RIGHT playback device  102   a . In a related embodiment, the LEFT playback device  102   j  may communicate with other network devices via the point-to-point connection and/or other connections via the LAN. 
     The network router  106  may be coupled to one or more remote computing device(s)  105  via a wide area network (WAN)  107 . In some embodiments, the remote computing device(s) may be cloud servers. The remote computing device(s)  105  may be configured to interact with the media playback system  100  in various ways. For example, the remote computing device(s) may be configured to facilitate streaming and controlling playback of media content, such as audio, in the home environment. In one aspect of the technology described in greater detail below, the remote computing device(s)  105  are configured to provide an enhanced VAS  160  for the media playback system  100 . 
     In some embodiments, one or more of the playback devices  102  may include an on-board (e.g., integrated) network microphone device. For example, the playback devices  102   a - e  include corresponding NMDs  103   a - e , respectively. Playback devices that include network devices may be referred to herein interchangeably as a playback device or a network microphone device unless expressly stated otherwise. 
     In some embodiments, one or more of the NMDs  103  may be a stand-alone device. For example, the NMDs  103   f  and  103   g  may be stand-alone network microphone devices. A stand-alone network microphone device may omit components typically included in a playback device, such as a speaker or related electronics. In such cases, a stand-alone network microphone device might not produce audio output or may produce limited audio output (e.g., relatively low-quality output relative to quality of output by a playback device). 
     In some embodiments, one or more network microphone devices can be assigned to a playback device or a group of playback devices. In some embodiments, a network microphone device can be assigned to a playback device that does not include an onboard network microphone device. For example, the NMD  103   f  may be assigned to one or more of the playback devices  102  in its vicinity, such as one or both of the playback devices  102   i  and  102   l  in the kitchen and dining room spaces, respectively. In such a case, the NMD  103   f  may output audio through the playback device(s) to which it is assigned. Further details regarding assignment of network microphone devices are described, for example, in U.S. application Ser. No. 15/098,867 filed on Apr. 14, 2016, and titled “Default Playback Device Designation,” and U.S. application Ser. No. 15/098,892 filed on Apr. 14, 2016 and titled “Default Playback Devices.” Each of these applications is incorporated herein by reference in its entirety. 
     In some embodiments, a network microphone device may be configured such that it is dedicated exclusively to a particular VAS. In one example, the NMD  103   a  in the living room space may be dedicated exclusively to the enhanced VAS  160 . In such case, the NMD  102   a  might not invoke any other VAS except the enhanced VAS  160 . In a related example, other ones of the NMDs  103  may be configured to invoke the enhanced  160  VAS and one or more other VASes, such as a traditional VAS. Other examples of bonding and assigning network microphone devices to playback devices and/or VASes are possible. In some embodiments, the NMDs  103  might not be bonded or assigned in a particular manner. 
     Further aspects relating to the different components of the example media playback system  100  and how the different components may interact to provide a user with a media experience may be found in the following sections. While discussions herein may generally refer to the example media playback system  100 , technologies described herein are not limited to applications within, among other things, the home environment as shown in  FIG.  1   . For instance, the technologies described herein may be useful in other home environment configurations comprising more or fewer of any of the playback, network microphone, and/or controller devices  102 - 104 . Additionally, the technologies described herein may be useful in environments where multi-zone audio may be desired, such as, for example, a commercial setting like a restaurant, mall or airport, a vehicle like a sports utility vehicle (SUV), bus or car, a ship or boat, an airplane, and so on. 
     a. Example Playback Devices 
       FIG.  2    is a functional block diagram illustrating certain aspects of a selected one of the playback devices  102  shown in  FIG.  1   . As shown, such a playback device may include a processor  212 , software components  214 , memory  216 , audio processing components  218 , audio amplifier(s)  220 , speaker(s)  222 , and a network interface  230  including wireless interface(s)  232  and wired interface(s)  234 . In some embodiments, a playback device might not include the speaker(s)  222 , but rather a speaker interface for connecting the playback device to external speakers. In certain embodiments, the playback device includes neither the speaker(s)  222  nor the audio amplifier(s)  222 , but rather an audio interface for connecting a playback device to an external audio amplifier or audio-visual receiver. 
     A playback device may further include a user interface  236 . The user interface  236  may facilitate user interactions independent of or in conjunction with one or more of the controller devices  104 . In various embodiments, the user interface  236  includes one or more of physical buttons and/or graphical interfaces provided on touch sensitive screen(s) and/or surface(s), among other possibilities, for a user to directly provide input. The user interface  236  may further include one or more of lights and the speaker(s) to provide visual and/or audio feedback to a user. 
     In some embodiments, the processor  212  may be a clock-driven computing component configured to process input data according to instructions stored in the memory  216 . The memory  216  may be a tangible computer-readable medium configured to store instructions executable by the processor  212 . For example, the memory  216  may be data storage that can be loaded with one or more of the software components  214  executable by the processor  212  to achieve certain functions. In one example, the functions may involve a playback device retrieving audio data from an audio source or another playback device. In another example, the functions may involve a playback device sending audio data to another device on a network. In yet another example, the functions may involve pairing of a playback device with one or more other playback devices to create a multi-channel audio environment. 
     Certain functions may involve a playback device synchronizing playback of audio content with one or more other playback devices. During synchronous playback, a listener should not perceive time-delay differences between playback of the audio content by the synchronized playback devices. U.S. Pat. No. 8,234,395 filed Apr. 4, 2004, and titled “System and method for synchronizing operations among a plurality of independently clocked digital data processing devices,” which is hereby incorporated by reference in its entirety, provides in more detail some examples for audio playback synchronization among playback devices. 
     The memory  216  may be further configured to store data associated with a playback device. For example, the memory may store data corresponding to one or more zones and/or zone groups a playback device is a part of One or more of the zones and/or zone groups may be named according to the room or space in which device(s) are located. For example, the playback and network microphone devices in the living room space shown in  FIG.  1    may be referred to as a zone group named Living Room. As another example, the playback device  102   l  in the dining room space may be named as a zone “Dining Room.” The zones and/or zone groups may also have uniquely assigned names, such as “Nick&#39;s Room,” as shown in  FIG.  1   . 
     The memory  216  may be further configured to store other data. Such data may pertain to audio sources accessible by a playback device or a playback queue that the playback device (or some other playback device(s)) may be associated with. The data stored in the memory  216  may be stored as one or more state variables that are periodically updated and used to describe the state of the playback device. The memory  216  may also include the data associated with the state of the other devices of the media system, and shared from time to time among the devices so that one or more of the devices have the most recent data associated with the system. Other embodiments are also possible. 
     The audio processing components  218  may include one or more digital-to-analog converters (DAC), an audio preprocessing component, an audio enhancement component or a digital signal processor (DSP), and so on. In some embodiments, one or more of the audio processing components  218  may be a subcomponent of the processor  212 . In one example, audio content may be processed and/or intentionally altered by the audio processing components  218  to produce audio signals. The produced audio signals may then be provided to the audio amplifier(s)  210  for amplification and playback through speaker(s)  212 . Particularly, the audio amplifier(s)  210  may include devices configured to amplify audio signals to a level for driving one or more of the speakers  212 . The speaker(s)  212  may include an individual transducer (e.g., a “driver”) or a complete speaker system involving an enclosure with one or more drivers. A particular driver of the speaker(s)  212  may include, for example, a subwoofer (e.g., for low frequencies), a mid-range driver (e.g., for middle frequencies), and/or a tweeter (e.g., for high frequencies). In some cases, each transducer in the one or more speakers  212  may be driven by an individual corresponding audio amplifier of the audio amplifier(s)  210 . In addition to producing analog signals for playback, the audio processing components  208  may be configured to process audio content to be sent to one or more other playback devices for playback. 
     Audio content to be processed and/or played back by a playback device may be received from an external source, such as via an audio line-in input connection (e.g., an auto-detecting 3.5 mm audio line-in connection) or the network interface  230 . 
     The network interface  230  may be configured to facilitate a data flow between a playback device and one or more other devices on a data network. As such, a playback device may be configured to receive audio content over the data network from one or more other playback devices in communication with a playback device, network devices within a local area network, or audio content sources over a wide area network such as the Internet. In one example, the audio content and other signals transmitted and received by a playback device may be transmitted in the form of digital packet data containing an Internet Protocol (IP)-based source address and IP-based destination addresses. In such a case, the network interface  230  may be configured to parse the digital packet data such that the data destined for a playback device is properly received and processed by the playback device. 
     As shown, the network interface  230  may include wireless interface(s)  232  and wired interface(s)  234 . The wireless interface(s)  232  may provide network interface functions for a playback device to wirelessly communicate with other devices (e.g., other playback device(s), speaker(s), receiver(s), network device(s), control device(s) within a data network the playback device is associated with) in accordance with a communication protocol (e.g., any wireless standard including IEEE 802.11a, 802.11b, 802.11g, 802.11n, 802.11ac, 802.15, 4G mobile communication standard, and so on). The wired interface(s)  234  may provide network interface functions for a playback device to communicate over a wired connection with other devices in accordance with a communication protocol (e.g., IEEE 802.3). While the network interface  230  shown in  FIG.  2    includes both wireless interface(s)  232  and wired interface(s)  234 , the network interface  230  may in some embodiments include only wireless interface(s) or only wired interface(s). 
     In some embodiments, a playback device and one other playback device may be paired to play two separate audio components of audio content. For example, the LEFT playback device  102   j  in the Living Room may be configured to play a left channel audio component, while the RIGHT playback device  102   a  may be configured to play a right channel audio component, thereby producing or enhancing a stereo effect of the audio content. Similarly, the playback device  102   l  designated to the Dining Room may be configured to play a left channel audio component, while the playback device  102   i  designated to the Kitchen may be configured to play a right channel audio component. Paired playback devices may further play audio content in synchrony with other playback devices. Paired playback device may also be referred to as “bonded playback devices. 
     In some embodiments, one or more of the playback devices may be sonically consolidated with one or more other playback devices to form a single, consolidated playback device. A consolidated playback device may include separate playback devices each having additional or different speaker drivers through which audio content may be rendered. For example, a playback device designed to render low frequency range audio content (e.g., the playback device  102   k  designated as a subwoofer or “SUB”) may be consolidated with a full-frequency playback device (e.g., the playback device  102   b  designated as “FRONT”) to render the lower frequency range of the consolidated device. In such a case, the full frequency playback device, when consolidated with the low frequency playback device, may be configured to render only the mid and high frequency components of audio content, while the low-frequency playback device renders the low frequency component of the audio content. The consolidated playback device may be paired or consolidated with one or more other playback devices. For example,  FIG.  1    shows the SUB playback device  102   k  consolidated with the FRONT playback device  102   b  to form subwoofer and center channels, and further consolidated with the RIGHT playback device  102   a  and the LEFT playback device  102   j.    
     As discussed above, a playback device may include a network microphone device, such as one of the NMDs  103 , as show in  FIG.  2   . A network microphone device may share some or all the components of a playback device, such as the processor  212 , the memory  216 , the microphone(s)  224 , etc. In other examples, a network microphone device includes components that are dedicated exclusively to operational aspects of the network microphone device. For example, a network microphone device may include far-field microphones and/or voice processing components, which in some instances a playback device may not include. In another example, a network microphone device may include a touch-sensitive button for enabling/disabling a microphone. In yet another example, a network microphone device can be a stand-alone device, as discussed above. 
     By way of illustration, SONOS, Inc. presently offers (or has offered) for sale certain playback devices including a “PLAY:1,” “PLAY:3,” “PLAY:5,” “PLAYBAR,” “CONNECT:AMP,” “CONNECT,” and “SUB.” Any other past, present, and/or future playback devices may additionally or alternatively be used to implement the playback devices of example embodiments disclosed herein. Additionally, it is understood that a playback device is not limited to the example illustrated in  FIG.  2    or to the SONOS product offerings. For example, a playback device may include a wired or wireless headphone. In another example, a playback device may include or interact with a docking station for personal mobile media playback devices. In yet another example, a playback device may be integral to another device or component such as a television, a lighting fixture, or some other device for indoor or outdoor use. 
     b. Example Playback Zone Configurations 
     Referring back to the media playback system  100  of  FIG.  1   , the media playback system  100  may be established with one or more playback zones, after which one or more of the playback and/or network devices  102 - 103  may be added or removed to arrive at the example configuration shown in  FIG.  1   . As discussed above, zones and zone groups may be given a unique name and/or a name corresponding to the space in which device(s) are located. 
     In one example, one or more playback zones in the environment of  FIG.  1    may each be playing different audio content. For instance, the user may be grilling in the Balcony zone and listening to hip hop music being played by the playback device  102   c  while another user is preparing food in the Kitchen zone and listening to classical music being played by the playback device  102   i . In another example, a playback zone may play the same audio content in synchrony with another playback zone. For instance, the user may be in the Office zone where the playback device  102   d  is playing the same hip-hop music that is being playing by playback device  102   c  in the Balcony zone. In such a case, playback devices  102   c  and  102   d  may be playing the hip-hop in synchrony such that the user may seamlessly (or at least substantially seamlessly) enjoy the audio content that is being played out-loud while moving between different playback zones. Synchronization among playback zones may be achieved in a manner similar to that of synchronization among playback devices, as described in previously referenced U.S. Pat. No. 8,234,395. 
     A network microphone device may receive voice inputs from a user in its vicinity. A network microphone device may capture a voice input upon detection of the user speaking the input. For instance, in the example shown in  FIG.  1   , the NMD  103   a  may capture the voice input of a user in the vicinity of the Living Room, Dining Room, and/or Kitchen zones. In some instances, other network microphone devices in the home environment, such as the NMD  104   f  in the Kitchen and/or the other NMD  104   b  in the Living Room may capture the same voice input. In such instances, network devices that detect the voice input may be configured to arbitrate between one another so that fewer or only the most proximate one of the NMDs  103  process the user&#39;s voice input. Other examples for selecting network microphone devices for processing voice input can be found, for example, in U.S. patent application Ser. No. 15/171,180 fled Jun. 9, 2016, and titled “Dynamic Player Selection for Audio Signal Processing” and U.S. patent application Ser. No. 15/211,748 filed Jul. 15, 2016, and titled “Voice Detection by Multiple Devices.” Each of these references is incorporated herein by reference in its entirety. A network microphone device may control selected playback and/or network microphone devices  102 - 103  in response to voice inputs, as described in greater detail below. 
     As suggested above, the zone configurations of the media playback system  100  may be dynamically modified. As such, the media playback system  100  may support numerous configurations. For example, if a user physically moves one or more playback devices to or from a zone, the media playback system  100  may be reconfigured to accommodate the change(s). For instance, if the user physically moves the playback device  102   c  from the Balcony zone to the Office zone, the Office zone may now include both the playback devices  102   c  and  102   d . In some cases, the use may pair or group the moved playback device  102   c  with the Office zone and/or rename the players in the Office zone using, e.g., one of the controller devices  104  and/or voice input. As another example, if one or more playback devices  102  are moved to a particular area in the home environment that is not already a playback zone, the moved playback device(s) may be renamed or associated with a playback zone for the particular area. 
     Further, different playback zones of the media playback system  100  may be dynamically combined into zone groups or split up into individual playback zones. For example, the Dining Room zone and the Kitchen zone may be combined into a zone group for a dinner party such that playback devices  102   i  and  102   l  may render audio content in synchrony. As another example, playback devices  102  consolidated in the Living Room zone for the previously described consolidated TV arrangement may be split into (i) a television zone and (ii) a separate listening zone. The television zone may include the FRONT playback device  102   b . The listening zone may include the RIGHT, LEFT, and SUB playback devices  102   a ,  102   j , and  102   k , which may be grouped, paired, or consolidated, as described above. Splitting the Living Room zone in such a manner may allow one user to listen to music in the listening zone in one area of the living room space, and another user to watch the television in another area of the living room space. In a related example, a user may implement either of the NMD  103   a  or  103   b  to control the Living Room zone before it is separated into the television zone and the listening zone. Once separated, the listening zone may be controlled by a user in the vicinity of the NMD  103   a , and the television zone may be controlled by a user in the vicinity of the NMD  103   b . As described above, however, any of the NMDs  103  may be configured to control the various playback and other devices of the media playback system  100 . 
     c. Example Controller Devices 
       FIG.  3    is a functional block diagram illustrating certain aspects of a selected one of the controller devices  104  of the media playback system  100  of  FIG.  1   . Such controller devices may also be referred to as a controller. The controller device shown in  FIG.  3    may include components that are generally similar to certain components of the network devices described above, such as a processor  312 , memory  316 , microphone(s)  324 , and a network interface  330 . In one example, a controller device may be a dedicated controller for the media playback system  100 . In another example, a controller device may be a network device on which media playback system controller application software may be installed, such as for example, an iPhone™ iPad™ or any other smart phone, tablet or network device (e.g., a networked computer such as a PC or Mac™). 
     The memory  316  of a controller device may be configured to store controller application software and other data associated with the media playback system  100  and a user of the system  100 . The memory  316  may be loaded with one or more software components  314  executable by the processor  312  to achieve certain functions, such as facilitating user access, control, and configuration of the media playback system  100 . A controller device communicates with other network devices over the network interface  330 , such as a wireless interface, as described above. 
     In one example, data and information (e.g., such as a state variable) may be communicated between a controller device and other devices via the network interface  330 . For instance, playback zone and zone group configurations in the media playback system  100  may be received by a controller device from a playback device, a network microphone device, or another network device, or transmitted by the controller device to another playback device or network device via the network interface  306 . In some cases, the other network device may be another controller device. 
     Playback device control commands such as volume control and audio playback control may also be communicated from a controller device to a playback device via the network interface  330 . As suggested above, changes to configurations of the media playback system  100  may also be performed by a user using the controller device. The configuration changes may include adding/removing one or more playback devices to/from a zone, adding/removing one or more zones to/from a zone group, forming a bonded or consolidated player, separating one or more playback devices from a bonded or consolidated player, among others. 
     The user interface(s)  340  of a controller device may be configured to facilitate user access and control of the media playback system  100 , by providing controller interface(s) such as the controller interfaces  400   a  and  400   b  (collectively “controller interface  440 ”) shown in  FIGS.  4 A and  4 B , respectively. Referring to  FIGS.  4 A and  4 B  together, the controller interface  440  includes a playback control region  442 , a playback zone region  443 , a playback status region  444 , a playback queue region  446 , and a sources region  448 . The user interface  400  as shown is just one example of a user interface that may be provided on a network device such as the controller device shown in  FIG.  3    and accessed by users to control a media playback system such as the media playback system  100 . Other user interfaces of varying formats, styles, and interactive sequences may alternatively be implemented on one or more network devices to provide comparable control access to a media playback system. 
     The playback control region  442  ( FIG.  4 A ) may include selectable (e.g., by way of touch or by using a cursor) icons to cause playback devices in a selected playback zone or zone group to play or pause, fast forward, rewind, skip to next, skip to previous, enter/exit shuffle mode, enter/exit repeat mode, enter/exit cross fade mode. The playback control region  442  may also include selectable icons to modify equalization settings, and playback volume, among other possibilities. 
     The playback zone region  443  ( FIG.  4 B ) may include representations of playback zones within the media playback system  100 . In some embodiments, the graphical representations of playback zones may be selectable to bring up additional selectable icons to manage or configure the playback zones in the media playback system, such as a creation of bonded zones, creation of zone groups, separation of zone groups, and renaming of zone groups, among other possibilities. 
     For example, as shown, a “group” icon may be provided within each of the graphical representations of playback zones. The “group” icon provided within a graphical representation of a particular zone may be selectable to bring up options to select one or more other zones in the media playback system to be grouped with the particular zone. Once grouped, playback devices in the zones that have been grouped with the particular zone will be configured to play audio content in synchrony with the playback device(s) in the particular zone. Analogously, a “group” icon may be provided within a graphical representation of a zone group. In this case, the “group” icon may be selectable to bring up options to deselect one or more zones in the zone group to be removed from the zone group. Other interactions and implementations for grouping and ungrouping zones via a user interface such as the user interface  400  are also possible. The representations of playback zones in the playback zone region  443  ( FIG.  4 B ) may be dynamically updated as playback zone or zone group configurations are modified. 
     The playback status region  444  ( FIG.  4 A ) may include graphical representations of audio content that is presently being played, previously played, or scheduled to play next in the selected playback zone or zone group. The selected playback zone or zone group may be visually distinguished on the user interface, such as within the playback zone region  443  and/or the playback status region  444 . The graphical representations may include track title, artist name, album name, album year, track length, and other relevant information that may be useful for the user to know when controlling the media playback system via the user interface  440 . 
     The playback queue region  446  may include graphical representations of audio content in a playback queue associated with the selected playback zone or zone group. In some embodiments, each playback zone or zone group may be associated with a playback queue containing information corresponding to zero or more audio items for playback by the playback zone or zone group. For instance, each audio item in the playback queue may comprise a uniform resource identifier (URI), a uniform resource locator (URL) or some other identifier that may be used by a playback device in the playback zone or zone group to find and/or retrieve the audio item from a local audio content source or a networked audio content source, possibly for playback by the playback device. 
     In one example, a playlist may be added to a playback queue, in which case information corresponding to each audio item in the playlist may be added to the playback queue. In another example, audio items in a playback queue may be saved as a playlist. In a further example, a playback queue may be empty, or populated but “not in use” when the playback zone or zone group is playing continuously streaming audio content, such as Internet radio that may continue to play until otherwise stopped, rather than discrete audio items that have playback durations. In an alternative embodiment, a playback queue can include Internet radio and/or other streaming audio content items and be “in use” when the playback zone or zone group is playing those items. Other examples are also possible. 
     When playback zones or zone groups are “grouped” or “ungrouped,” playback queues associated with the affected playback zones or zone groups may be cleared or re-associated. For example, if a first playback zone including a first playback queue is grouped with a second playback zone including a second playback queue, the established zone group may have an associated playback queue that is initially empty, that contains audio items from the first playback queue (such as if the second playback zone was added to the first playback zone), that contains audio items from the second playback queue (such as if the first playback zone was added to the second playback zone), or a combination of audio items from both the first and second playback queues. Subsequently, if the established zone group is ungrouped, the resulting first playback zone may be re-associated with the previous first playback queue, or be associated with a new playback queue that is empty or contains audio items from the playback queue associated with the established zone group before the established zone group was ungrouped. Similarly, the resulting second playback zone may be re-associated with the previous second playback queue, or be associated with a new playback queue that is empty, or contains audio items from the playback queue associated with the established zone group before the established zone group was ungrouped. Other examples are also possible. 
     With reference still to  FIGS.  4 A and  4 B , the graphical representations of audio content in the playback queue region  446  ( FIG.  4 B ) may include track titles, artist names, track lengths, and other relevant information associated with the audio content in the playback queue. In one example, graphical representations of audio content may be selectable to bring up additional selectable icons to manage and/or manipulate the playback queue and/or audio content represented in the playback queue. For instance, a represented audio content may be removed from the playback queue, moved to a different position within the playback queue, or selected to be played immediately, or after any currently playing audio content, among other possibilities. A playback queue associated with a playback zone or zone group may be stored in a memory on one or more playback devices in the playback zone or zone group, on a playback device that is not in the playback zone or zone group, and/or some other designated device. Playback of such a playback queue may involve one or more playback devices playing back media items of the queue, perhaps in sequential or random order. 
     The sources region  448  may include graphical representations of selectable audio content sources and selectable voice assistants associated with a corresponding VAS. The VASes may be selectively assigned. In some examples, multiple VASes, such as AMAZON&#39;s ALEXA® and another voice service, may be invokable by the same network microphone device. In some embodiments, a user may assign a VAS exclusively to one or more network microphone devices, as discussed above. For example, a user may assign first VAS to one or both of the NMDs  102   a  and  102   b  in the living room space shown in  FIG.  1   , and a second VAS to the NMD  103   f  in the kitchen space. Other examples are possible. 
     d. Example Audio Content Sources 
     The audio sources in the sources region  448  may be audio content sources from which audio content may be retrieved and played by the selected playback zone or zone group. One or more playback devices in a zone or zone group may be configured to retrieve for playback audio content (e.g., according to a corresponding URI or URL for the audio content) from a variety of available audio content sources. In one example, audio content may be retrieved by a playback device directly from a corresponding audio content source (e.g., a line-in connection). In another example, audio content may be provided to a playback device over a network via one or more other playback devices or network devices. 
     Example audio content sources may include a memory of one or more playback devices in a media playback system such as the media playback system  100  of  FIG.  1   , local music libraries on one or more network devices (such as a controller device, a network-enabled personal computer, or a networked-attached storage (NAS), for example), streaming audio services providing audio content via the Internet (e.g., the cloud), or audio sources connected to the media playback system via a line-in input connection on a playback device or network devise, among other possibilities. 
     In some embodiments, audio content sources may be regularly added or removed from a media playback system such as the media playback system  100  of  FIG.  1   . In one example, an indexing of audio items may be performed whenever one or more audio content sources are added, removed or updated. Indexing of audio items may involve scanning for identifiable audio items in all folders/directory shared over a network accessible by playback devices in the media playback system, and generating or updating an audio content database containing metadata (e.g., title, artist, album, track length, among others) and other associated information, such as a URI or URL for each identifiable audio item found. Other examples for managing and maintaining audio content sources may also be possible. 
     e. Example Network Microphone Devices 
       FIG.  5 A  is a functional block diagram showing additional features of one or more of the NMDs  103  in accordance with aspects of the disclosure. The network microphone device shown in  FIG.  5 A  may include components that are generally similar to certain components of network microphone devices described above, such as the processor  212  ( FIG.  2   ), network interface  230  ( FIG.  2   ), microphone(s)  224 , and the memory  216 . Although not shown for purposes of clarity, a network microphone device may include other components, such as speakers, amplifiers, signal processors, as discussed above. 
     The microphone(s)  224  may be a plurality of microphones arranged to detect sound in the environment of the network microphone device. In one example, the microphone(s)  224  may be arranged to detect audio from one or more directions relative to the network microphone device. The microphone(s)  224  may be sensitive to a portion of a frequency range. In one example, a first subset of the microphone(s)  224  may be sensitive to a first frequency range, while a second subset of the microphone ( 2 )  224  may be sensitive to a second frequency range. The microphone(s)  224  may further be arranged to capture location information of an audio source (e.g., voice, audible sound) and/or to assist in filtering background noise. Notably, in some embodiments the microphone(s)  224  may have a single microphone rather than a plurality of microphones. 
     A network microphone device may further include wake-word detector  552 , beam former  553 , acoustic echo canceller (AEC)  554 , and speech/text conversion  555  (e.g., voice-to-text and text-to-voice). In various embodiments, one or more of the wake-word detector  552 , beam former  553 , AEC  554 , and speech/text conversion  555  may be a subcomponent of the processor  212 , or implemented in software stored in memory  216  which is executable by the processor  212 . 
     The wake-word detector  552  is configured to monitor and analyze received audio to determine if any wake words are present in the audio. The wake-word detector  552  may analyze the received audio using a wake word detection algorithm. If the wake-word detector  552  detects a wake word, a network microphone device may process voice input contained in the received audio. Example wake word detection algorithms accept audio as input and provide an indication of whether a wake word is present in the audio. Many first- and third-party wake word detection algorithms are known and commercially available. For instance, operators of a voice service may make their algorithm available for use in third-party devices. Alternatively, an algorithm may be trained to detect certain wake-words. 
     In some embodiments, the wake-word detector  552  runs multiple wake word detections algorithms on the received audio simultaneously (or substantially simultaneously). As noted above, different voice services (e.g. AMAZON&#39;s ALEXA®, APPLE&#39;s SIRI®, or MICROSOFT&#39;s CORTANA®) each use a different wake word for invoking their respective voice service. To support multiple services, the wake word detector  552  may run the received audio through the wake word detection algorithm for each supported voice service in parallel. 
     The beam former  553  and AEC  554  are configured to detect an audio signal and determine aspects of voice input within the detect audio, such as the direction, amplitude, frequency spectrum, etc. For example, the beam former  553  and AEC  554  may be used in a process to determine an approximate distance between a network microphone device and a user speaking to the network microphone device. In another example, a network microphone device may detective a relative proximity of a user to another network microphone device in a media playback system. 
       FIG.  5 B  is a diagram of an example voice input in accordance with aspects of the disclosure. The voice input may be captured by a network microphone device, such as by one or more of the NMDs  103  shown in  FIG.  1   . The voice input may include a wake word portion  557   a  and a voice utterance portion  557   b  (collectively “voice input  557 ”). In some embodiments, the wake word  557   a  can be a known wake word, such as “Alexa,” which is associated with AMAZON&#39;s ALEXA®). 
     In some embodiments, a network microphone device may output an audible and/or visible response upon detection of the wake word portion  557   a . In addition or alternately, a network microphone device may output an audible and/or visible response after processing a voice input and/or a series of voice inputs (e.g., in the case of a multi-turn request). 
     The voice utterance portion  557   b  may include, for example, one or more spoken commands  558  (identified individually as a first command  558   a  and a second command  558   b ) and one or more spoken keywords  559  (identified individually as a first keyword  559   a  and a second keyword  559   b ). In one example, the first command  557   a  can be a command to play music, such as a specific song, album, playlist, etc. In this example, the keywords  559  may be one or words identifying one or more zones in which the music is to be played, such as the Living Room and the Dining Room shown in  FIG.  1   . In some examples, the voice utterance portion  557   b  can include other information, such as detected pauses (e.g., periods of non-speech) between words spoken by a user, as shown in  FIG.  5 B . The pauses may demarcate the locations of separate commands, keywords, or other information spoke by the user within the voice utterance portion  557   b.    
     In some embodiments, the media playback system  100  is configured to temporarily reduce the volume of audio content that it is playing while detecting the wake word portion  557   a . The media playback system  100  may restore the volume after processing the voice input  557 , as shown in  FIG.  5 B . Such a process can be referred to as ducking, examples of which are disclosed in U.S. patent application Ser. No. 15/277,810 filed Sep. 27, 2016 and titled “Audio Playback Settings for Voice Interaction,” which is incorporated herein by reference in its entirety. 
     f. Example Network System 
       FIG.  6    is a functional block diagram showing additional details of the remote computing device(s)  105  in  FIG.  1   . In various embodiments, the remote computing device(s)  105  may receive voice inputs from one or more of the NMDs  103  over the WAN  107  shown in  FIG.  1   . For purposes of illustration, selected communication paths of the voice input  557  ( FIG.  5 B ) are represented by arrows in  FIG.  6   . In one embodiment, the voice input  557  processed by the remote computing device(s)  105  may include the voice utterance portion  557   b  ( FIG.  5 B ). In another embodiment, the processed voice input  557  may include both the voice utterance portion  557   b  and the wake word  557   a  ( FIG.  5 B ) 
     The remote computing device(s)  105  include a system controller  612  comprising one or more processors, an intent engine  602 , and a memory  616 . The memory  616  may be a tangible computer-readable medium configured to store instructions executable by the system controller  612  and/or one or more of the playback, network microphone, and/or controller devices  102 - 104 . 
     The intent engine  662  is configured to process a voice input and determine an intent of the input. In some embodiments, the intent engine  662  may be a subcomponent of the system controller  612 . The intent engine  662  may interact with one or more database(s), such as one or more VAS database(s)  664 , to process voice inputs. The VAS database(s)  664  may reside in the memory  616  or elsewhere, such as in memory of one or more of the playback, network microphone, and/or controller devices  102 - 104 . In some embodiments, the VAS database(s)  664  may be updated for adaptive learning and feedback based on the voice input processing. The VAS database(s)  664  may store various user data, analytics, catalogs, and other information for NLU-related and/or other processing. 
     The remote computing device(s)  105  may exchange various feedback, information, instructions, and/or related data with the various playback, network microphone, and/or controller devices  102 - 104  of the media playback system  100 . Such exchanges may be related to or independent of transmitted messages containing voice inputs. In some embodiments, the remote computing device(s)  105  and the media playback system  100  may exchange data via communication paths as described herein and/or using a metadata exchange channel as described in U.S. application Ser. No. 15/131,244 filed Apr. 18, 2016, and titled “Metadata exchange involving a networked playback system and a networked microphone system, which is incorporated by reference in its entirety. 
     Processing of a voice input by devices of the media playback system  100  may be carried out at least partially in parallel with processing of the voice input by the remote computing device(s)  105 . Additionally, the speech/text conversion components  555  of a network microphone device may convert responses from the remote computing device(s)  105  to speech for audible output via one or more speakers. 
     III. Example Acoustic Echo Cancellation Techniques 
     As discussed above, some embodiments described herein involve acoustic echo cancellation.  FIG.  8 A  is a functional block diagram of an acoustic echo cancellation pipeline  800   a  configured to be implemented within a playback device that includes a NMD, such as NMDs  103   a - e . By way of example, the acoustic echo cancellation pipeline  800   a  is described as being implemented within the playback device  102  of  FIG.  2   . However, in other implementations, acoustic echo cancellation pipeline  800   a  may be implemented in an NMD that is not necessarily a playback device (e.g., a device that doesn&#39;t include speakers, or includes relatively low-output speakers configured to provide audio feedback to voice inputs), such as NMDs  103   f - g.    
     In operation, acoustic echo cancellation pipeline  800   a  may be activated when the playback device  102  is playing back audio content. As noted above, acoustic echo cancellation can be used to remove acoustic echo (i.e., the sound of the audio playback and reflections and/or other acoustic artifacts from the acoustic environment) from the signal captured by microphone(s) of the networked microphone device. When effective, acoustic echo cancellation improves the signal-to-noise ratio of a voice input with respect to other sound within the acoustic environment. In some implementations, when audio playback is paused or otherwise idle, the acoustic echo cancellation pipeline  800   a  is bypassed or otherwise disabled. 
     As shown in  FIG.  8 A , the microphone array  224  ( FIG.  2   ) is configured to capture a “measured signal,” which is an input to the acoustic echo cancellation pipeline  800   a . As described above in reference to  FIGS.  2  and  5   , the microphone array  224  can be configured to capture audio within an acoustic environment in an attempt to detect voice inputs (e.g., wake-words and/or utterances) from one or more users. When the playback device  102  plays back audio content via speakers  222  ( FIG.  2   ), the microphone array  224  can capture audio that also includes audio signals representing sound produced by speakers  222  in playing back the audio content, as well as other sound being produced within the acoustic environment. 
     At block  870   a , the measured signal is pre-processed in advance of acoustic echo cancellation. Pre-processing of the measured signal may involve analog-to-digital conversion of the microphone array signals. Other pre-processing may include sample rate conversion, de-jittering, de-interleaving, or filtering, among other examples. The term “measured signal” is generally used to refer to the signal captured by the microphone array  224  before and after any pre-processing. 
     As shown in  FIG.  8 A , another input to the acoustic echo cancellation pipeline  800   a  is a “reference signal.” The reference signal can represent the audio content being played back by the speakers  222  ( FIG.  2   ). As shown, the reference signal is routed from the audio processing components  218 . In an effort to more closely represent the audio content being played back by the speakers  222 , the reference signal may be taken from a point in an audio processing pipeline of the audio processing components  218  that closely represents the expected analog audio output of speakers  222 . Since each stage of an audio processing pipeline may introduce artifacts, the point in the audio processing pipeline of the audio processing components  218  that closely represents the expected analog audio output of the speakers  222  is typically near the end of the pipeline. 
     As noted above, although the acoustic echo cancellation pipeline  800   a  is shown by way of example as being illustrated within the playback device  102 , the acoustic echo cancellation pipeline  800   a  may alternatively be implemented within a dedicated NMD such as NMD  103   f - g  of  FIG.  1   . In such examples, the reference signal may sent from the playback device(s) that are playing back audio content to the NMD, perhaps via a network interface or other communications interface, such as a line-in interface. 
     At block  870   b , the reference signal is pre-processed in advance of acoustic echo cancellation. Pre-processing of the reference signal may involve sample rate conversion, de-jittering, de-interleaving, time-delay, or filtering, among other examples. The term “measured signal” is generally used to refer to the signal captured by the microphone array  224  before and after any pre-processing. 
     Pre-processing the measured signal and the reference signals readies the signals for mixing during acoustic echo cancellation. For instance, since audio content is output by the speakers  222  before the microphone array  224  captures a representation of that same content, time-delay may be introduced to the reference signal to time-align the measured and reference signals. Similarly, since the respective sample rates of analog-to-digital conversation of the analog microphone signals and the reference signal from the audio processing components  218  may be different, sample rate conversation of one or both of the signals may convert the signal(s) into the same or otherwise compatible sample rates. Other similar pre-processing may be performed in blocks  870   a  and  870   b  to render the measured signals and reference signals compatible. 
     At block  871   a , the measured and reference signals are converted into the short-time Fourier transform domain. Acoustic echo cancellation in the STFT domain may lessen the processing requirements of acoustic echo cancellation as compared with acoustic echo cancellation in other domains, such as the Frequency-Dependent Adaptive Filter (“FDAF”) domain. As such, by processing in the STFT domain, additional techniques for acoustic echo cancellation may become practical. 
     As those of ordinary skill in the art will appreciate, a STFT is a transform used to determine the sinusoidal frequency and phase content of local sections (referred to as “frames” or “blocks”) of a signal as it changes over time. To compute a STFTs of the measured and reference signals, each signal is divided into a plurality of frames. In an example implementation, each frame is 16 milliseconds (ms) long. The number of samples in a 16 ms frame may vary based on the sample rate of the measured and reference signals. 
     Given a signal x(n), the signal is transformed to the STFT domain by:
 
 X   k [ m ]=Σ n=0   N-1   x [ n+mR ] w   A [ n ]ω N   kn ,
 
where k is the frequency index, m is the frame index, N is the frame size, R is the frame shift size, w A  [n] is an analysis window of size N, and
 
     
       
         
           
             
               
                 ω 
                 N 
               
               = 
               
                 exp 
                 ⁡ 
                 ( 
                 
                   
                     - 
                     j 
                   
                   ⁢ 
                   
                     
                       2 
                       ⁢ 
                       π 
                     
                     N 
                   
                 
                 ) 
               
             
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     Referring now to AEC  554  ( FIG.  5 A ), after being converted into the STFT domain, the measured and reference signals are provided as input to the AEC  554 , as shown in  FIG.  8 A . The acoustic echo cancellation performed by the AEC  554  on the measured signal is an iterative process. Each iteration of the AEC  554  processes a respective frame of the measured signal using a respective frame of the reference signal. Such processing includes passing a frame of the reference signal through the adaptive filter  872  to yield a frame of a model signal. The adaptive filter  872  is intended to transform the reference signal into the measured signal with minimal error. In other words, the model signal is an estimate of the acoustic echo. 
     To cancel the acoustic echo from the measured signal, the measured signal and the model signal are provided to a redaction function  873 . Redaction function  873  redacts the model signal from the measured signal, thereby cancelling the estimated acoustic echo from the measured signal yielding an output signal. In some examples, the redaction function  873  redacts the model signal from the measured signal by inverting the model signal via inverter  874  and mixing the inverted model signal with a frame of the measured signal with mixer  875 . In effect, this mixing removes the audio playback (the reference signal) from the measured signal, thereby cancelling the echo (i.e., the audio playback and associated acoustic effects) from the measured signal. Alternate implementations may use other techniques for redaction. 
     At block  871   b , the output signal of AEC  554  is transformed back by applying the inverse STFT. The inverse STFT is applied by:
 
 x [ n ]=Σ m Σ k=0   N-1   X   k [ m ] w   S [ n−mR ]ω N   −k(n−mR)  
 
where w s  [n] is a synthesis window.
 
     After block  871   b , the output signal is provided to a voice input processing pipeline at block  880 . Voice input processing may involve wake-word detection, voice/speech conversion, and/or sending one or more voice utterances to a voice assistant service, among other examples. 
     Turning now in more detail to internal aspects of the AEC  554 , at block  872 , the reference signal in the STFT domain is passed through the adaptive filter  872 . As noted above, the adaptive filter  872  is a transfer function that adapts during each iteration of the AEC  554  in an attempt to transform the reference signal into the measured signal with diminishing error. Passing a frame of the reference signal through adaptive filter  872  yields a frame of a model signal. The model signal is an estimate of the acoustic echo of the reference signal (i.e., the audio that is being cancelled). 
     Within examples, adaptive filter  872  implements multi-delay adaptive filtering. To illustrate example multi-delay adaptive filtering, let N be the multi-delay filter (MDF) block size, K be the number of blocks and F 2N  denote the 2N×2N Fourier transform matrix, and the frequency-domain signals for frame m are:
 
 e ( m )= F   2N [0 1×N   ,e ( mN ), . . . , e ( mN+N− 1)] T ,
 
 X   k ( m )=diag{ F   2N [ x (( m−k− 1) N− 1), . . .  x (( m−k+ 1) N− 1)] T },
 
 d ( m )= F   2N [ O   1×N   ,d ( mN ), . . . , d ( mN+N− 1)] T ,
 
where d(m) is the modeled signal, e(m) is the modeling error, and X k (m) is the measured signal. The MDF algorithm then becomes:
 
 e ( m )= d ( m )− ŷ ( m ),
 
 ŷ ( m )=Σ k=0   k−1   G   1   X   k ( m ) ĥ   k ( m− 1),
 
with model update:
 
∀ k: ĥ   k ( m )= ĥ   k ( m− 1)+ G   2 μ m ( m )∇ ĥ   k ( m ), and
 
∇ ĥ   k ( m )= P   X     k     X     k     −1 ( m ) X   k   H ( m ) e ( m ),
 
where G 1  and G 2  are matrices which select certain time-domain parts of the signal in the frequency domain,
 
                   G   1     =         F     2   ⁢   N       [           0     N   ×   N             0     N   ×   N                 0     N   ×   N             I     N   ×   N             ]     ⁢     F     2   ⁢   N       -   1           ,   
   and     ⁢   
       G   2     =         F     2   ⁢   N       [           1     N   ×   N             0     N   ×   N                 0     N   ×   N             0     N   ×   N             ]     ⁢       F     2   ⁢   N       -   1       .               
The matrix P X     k     X     k   (m)=X k   H (m)X k (m) is a diagonal approximation of the input power spectral density matrix. To reduce the variance of the power spectrum estimate, the instantaneous power estimate may be substituted by its smoothed version,
 
 P   X     k     X     k   ( m )=β P   X     k     X     k   ( m− 1)+(1−β) X   k   H ( m ) X   k ( m ),
 
where β is the smoothing term. This example also assumes a fixed step-size (how much the filter is adapted during each iteration) for each partition μ(m)=μ 0 I, however the step size may be varied in some implementations.
 
     Example implementations of adaptive filter  872  implement cross-band filtering. To illustrate such filtering, let y[n] be the near-end measured signal, which includes the near-end speech and/or noise v[n] mixed with the acoustic echo d[n]=h[n]*x[n], where h[n] is the impulse response of the system, x[n] is the far-end reference signal, and * is the convolution operator. Let x[m]=[x[mR], . . . x[mR+N−1]] T  be the m th  reference signal vector, w A =[w A [0], . . . , w A [N−1]] T  be the analysis window vector, (F) k+1,n+1 =w N   kn , k, n=0 . . . , N−1 be the N×N discrete Fourier transform matrix, and x[m]=F(w A ∘x[m])=[X 0 [m], . . . , X N-1 [m]] T  be the DFT of the windowed reference signal vector, where ∘ is the Hadamard (element-wise) product operator and {·}T is the transpose operator. 
     As noted above, passing a frame of the reference signal through the adaptive filter  872  yields a frame of a model signal. Given a transfer function H, the acoustic echo can be represented in the STFT domain as
 
   d   [ m ]=Σ i=0   M-1   H   i [ m− 1] x [ m−i ],
 
where  d [m] is the DFT of the m th  frame echo signal, H i  is the i th  impulse response matrix (i.e., the filter for the m th  iteration of the AEC  554 ), and M is the filter length in the STFT domain.
 
     Given the foregoing, acoustic echo cancellation by the AEC  554  can be expressed in the STFT domain as:
         x[m]=F(w A ∘[x[mR], . . . , x[mR+N−1]] T , where  x [m] is the reference signal,     y [m]=F(w A ∘[y[mR], . . . , y[mR+N−1]] T ), where  y [m] is the measured signal, and     e [m]= y [m]− {circumflex over (d)} [m]= y [m]−Σ i=0   M-1 Ĥ i [m−1]x[m−i], where  e [m] is the output signal. As noted above, the redaction function  808  redacts the model signal  {circumflex over (d)} [m] from the measured signal.       

     When noise and/or speech are present in the measured signal, the error signal vector is given by
 
   e   [ m ]=   v   [ m ]+   d   [ m ]−   {circumflex over (d)}   [ m ]=   v   [ m ]+   b   [ m ],
 
where  v [m] and  b [m] is the noise vector and the noise-free error signal vector (a.k.a., the true error signal), respectively, in the STFT domain. Since the error signal  e [m] deviates from the true, noise-free, echo signal vector  b [m], the adaptive filter may diverge from the optimal solution due to near-end interference (e.g., one or more second voices in a double-talk condition). Some implementations may halt or otherwise disable adaptation of the filter during such conditions to avoid introducing noise into the signal, possibly using a double-talk detector. However, such implementations have the disadvantage that acoustic echo is not effectively cancelled from the measured signal while the AEC filter is disabled (or not adapting). To tolerate significant near-end interference  v [m] (e.g., double-talk), one or more robustness constraints are introduced to stabilize the filter update.
 
     Namely, at block  876 , the AEC  554  estimates the true error signal. The true error signal  b [m] is the difference between the actual acoustic echo  d [m] and the estimated acoustic echo  {circumflex over (d)} [m] produced by the adaptive filter  872 . The output signal, renamed as the error signal, which includes the audio in the room other than the acoustic echo (e.g., one or more voices) as well as the true error signal, is provided as input to block  876 . Ultimately, the true error signal is used in determining an update filter at block  878 , which is summed with the adaptive filter  872  to yield the adaptive filter for the next iteration. 
     In some examples, estimating the true error signal may involve limiting the error if it exceeds a certain magnitude threshold. Such limiting may prevent unwanted divergence in noise conditions (e.g., double talk). Limiting the error may involve error recovery non-linearity (ERN) which can express the estimated true error signal ϕ(E k (m)) as a non-linear clipping function: 
     
       
         
           
             
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     This non-linear clipping function limits the error signal when its magnitude is above a certain threshold T k [m]. This threshold is estimated based on the near-end (measured) signal statistics and is approximated by T k [m]=√{square root over (S ee,k [m])} with
 
 S   ee,k [ m ]≡ E{|E   k [ m ]| 2   }≈βS   ee,k [ m− 1]+(1−β)| E   k [ m ]| 2 ,
 
where S ee,k [m] is the power spectral density (PSD) of the error signal, E{⋅} is the expectation operator, and 0&lt;&lt;β&lt;&lt;1 is a forgetting factor. This non-linear clipping function is provided by way of example. Other functions may be implemented as well to estimate the true error signal.
 
     Given the foregoing, the true error signal ϕ(E k (m)) can be determined as follows: 
                     s   _     xx     [   m   ]     =       β   ⁢           s   _       xx     [     m   -   1     ]       +       (     1   -   β     )     ⁢     (           x   _     [   m   ]     ∘     x   _       *     [   m   ]       )           ,   
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Recall that  x [m] represents the reference signal and  e [m] represents the error signal, which is the measured signal with the model signal redacted.
 
     At block  877 , the normalized least mean square of the true error signal is determined. In the normalized least square algorithm, the least mean square of the error is normalized with the power of the input (e.g., the reference signal). This has the effect of varying the step size of the algorithm to make it more noise-robust. 
     Normalization with respect to the power of the input can be expressed as
 
   n     xx [ m ]=( s   xx [ m ]+δ1 N×1 ) ∘(−1) ,
 
where {⋅} ∘(−1)  is the Hadamard (element-wise) inverse operator, 1 N×1 =[1, . . . , 1] T , δ is a regularization term and  s   xx [m]=E{ x [m]∘x*[m]}≡[S xx,0 [m], . . . , S xx,N-1 [m]] T  is the PSD vector of the reference signal with {⋅}* being the element-wise complex conjugate operator.
 
     In some cases, noise robustness may be further improved by applying a frequency dependent regularization term. For instance, such a term may be expressed as: 
                 δ   k     [   m   ]     =     γ   ⁢           S     ee   ,   k     2     [   m   ]         S     xx   ,   k       [   m   ]       .             
This term scales down the step-size automatically when the near-end (measured) signal is large, helping to keep adaption of the filter robust.
 
     At block  878 , an update filter is determined. As noted above, ultimately, the update filter is summed with the filter used in the current iteration of the AEC  554  to yield the filter for the next iteration of the AEC  554 . Generally, during the first iterations of the AEC  554 , some error exists in the cancellation of the echo from the measured signal. However, over successive iterations of the AEC  554 , this error is diminished. In particular, during each iteration of the AEC  554 , the adaptive filter  872  is updated for the next iteration based on error from the current iteration. In this way, during successive iterations of the AEC  554 , the AEC  554  mathematically converges to a cancellation of the audio playback by the speakers  222  ( FIG.  2   ). In this way, the filter adapts during a successive iteration of the AEC based on error from the previous iteration. 
     In the first iteration of the AEC  554 , an initial filter is utilized, as no adaptation has yet occurred. In some implementations, the initial filter is a transfer function representing the acoustic coupling between speakers  222  and microphones  224 . In some embodiments, the initial filter comprises a transfer function generated using measurements performed in an anechoic chamber. The generated transfer function can represent an acoustic coupling between the speakers  222  and the microphones  224  without any room effect. Such an initial filter could be used in any acoustic environment. Alternatively, in an effort to start the adaptive filter in a state that more closely matches the actual acoustic environment in which the playback device is located, a transfer function representing an acoustic coupling between the speakers  222  and the microphones  224  may be determined during a calibration procedure that involves microphones  224  recording audio output by speakers  222  in a quiet room (e.g., with minimal noise). Other initial filters may be used as well, although a filter that poorly represents the acoustic coupling between the speakers  222  and the microphones  224  may provide a less optimal starting point for the AEC  554  and result in convergence requiring additional iterations of the AEC  554 . 
     In subsequent iterations of the AEC, the adaptive filter  872  can continue to adapt. During each n th  iteration of the AEC, an n+1 th  instance of the adaptive filter  806  is determined for the next iteration of the AEC. In particular, during the n th  iteration of the AEC  554 , the n th  instance of the adaptive filter  872  is summed with an n th  update filter to yield the n+1 th  instance of the adaptive filter  872 . The n th  update filter is based on the modelling error of the filter during the n th  iteration. 
     To illustrate, let Ĥ be an adaptive filter matrix. For a filter having K blocks, to improve the modeling accuracy, 2K cross-terms, or 2K off-diagonal bands are added around the main diagonal terms of H without increasing the computational complexity to an impractical extent. Recall that K In this example, Ĥ has 2K+1 diagonal bands. The model signal (i.e., the estimated acoustic echo) can be written as
 
   {circumflex over (d)}   [ m ]=Σ i=0   M-1   Ĥ   i [ m− 1]   x   [ m−i ],
 
and the adaptive filter matrix can be updated from iteration to iteration using
 
 Ĥ   i [ m ]= Ĥ   i [ m− 1]+ G∘ΔĤ   i [ m ], i= 0, . . .  M− 1,
 
where ΔĤ i [m] is an update matrix for the filter coefficients matrix and G=Σ k=−K   K P k  is a matrix that selects the 2K+1 diagonal bands. P is a permutation matrix defined as
 
     
       
         
           
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     The matrix G limits the number of crossband filters that are useful for system identification in the STFT domain since increasing the number of crossband filters does not necessarily lead to a lower steady-state error. 
     As noted above, the n th  update filter is based on the modelling error of the filter during the n th  iteration. Using a least mean squares algorithm, the update filter is given by
 
 Ĥ   i   LMS [ m ]=μ   e   [ m ]   x     H [ m−i ],
 
where  e [m]= y [m]− {circumflex over (d)} [m] is the error signal vector in the STFT domain, μ&gt;0 is a step-size, and {⋅} H  is the Hermitian transpose operator. As compared with FDAD-type algorithms, this update filter takes into account the contribution of the cross-frequency components of the reference signal without relying on the DFT and IDFT for cancelling the aliased components, which allows for a simplified processing pipeline with less complexity.
 
     As noted above, as an alternative to the least mean squares, a normalized least mean squares algorithm may be implemented to improve noise-robustness. Using the NMLS from block  818 , the update filter is given by:
 
Δ Ĥ   i   NLMS [ m ]=μ   e   [ m ](   n   [ m ]∘   x   [ m− 1]) H ,
 
where the reference signal is normalized by its signal power before being multiplied by the error signal in block  818 . Note that each element of the NLMS update matrix is given as:
 
                 (     Δ   ⁢         H   ^     i   NLMS     [   m   ]       )         k   +   1     ,     l   +   1         =     μ   ⁢         ϕ   ⁡   (       E   k     [   m   ]     )     ⁢       X   l   *     [     m   -   1     ]             S     xx   ,   l       [   m   ]     +   δ               
In implementations in which the cross-frequency dependent regularization term is utilized, then then the NMLS update matrix is given by:
 
     
       
         
           
             
               
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     Given the foregoing, a noise-robust adaptive step size for the AEC can be expressed in matrix form as: 
     
       
         
           
             
               
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     Then the update matrix is given as:
 
Δ Ĥ   i [ m ]=μ M [ m ]∘(ϕ( e [ m ])   x     H [ m− 1]), i= 0, . . . , M− 1
 
where ϕ( e [m])≡[ϕ(E 0 [m]), . . . , ϕ(E N-1 [m−1])] T  is the estimate of the true error signal vector after applying ERN.
 
     As noted above, particular, during the n th  iteration of the AEC  554 , the n th  instance of the adaptive filter  872  is summed with an n th  update filter to yield the n+1 th  instance of the adaptive filter  872 . Given the example above, the adaptive filter is represented as:
 
 Ĥ   i [ m ]= Ĥ   i [ m− 1]+ G∘ΔĤ   i [ m ], i= 0, . . . , M− 1
 
     At block  879 , a sparsity criterion is applied to the output of the update filter  878 . A sparsity criterion may deactivate inactive portions of the filter. This allows use of a high order multi delay filter where only the partitions that correspond to the actual model are active, thereby reducing computation requirements. Although  FIG.  8 A  suggests that the sparsity criterion is applied after determination of the update filter  879 , the sparsity criterion may be applied either before or after the update filter. 
     The sparsity criterion may implemented as a thresholding operator: 
                 T   ε     (     h   j     )     =     {             0   ,                    h   j          1     ≤     ε   j                   h   j     ,                    h   j          1     &gt;     ε   j             ,             
which distinguishes between active and inactive partitions. Within examples, ε j  is in the order of the estimated noise level normalized for the block length. T ε (h j ) attempts to solve
 
                       min                 h   j     (   m   )     ∈     ℝ       B   j     ⁢   N               ⁢              e   j     (   m   )          2   2       +       γ   j     ⁢              h   j     (   m   )          1         ,         
where γ j  controls the sparsity of the j th  filter. In some examples, the thresholding operator can be applied to the filter update step of the NMLS algorithm, which then becomes:
 
∀ j: ĥ   j ( m )= T   ε ( ĥ   j ( m− 1)+ G   2     j   μ 0 ( m )∇ ĥ   j ( m )).
 
Applying the sparsity constraint during each iteration of the AEC results in a Landweber iteration with thresholding, which contributes to the noise robustness of the AEC.
 
     In example implementations, acoustic echo cancellation pipeline  800   a  may be integrated into an audio processing pipeline that includes additional audio processing of microphone-captured audio such as beam forming, blind source separation, and frequency gating before the microphone-captured audio is processed as a voice input to a voice service. 
       FIG.  8 B  is a functional block diagram of an audio processing pipeline  800   b  that integrates acoustic echo cancellation pipeline  800   a . As shown in  FIG.  8 B , other voice processing functions such as beamforming (via the beam former  553 ), blind signal separation (via the blind signal separator  882 ), and frequency gating (via the frequency gating component  881 ) are performed in the STFT domain using the AEC signals. By performing these functions in conjunction with AEC in the STFT domain, the overall audio processing pipeline can be less complex than conventional AEC approaches as fewer applications of the DFT and inverse DFT are involved, reducing the overall computational complexity of the audio processing pipeline. 
     IV. Example Acoustic Echo Cancellation 
     As discussed above, embodiments described herein may involve acoustic echo cancellation.  FIG.  9    is a flow diagram of an example implementation  900  by which a system (e.g., the playback device  102 , the NMD  103 , and/or the control device  104 ,) may perform noise-robust acoustic echo cancellation in the STFT domain. In some embodiments, the implementation  900  can comprise instructions stored on a memory (e.g., the memory  216  and/or the memory  316 ) and executable by one or more processors (e.g., the processor  212  and/or the processor  312 ). 
     a. Causing One or More Speakers to Play Back Audio Content 
     At block  902 , the implementation  900  causes one or more speakers to play back audio content. For instance, the implementation  900  can be configured to cause a playback device (e.g., the playback device  102  of  FIG.  2   ) to play back audio content via one or more speakers (e.g., the speakers  222 ). Example audio content includes audio tracks, audio with video (e.g., home theatre), streaming audio content, and many others. Prior to playback, the playback device may process and/or amplify the audio content via an audio stage, which may include audio processing components (e.g., the audio processing components  218  of  FIG.  2   ) and/or one or more audio amplifiers (e.g., the audio amplifiers  220  of  FIG.  2   ). 
     As noted above, the audio content may be designed for playback by the playback device  102  by another device. For instance, a controller device (e.g., the controller devices  103   a  and/or  103   b  of  FIG.  1   , the control device  104  of  FIG.  3   ) may instruct a playback device to play back certain audio content by causing that content to be placed in a playback queue of the playback device. Placing an audio track or other audio content into such a queue can cause the playback device to retrieve the audio content after playback is initiated via a control on the controller device  104  and/or on the playback device  102  itself (e.g., via a Play/Pause button). 
     b. Capture Audio within Acoustic Environment 
     At block  904 , the implementation  900  captures audio within the acoustic environment. For instance, the implementation  900  can be configures to capture audio within an acoustic environment via an NMD (e.g., the NMD  103  of  FIG.  2   ) having one or more microphones (e.g., two or more microphones of microphone array  224 ). Capturing audio may involve recording audio within an acoustic environment and/or processing of the recorded audio (e.g., analog-to-digital conversation). 
     In some embodiments, the implementation  900  is configured to capture audio within an acoustic environment while one or more playback devices are also playing back audio content within the acoustic environment. The captured audio can include, for example, audio signals representing acoustic echoes caused by playback of the audio content in the acoustic environment. The captured audio may also include audio signals representing speech (e.g., voice input to a voice assistant service or other speech such as conversation) as well as other sounds or noise present in the acoustic environment. 
     c. Receive Output Signal from Audio Stage 
     At block  906 , the implementation  900  receives an output signal from the audio stage. For instance, the implementation  900  can be configured to receive an output signal from the audio stage of the playback device  200 . As described above in reference to  FIG.  8 A , the output signal can represent audio content played back by the playback device  200 . Ultimately, the output signal becomes a reference signal for acoustic echo cancellation. Accordingly, within examples, the output signal is routed from a point in the audio pipeline of the playback device that closely represents the actual output produced by the speakers  224  of the playback device  200 . Since each stage of an audio processing pipeline may introduce its own artifacts, the point in the audio processing pipeline that closely represents the expected analog audio output of the speakers is typically near the end of the pipeline. 
     In some embodiments, the implementation  900  is configured to receive the output signal internally from the audio pipeline such as, for example, when an NMD in is consolidated in a playback device (e.g., as with NMD  103  of playback device  102  shown in  FIG.  2   ). In other embodiments, however, the implementation  900  is configured to receive the output signal via an input interface, such as a network interface (e.g., network interface  230 ) or a line-in interface, among other examples. 
     d. Determine Measured and Referenced Signals in STFT Domain 
     At block  908 , the implementation  900  is configured to determine measured and reference signals in an STFT domain. For instance, the system may determine a measured signal based on the captured audio and a reference signal based on the output signal from the audio stage of the playback device. 
     Determining the measured signal may involve processing and/or conditioning of the captured audio prior to acoustic echo cancellation. As described above in reference to  FIGS.  8 A and  8 B , acoustic echo cancellation in the STFT domain may occur on a frame-by-frame basis, with each frame including a series of samples (e.g., 16 ms of samples). As such the measured signal may include a series of frames representing the captured audio within the acoustic environment. Frames of the captured audio may be pre-processed (e.g., as described with respect to block  870   a  of  FIG.  8 A ) and then converted into the STFT domain (e.g., as described with respect to block  871   a  of  FIG.  8 A ) to yield a measured signal for input to an AEC (e.g., AEC  554 ). 
     Determining the reference signal may involve similarly involve processing and/or conditioning prior to AEC. Like the measured signal, the output signal from the audio stage may be divided into a series of frames representing portions of a reference signal. Frames of the output signal may be pre-processed (e.g., as described with respect to block  870   b  of  FIG.  8 A ) and then converted into the STFT domain (e.g., as described with respect to block  871   a  of  FIG.  8 A ) to yield a reference signal for input to an AEC (e.g., AEC  554 ). 
     e. Determine Frames of Output Signal 
     At block  910 , the implementation  900  is configured to determine frames of an output signal from an AEC. In some embodiments, for example, the implementation  900  comprises an AEC (such as the AEC  554  of  FIGS.  8 A and  8 B ) configured to determine frames of an output signal during each iteration of the AEC. As described above with respect to  FIG.  8 A , during each n th  iteration of AEC  554 , an n th  frame of the reference signal through an n th  instance of adaptive filter  872  yielding an n th  frame of a model signal. Then the n th  frame of the output signal is generated by redacting the n th  frame of the model signal from the n th  frame of the measured signal (e.g., using redaction function  808 ). 
     As further described above, an output signal  e [m] can be defined in example implementations as
 
   e   [ m ]=   y   [ m ]−   {circumflex over (d)}   [ m ]=   y   [ m ]−Σ i=0   M-1   Ĥ   i [ m− 1]   x   [ m−i ],
 
where the reference signal  x [m]=F(w A  ∘[x[mR], . . . , x[mR+N−1]] T ) and the measured signal  y [m]=F(w A ∘[y[mR], . . . , y[mR+N−1]] T .
 
     f. Update Adaptive Filter During Each Iteration of AEC 
     At block  912 , the implementation  900  is configured to update the adaptive filter during one or more iterations of the AEC as described, for example, with reference to AEC  554  in  FIG.  8 A . Recall that, during each n th  iteration, an n th  update matrix is determined based on a “true” error signal representing a difference between the n th  frame of the model signal and the n th  frame of the reference signal less audio signals representing sound from sources other than an n th  frame of the audio signals representing sound produced by the one or more speakers in playing back the n th  frame of the reference signal. This error signal can be referred to as the true error signal and can be determined using an ERN function that limits the error signal to a threshold magnitude, as described with respect to block  876  in  FIG.  8 A . The n+1 th  instance of the adaptive filter for the next iteration of the AEC  554  is generated by summing the n th  instance of the adaptive filter with the n th  update filter. 
     In an effort to increase robustness of the AEC  554  in view of significant noise, the adaptive filter may adapt according to a NMLS algorithm. Under such an algorithm, the true error signal may be normalized according to the power of the input (e.g., the reference signal), as described in block  877  of  FIG.  8 A . Further, AEC  554  may apply a sparse partition criterion that deactivates inactive portions of the adaptive filter (e.g., zeroes out frequency bands of the NMLS having less than a threshold energy), as described in block  879  for instance. Further, AEC  554  may apply a frequency-dependent regularization parameter to adapt an NMLS learning rate of change between AEC iterations according to a magnitude of the measured signal, as described in block  878  of  FIG.  8 A . 
     Given such features, the AEC may convert the sparse NMLS of the n th  frame of the error signal to the n th  update filter. Such conversion may involve converting the sparse NMLS of the n th  frame to a matrix of filter coefficients and cross-band filtering the matrix of filter coefficients to generate the n th  update filter, as described with respect to block  878  of  FIG.  8 A . 
     g. Send Output Signal as Voice Input to Voice Service(s) for Processing 
     At block  914 , the implementation  900  is configured to send the output signal as a voice input to one or more voice services for processing of the voice input. In some embodiments, the implementation  900  processes the output signal as a voice input as described with respect to  FIGS.  5 A and  5 B . Such processing may involve detecting one or more wake words and one or more utterances. Further, such processing may involve voice-to-speech conversion of the voice utterances, and transmitting the voice utterances to a voice assistant services with a respect to process the utterance as a voice input. Such transmitting may occur via a network interface, such as network interface  230 . 
     V. Conclusion 
     The description above discloses, among other things, various example systems, methods, apparatus, and articles of manufacture including, among other components, firmware and/or software executed on hardware. In one embodiment, for example, a playback device (playback device  102 ) and/or a network microphone device (network microphone device  103 ) is configured to perform acoustic echo cancellation in an acoustic environment (e.g., via implementation  900 ). It is understood that such examples are merely illustrative and should not be considered as limiting. For example, it is contemplated that any or all of the firmware, hardware, and/or software aspects or components can be embodied exclusively in hardware, exclusively in software, exclusively in firmware, or in any combination of hardware, software, and/or firmware. Accordingly, the examples provided are not the only way(s) to implement such systems, methods, apparatus, and/or articles of manufacture. 
     (Feature 1) A method to be performed by a system, the method comprising causing, via an audio stage, the one or more speakers to play back audio content; while audio content is playing back via the one or more speakers, capturing, via the one or more microphones, audio within an acoustic environment, wherein the captured audio comprises audio signals representing sound produced by the one or more speakers in playing back the audio content; receiving an output signal from the audio stage representing the audio content being played back by the one or more speakers; determining a measured signal comprising a series of frames representing the captured audio within the acoustic environment by transforming into a short time Fourier transform (STFT) domain the captured audio within the acoustic environment; determining a reference signal comprising a series of frames representing the audio content being played back via the one or more speakers by transforming into the STFT domain the received output signal from the audio stage; during each n th  iteration of an acoustic echo canceller (AEC): determining an n th  frame of an output signal, wherein determining the n th  frame of the output signal comprises: generating an n th  frame of a model signal by passing an n th  frame of the reference signal through an n th  instance of an adaptive filter, wherein the first instance of the adaptive filter is an initial filter; and generating the n th  frame of the output signal by redacting the n th  frame of the model signal from an n th  frame of the measured signal; determining a n+1 th  instance of the adaptive filter for a next iteration of the AEC, wherein determining the n+1 th  instance of the adaptive filter for the next iteration of the AEC comprises: determining an n th  frame of an error signal, the n th  frame of the error signal representing a difference between the n th  frame of the model signal and the n th  frame of the reference signal less audio signals representing sound from sources other than an n th  frame of the audio signals representing sound produced by the one or more speakers in playing back the n th  frame of the reference signal; determining a normalized least mean square (NMLS) of the n th  frame of the error signal; determining a sparse NMLS of the n th  frame of the error signal by applying to the NMLS of the n th  frame of the error signal, a sparse partition criterion that zeroes out frequency bands of the NMLS having less than a threshold energy; converting the sparse NMLS of the n th  frame of the error signal to an n th  update filter; and generating the n+1 th  instance of the adaptive filter for the next iteration of the AEC by summing the n th  instance of the adaptive filter with the n th  update filter; and sending the output signal as a voice input to one or more voice services for processing of the voice input. 
     (Feature 2) The method of feature 1, further comprising before determining the NMLS of the n th  frame of the error signal, applying an error recovery non-linearity function to the error signal to limit the error signal to a threshold magnitude, wherein determining the normalized least mean square (NMLS) of the n th  frame of the error signal comprises determining the NMLS of the nth frame of the limited error signal. 
     (Feature 3) The method of feature 2, wherein the error recovery non-linearity function comprises a non-linear clipping function that limits portions of the error signal that are above the threshold magnitude to the threshold magnitude. 
     (Feature 4) The method of feature 1, wherein determining the normalized least mean square (NMLS) of the n th  frame of the error signal comprises: applying a frequency-dependent regularization parameter to adapt an NMLS learning rate of change between AEC iterations according to a magnitude of the measured signal. 
     (Feature 5) The method of feature 1, wherein converting the sparse NMLS of the n th  frame of the error signal to the n th  update filter comprises: converting the sparse NMLS of the n th  frame to a matrix of filter coefficients; and cross-band filtering the matrix of filter coefficients to generate the n th  update filter. 
     (Feature 6) The method of feature 1, wherein the system excludes a double-talk detector that disables the AEC when a double-talk condition is detected, wherein capturing audio within the acoustic environment comprises capturing audio signals representing sound produced by two or more voices. 
     (Feature 7) The method of feature 1, wherein the system comprises a playback device comprising a first network interface and the one or more speakers; and a networked-microphone device comprising a second network interface, the one or more microphones, the one or more processors, and the data storage storing instructions executable by the one or more processors, wherein the first network interface and the second network interface are configured to communicatively couple the playback device and the networked-microphone device. 
     (Feature 8) The method of feature 1, wherein the system comprises a playback device comprising a housing configured to house the one or more speakers and the one or more microphones. 
     (Feature 9) A tangible, non-transitory computer-readable medium having stored therein instructions executable by one or more processors to cause a device to perform the method of any of features 1-8. 
     (Feature 10) A device configured to perform the method of any of features 1-8. 
     (Feature 11) A media playback system configured to perform the method of any of features 1-8. 
     The specification is presented largely in terms of illustrative environments, systems, procedures, steps, logic blocks, processing, and other symbolic representations that directly or indirectly resemble the operations of data processing devices coupled to networks. These process descriptions and representations are typically used by those skilled in the art to most effectively convey the substance of their work to others skilled in the art. Numerous specific details are set forth to provide a thorough understanding of the present disclosure. However, it is understood to those skilled in the art that certain embodiments of the present disclosure can be practiced without certain, specific details. In other instances, well known methods, procedures, components, and circuitry have not been described in detail to avoid unnecessarily obscuring aspects of the embodiments. Accordingly, the scope of the present disclosure is defined by the appended claims rather than the forgoing description of embodiments. 
     When any of the appended claims are read to cover a purely software and/or firmware implementation, at least one of the elements in at least one example is hereby expressly defined to include a tangible, non-transitory medium such as a memory, DVD, CD, Blu-ray, and so on, storing the software and/or firmware.