Patent Publication Number: US-2019182589-A1

Title: Excursion control based on an audio signal bandwidth estimate obtained from back-emf analysis

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority to India Provisional Patent Application No. 201741043943, filed Dec. 7, 2017, titled “Novel Narrow Band Stabilization Algorithm for Adaptive Parameter Estimation of Loudspeakers,” which is hereby incorporated herein by reference in its entirety. 
     BACKGROUND 
     Speakers in consumer products (e.g., speakers in a mobile phone or tablet) are prone to mechanical failures if driven at high power levels. As the movement of speaker diaphragm increases at high power levels, the likelihood of damage, such as bottoming of the suspension, increases. Despite being prone to mechanical failures, there is an ever increasing demand in the market for louder audio from smaller speakers. 
     To prevent mechanical failures of speakers, existing system designs attempt to maintain the power level to the speaker voice coil within a safe operating range. Such attempts can be passive or dynamic. Dynamically controlling the power level to the speaker voice coil to avoid mechanical failures is challenging due to several variables, including changes to speaker characteristics over time due to temperature, aging and manufacturing tolerances. These variations often cause misalignment in speaker protection systems. 
     One strategy to account for changes in speaker characteristics over time is to track speaker parameters in real-time and then respond to changes by adjusting the speaker protection system. Previous efforts to track speaker parameters include using real-time voltage and current measurements and an adaptive algorithm to characterize a speaker. While some existing speaker parameter tracking algorithms are reliable for wideband input signals, accounting for narrowband input signals (e.g., piano music) continues to be problematic, Efforts to improve narrowband signal detection and response options are ongoing. 
     SUMMARY 
     In accordance with at least one example of the disclosure, a system comprises a filter circuit configured to adjust digitized audio signal values based on filter parameters. The system also comprises a filter parameter selection circuit configured to determine an audio signal bandwidth estimate based on back-EMF analysis and to supply different sets of filter parameters to the filter circuit based on the audio signal bandwidth estimate and a predetermined threshold. The system also comprises a digital-to-analog converter (DAC) configured to convert an output of the filter circuit into an analog audio signal to be amplified. 
     In accordance with at least one example of the disclosure, an amplifier device comprises circuitry configured to determine an audio signal bandwidth estimate based on back-EMF analysis, to obtain different sets of filter parameters, to select one of the different sets of filter parameters based on the audio signal bandwidth estimate and a predetermined threshold, to perform a filter operation on digitized audio signal values based on a selected one of the different sets of filter parameters, and to output a result of the filter operation. The amplifier device also comprises a DAC configured to convert the result of the filter operation to an analog audio signal. The amplifier device also comprises an amplifier configured to amplify the analog audio signal. 
     In accordance with at least one example of the disclosure, an audio signal amplification method comprises receiving a digitized audio signal. The method also comprises determining if the digitized audio signal is a narrowband audio signal or wideband audio signal based on back-EMF analysis. In response to determining that the digitized audio signal is a wideband audio signal, a current set of filter parameters is selected. In response to determining that the digitized audio signal is a narrowband audio signal, a previous set of filter parameters is selected. The method also comprises filtering the digitized audio signal based on the selected set of filter parameters. The method also comprises converting a result of the filtering into an analog audio signal, and amplifying the analog audio signal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a detailed description of various examples, reference will now be made to the accompanying drawings in which: 
         FIG. 1  shows a block diagram of an audio system in accordance with various examples; 
         FIG. 2  shows a block diagram of control components for an audio system in accordance with various examples; 
         FIG. 3  shows a cross-sectional view of a speaker and a filter parameter selection block for the speaker in accordance with various examples; 
         FIG. 4  shows another block diagram of an audio system in accordance with various examples; 
         FIG. 5  shows a flowchart of an excursion control method in accordance with various examples; 
         FIG. 6  shows an audio amplification system in accordance with various examples; 
         FIG. 7  shows an amplifier device in accordance with various examples; 
         FIG. 8  shows graphs comparing broadband and narrowband portions of an audio signal and related filter parameter tracking with and without narrowband stabilization in accordance with various examples; 
         FIGS. 9 and 10  show graphs representing adaptation behavior without and with narrowband stabilization; and 
         FIG. 11  shows a flowchart of an audio signal amplification method in accordance with various examples. 
     
    
    
     DETAILED DESCRIPTION 
     The disclosed examples are directed to excursion control for a speaker based on an audio signal bandwidth estimate obtained from back-EMF analysis. In at least some examples, excursion control is achieved using an audio signal amplification technique, where the audio signal input to an amplifier has been modified using a filter. More specifically, in some examples, different sets of filter parameters (e.g., filter coefficients) for the filter are selected depending on whether the audio signal bandwidth estimate indicates an audio signal is a wideband or narrowband signal. If the audio signal bandwidth estimate indicates that an audio signal is a wideband signal, then a current set of filter parameters are selected. On the other hand, if the audio signal bandwidth estimate indicates that an audio signal is a narrowband signal, then a previous set of filter parameters are selected. In some examples, the different sets of filter parameters are based on an adaptive speaker parameter estimation process. Thus, if a narrowband audio signal is detected based on back-EMF analysis, a previous set of filter parameters obtained using the adaptive speaker parameter estimation process (e.g., the last known set of filter parameters based on a wideband audio signal) is selected for the filter. On the other hand, if a wideband audio signal is detected based on back-EMF analysis, a current (e.g., new) set of filter parameters obtained using the adaptive speaker parameter estimation process is selected. As desired, the selected set of filter parameters are scaled before being provided to the filter for use with adjusting an input audio signal. In some examples, speaker test results are used to determine if scaling is applied to a selected set of filter parameters. 
     In some examples, filter parameter selection operations are performed by a dedicated filter parameter selection circuit or programmable component. In other examples, filter parameter selection operations are perform by a digital signal processor that executes filter parameter selection instructions stored in memory. As used herein, a “filter parameter selection circuit” corresponds to a dedicated circuit, one or more programmable components, and/or a processor that executes instructions stored in memory to achieve the gain control operations described herein. In some examples, the filter parameter selection circuit is part of an audio signal amplification system, where the audio signal amplification system includes a filter that adjusts an audio signal based on the filter parameter values provided by the filter parameter selection circuit (e.g., the filter performs a power compression operation). In some examples, filter operations are performed by a dedicated filter circuit or programmable component. In other examples, filter operations are perform by a digital signal processor that executes filter instructions stored in a memory. As used herein, a “filter circuit” corresponds to a dedicated circuit, one or more programmable components, and/or a processor that executes instructions stored in memory to achieve the filter operations described herein. As used herein, “filter coefficients” are used to define an impulse response or transfer function of a filter. The filter circuit output is eventually amplified and provided to a speaker. In some examples, the filter parameter selection circuit and the filter circuit are part of an audio signal amplifier device (e.g., one or more integrated circuits in a package) included in a consumer product such as a mobile device with a speaker. Example mobile devices include cellular phones or tablets. In different examples, an audio signal amplifier device includes other components such as analog-to-digital converters (ADCs), digital-to-analog converters (DACs), voltage and current sensors, and an amplifier. 
     In at least some examples, back-EMF analysis of a speaker is based on a speaker model such as: 
     
       
         
           
             
               
                 
                   
                     
                       
                         H 
                         BEMF 
                       
                        
                       
                         ( 
                         s 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           
                             Bl 
                             2 
                           
                           
                             M 
                             ms 
                           
                         
                          
                         s 
                       
                       
                         
                           s 
                           2 
                         
                         + 
                         
                           s 
                            
                           
                             
                               R 
                               ms 
                             
                             
                               M 
                               ms 
                             
                           
                         
                         + 
                         
                           1 
                           
                             
                               M 
                               ms 
                             
                              
                             
                               C 
                               ms 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
           
         
       
     
     where H BEMF (s) is the back-EMF impedance value, Bl is the force factor (magnetic field), R ms  is the mechanical damping, M ms  is the mechanical mass, C ms  is the mechanical compliance, and s is the signal frequency. Using a speaker model such as Equation 1, dynamic adaptation of speaker parameters and the selection of filter parameters to be used for excursion control is possible even in narrowband audio signal scenarios as described herein. In some examples, Bl and R ms  are measured using a sample speaker from a speaker lot, where an offset value or margin (Δ) is selected so that the variation of 
     
       
         
           
             
               Bl 
               2 
             
             
               R 
               ms 
             
           
         
       
     
     across speaker lot, temperature and aging is within the given bound. In some examples, Δ depends on R ms  and is typically around 20%. In some examples, the offset value or margin is set based on available reliability/aging test data for a given speaker type or speaker lot. 
     In some examples, a back-EMF impedance transfer function for a speaker is estimated using adaptive speaker parameter estimation (e.g., based on normalized least-mean square optimization), where the parameters are constrained to keep the estimated transfer function shape as that of a band-pass filter. Accordingly, in some examples, the z-domain transfer function for the estimated back-EMF filter is of the form: 
     
       
         
           
             
               
                 
                   
                     
                       
                         H 
                         BEMF 
                       
                        
                       
                         ( 
                         z 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           b 
                           0 
                         
                          
                         
                           ( 
                           
                             1 
                             - 
                             
                               z 
                               
                                 - 
                                 2 
                               
                             
                           
                           ) 
                         
                       
                       
                         1 
                         + 
                         
                           
                             a 
                             1 
                           
                            
                           
                             z 
                             
                               - 
                               1 
                             
                           
                         
                         + 
                         
                           
                             a 
                             2 
                           
                            
                           
                             z 
                             
                               - 
                               2 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     2 
                     ) 
                   
                 
               
             
           
         
       
     
     where the peak value of the estimated back-EMF filter is given as: 
     
       
         
           
             
               
                 
                   
                     H 
                     
                       BEMF 
                        
                       _ 
                        
                       Peak 
                     
                   
                   = 
                   
                     
                       
                         Bl 
                         2 
                       
                       
                         R 
                         ms 
                       
                     
                     = 
                     
                       
                         
                           2 
                            
                           
                             b 
                             0 
                           
                         
                         
                           1 
                           - 
                           
                             a 
                             2 
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     3 
                     ) 
                   
                 
               
             
           
         
       
     
     In some examples, the back-EMF analysis involves determining if 
     
       
         
           
             
               
                 
                   Bl 
                   2 
                 
                 
                   R 
                   ms 
                 
               
                
               
                 ( 
                 
                   1 
                   - 
                   Δ 
                 
                 ) 
               
             
             ≤ 
             
               H 
               
                 BEMF 
                  
                 _ 
                  
                 Peak 
               
             
             ≤ 
             
               
                 
                   Bl 
                   2 
                 
                 
                   R 
                   ms 
                 
               
                
               
                 
                   ( 
                   
                     1 
                     + 
                     Δ 
                   
                   ) 
                 
                 . 
               
             
           
         
       
     
     If so, the input audio signal is designated as a wideband signal, and the current set of filter parameters obtained from an adaptive speaker parameter estimation process are selected for use with a filter (i.e., the current filter parameters obtained from adaptive speaker parameter estimation are used as filter coefficients by the filter). On the other hand, if 
     
       
         
           
             
               
                 H 
                 
                   BEMF 
                    
                   _ 
                    
                   Peak 
                 
               
               &gt; 
               
                 
                   
                     Bl 
                     2 
                   
                   
                     R 
                     ms 
                   
                 
                  
                 
                   ( 
                   
                     1 
                     + 
                     Δ 
                   
                   ) 
                 
               
             
             , 
             
               
                 or 
                  
                 
                     
                 
                  
                 
                   H 
                   
                     BEMF 
                      
                     _ 
                      
                     Peak 
                   
                 
               
               &lt; 
               
                 
                   
                     Bl 
                     2 
                   
                   
                     R 
                     ms 
                   
                 
                  
                 
                   ( 
                   
                     1 
                     - 
                     Δ 
                   
                   ) 
                 
               
             
             , 
           
         
       
     
     then the input audio signal is designated as a narrowband signal. In such case, the most recent filter parameters obtained from a wideband audio signal are selected for use with a filter (i.e., the most recent filter parameters obtained from adaptive speaker parameter estimation for a wideband audio signal are used as filter coefficients by the filter). To provide a better understanding, various filter parameter selection options, audio signal amplifier options, and related components are described using the figures as follows. 
       FIG. 1  shows a block diagram of a system  100  in accordance with various examples. As shown, the system  100  comprises a filter circuit  102  coupled to a filter parameter selection circuit  104 . In different examples, the filter circuit  102  corresponds to a dedicated circuit, one or more programmable components, and/or a processor that executes instructions stored in memory to achieve the filter operations described herein. Likewise, in different examples, the filter parameter selection circuit  104  corresponds to a dedicated circuit, one or more programmable components, and/or a processor that executes instructions stored in memory to achieve the gain control operations described herein. 
     In operation, the filter circuit  102  adjusts values of a digitized audio signal (AS 2 ) based in part on a set of filter parameters  136  or  138  provided by the filter parameter selection circuit  104 . In the example of  FIG. 1 , AS 2  is a digitized version of an analog audio signal (AS 1 ), where ADC  132  provides AS 2  based on AS 1 . The output of the filter circuit  102  is a filtered digital audio signal (AS 3 ) that is converted to a corresponding analog audio signal (AS 4 ) by DAC  128 . AS 4  is fed into an amplifier  122  to provide an amplified analog audio signal (AS 5 ) for the speaker  124 . During speaker operations, voltage and currents measurements for the speaker  124  are collected by a voltage/current sensor  126 . These voltage and current measurements are digitized by ADC  130  and provided to the filter parameter selection circuit  104  to perform a back-EMF analysis and/or other operations. 
     In at least some examples, the filter parameters provided by the filter parameter selection circuit  104  to the filter circuit  102  is dynamically selected. In some examples, selection of different sets of filter parameters  136  and  138  by the filter parameter selection circuit  104  involves various operations including adaptive speaker parameter estimation and determining an audio signal bandwidth estimate based on back-EMF analysis. In system  100 , adaptive speaker parameter estimation operations are performed by the parameter options block  108 . Meanwhile, operations to determine the audio signal bandwidth estimate are performed by the bandwidth analysis block  106 . If the audio signal bandwidth estimate indicates that the audio signal is a wideband audio signal (e.g., a back-EMF impedance transfer function peak magnitude is within a threshold level relative to a target back-EMF impedance transfer function peak magnitude), then a current set of filter parameters  110  determined by the parameter options block  108  is selected and provided to the filter circuit  102  (for use as filter coefficients to define an impulse response or transfer function provided by the filter circuit  102 ). On the other hand, if the audio signal bandwidth estimate indicates that an audio signal is a narrowband signal (e.g., a back-EMF impedance transfer function peak magnitude is not within a threshold level relative to a target back-EMF impedance transfer function peak magnitude), then a previous set of filter parameters  112  determined by the parameter options block  108  is selected and provided to the filter circuit  102  (for use as filter coefficients to define an impulse response or transfer function provided by the filter circuit  102 ). In some examples, a scaling factor  114  is applied to the selected set of filter parameters to be provided to the filter circuit  102 . The scaling factor  114  is applied, for example, in response to a condition detected by a condition detection block  116 . In some examples, the condition detection block  116  computes a Q-factor to determine the scaling. In one example, the Q-factor is given as: 
     
       
         
           
             
               
                 
                   
                     
                       Q 
                       - 
                       factor 
                     
                     = 
                     
                       
                         1 
                         
                           ( 
                           
                             
                               R 
                               ms 
                             
                             + 
                             
                               
                                 Bl 
                                 2 
                               
                               
                                 R 
                                 E 
                               
                             
                           
                           ) 
                         
                       
                        
                       
                         
                           
                             M 
                             ms 
                           
                           
                             C 
                             ms 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     4 
                     ) 
                   
                 
               
             
           
         
       
     
     where R E  is the DC resistance of the speaker  124  and the other values are described for Equation 1. In some examples, the scaling factor  114  and/or operations of the condition detection block  116  are based on speaker test results (e.g., factory test results). 
     In different examples, the filter circuit  102 , the filter parameter selection circuit  104 , the DAC  128 , the amplifier  122 , the voltage/current sensor  126 , and the ADC  130  are part of one or more integrated circuits.  FIG. 2  shows a block diagram  200  of system components in accordance with various examples. In block diagram  200 , a DSP  202  in communication with a memory  204  (e.g., RAM, ROM, flash memory) is represented, where the memory  204  stores filter instructions  102 A and filter parameter selection instructions  104 A to perform the operations described for the filter circuit  102  and the filter parameter selection circuit  104  of  FIG. 1 . In some examples, the DSP  202  corresponds to a specialized microprocessor for use in an audio signal processing scenario. In other examples, a general-purpose processor or other programmable component is used instead of the DSP  202 . In some examples, the memory  204  is separate from the DSP  202  as represented in  FIG. 2 . In other examples, the memory  204  is part of the DSP  202 . In different examples, the DSP  202  and the memory  204  correspond to one or more integrated circuits. In operation, the DSP  202  receives AS 2  and outputs AS 3  (see  FIG. 1 ), where AS 3  is a filtered version of AS 2 , and where filtering operations are based in part on a set of filter parameters selected as described herein. 
       FIG. 3  shows a cross-sectional view of a speaker  124 A and a filter parameter selection block  324  for the speaker  124 A in accordance with various examples. The speaker  124 A of  FIG. 3  is an example of the speaker  124  in  FIG. 1 , and the filter parameter selection block  324  represents hardware and/or software to perform a filter parameter selection algorithm such as the filter parameter selection algorithm given in the filter parameter selection block  324 . In at least some embodiments, the filter parameter selection block  324  corresponds to the filter parameter selection circuit  104  of  FIG. 1 . The purpose of the filter parameter selection block  324  is to provide excursion control for a speaker by selecting filter parameters based on an audio signal bandwidth estimate obtained from back-EMF analysis and related operations as described herein. 
     As shown, the speaker  124 A comprises a voice coil  310  that surrounds a magnet  305 , where magnetic circuit components  302  and  304  result in a magnetic field  306  that interacts with the voice coil  310 . A diaphragm  308  is attached to the voice coil  310  and to a frame  316 . During operations of the speaker  124 A, the diaphragm  308  has a directional displacement  318  due to movement of the voice coil  310  and the characteristics (e.g., rigidity/flexibility) of suspension material  312  between the diaphragm  308  and the frame  316 . Due to electrical resistance of the voice coil  310  and movement of the diaphragm  308  and suspension material  312 , heat and/or mechanical wear is generated during operations of the speaker  124 A. 
     The excursion control provided using the filter parameter selection block  324  and related components prevents mechanical and/or heat-based damage to components of the speaker  124 A based on adaptive speaker parameter estimation and narrowband stabilization. Also, as desired, the frame  316  includes ventilation gaps  314  to help move heat away from the diaphragm  308  and/or other components of the speaker  124 A. In some examples, the filter parameter selection algorithm employed by the filter parameter selection block  324  is given as: 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     b 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                   , 
                                   
                                     a 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                   , 
                                   
                                     a 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                   , 
                                   
                                     
                                       
                                         2 
                                          
                                         
                                           b 
                                           0 
                                         
                                       
                                       
                                         ( 
                                         
                                           1 
                                           - 
                                           
                                             a 
                                              
                                             
                                                 
                                             
                                              
                                             2 
                                           
                                         
                                         ) 
                                       
                                     
                                      
                                     within 
                                      
                                     
                                       
                                           
                                       
                                        
                                       
                                           
                                       
                                     
                                      
                                     threshold 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     previous 
                                      
                                     
                                         
                                     
                                      
                                     copy 
                                      
                                     
                                         
                                     
                                      
                                     of 
                                      
                                     
                                       
                                           
                                       
                                        
                                       
                                           
                                       
                                     
                                      
                                     b 
                                      
                                     
                                         
                                     
                                      
                                     0 
                                   
                                   , 
                                   
                                       
                                   
                                    
                                   
                                     a 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                   , 
                                   
                                     a 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                   , 
                                   
                                     
                                       2 
                                        
                                       
                                         b 
                                         0 
                                       
                                     
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         
                                           a 
                                            
                                           
                                               
                                           
                                            
                                           2 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             not 
                              
                             
                                 
                             
                              
                             within 
                              
                             
                               
                                   
                               
                                
                               
                                   
                               
                             
                              
                             threshold 
                           
                         
                       
                     
                     , 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   
                     ( 
                     5 
                     ) 
                   
                 
               
             
           
         
       
     
     In Equation 5, b0, a1, a2 correspond to current set of filter parameters obtained using adaptive speaker parameter estimation. Meanwhile, the previous copy of b0, a1, a2 corresponds to a previous set of filter parameter obtained using adaptive speaker parameter estimation. As shown in Equation 5, an example filter parameter selection algorithm selects b0, a1, a2 as the set of filter parameters when 
     
       
         
           
             
               2 
                
               b 
                
               
                   
               
                
               0 
             
             
               ( 
               
                 1 
                 - 
                 
                   a 
                    
                   
                       
                   
                    
                   2 
                 
               
               ) 
             
           
         
       
     
     is within a predetermined threshold. On the other hand, the example filter parameter selection algorithm selects a previous copy of b0, a1, a2 as the set of filter parameters when 
     
       
         
           
             
               2 
                
               b 
                
               
                   
               
                
               0 
             
             
               ( 
               
                 1 
                 - 
                 
                   a 
                    
                   
                       
                   
                    
                   2 
                 
               
               ) 
             
           
         
       
     
     is not within the predetermined threshold. The value of 
     
       
         
           
             
               2 
                
               b 
                
               
                   
               
                
               0 
             
             
               ( 
               
                 1 
                 - 
                 
                   a 
                    
                   
                       
                   
                    
                   2 
                 
               
               ) 
             
           
         
       
     
     corresponds to the peak value of a back-EMF impedance transfer function or filter, where the peak value indicates whether an audio signal is designated as a broadband signal or a narrowband signal 
     
       
         
           
             
               ( 
               
                 
                   e 
                   . 
                   g 
                   . 
                 
                 , 
                 
                   
                     H 
                     
                       BEMF 
                        
                       _ 
                        
                       Peak 
                     
                   
                   = 
                   
                     
                       
                         Bl 
                         2 
                       
                       
                         R 
                         ms 
                       
                     
                     = 
                     
                       
                         2 
                          
                         
                           b 
                           0 
                         
                       
                       
                         1 
                         - 
                         
                           a 
                           2 
                         
                       
                     
                   
                 
               
               ) 
             
             . 
           
         
       
     
     In some examples, if 
     
       
         
           
             
               
                 
                   
                     Bl 
                     
                       
                           
                       
                        
                       2 
                     
                   
                   
                     R 
                     ms 
                   
                 
                  
                 
                   ( 
                   
                     1 
                     - 
                     Δ 
                   
                   ) 
                 
               
               ≤ 
               
                 
                   2 
                    
                   
                       
                   
                    
                   b 
                    
                   
                       
                   
                    
                   0 
                 
                 
                   ( 
                   
                     1 
                     - 
                     
                       a 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   ) 
                 
               
               ≤ 
               
                 
                   
                     Bl 
                     
                       
                           
                       
                        
                       2 
                     
                   
                   
                     R 
                     ms 
                   
                 
                  
                 
                   ( 
                   
                     1 
                     + 
                     Δ 
                   
                   ) 
                 
               
             
             , 
           
         
       
     
     the input audio signal is designated as a wideband signal, and the current set of filter parameters (e.g., b0, a1, a2) obtained from an adaptive speaker parameter estimation process are selected for use with an excursion control filter. On the other hand, if 
     
       
         
           
             
               
                 
                   2 
                    
                   
                       
                   
                    
                   b 
                    
                   
                       
                   
                    
                   0 
                 
                 
                   ( 
                   
                     1 
                     - 
                     
                       a 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   ) 
                 
               
               &gt; 
               
                 
                   
                     Bl 
                     
                       
                           
                       
                        
                       2 
                     
                   
                   
                     R 
                     ms 
                   
                 
                  
                 
                   ( 
                   
                     1 
                     + 
                     Δ 
                   
                   ) 
                 
               
             
             , 
             
               
                 or 
                  
                 
                     
                 
                  
                 
                   
                     2 
                      
                     
                         
                     
                      
                     b 
                      
                     
                         
                     
                      
                     0 
                   
                   
                     ( 
                     
                       1 
                       - 
                       
                         a 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     ) 
                   
                 
               
               &lt; 
               
                 
                   
                     Bl 
                     
                       
                           
                       
                        
                       2 
                     
                   
                   
                     R 
                     ms 
                   
                 
                  
                 
                   ( 
                   
                     1 
                     - 
                     Δ 
                   
                   ) 
                 
               
             
             , 
           
         
       
     
     then the input audio signal is designated as a narrowband signal. In such case, the most recent filter parameters obtained from a wideband audio signal (e.g., a previous copy of b0, a1, a2) are selected for use with an excursion control filter. As previously discussed, in some examples, Bl and R ms  are measured using a sample speaker from a speaker lot, and Δ is selected so that the variation of 
     
       
         
           
             
               Bl 
               
                 
                     
                 
                  
                 2 
               
             
             
               R 
               ms 
             
           
         
       
     
     across the speaker lot, temperature and aging is within Δ. Again, in some examples, Δ depends on R ms  and is typically around 20%. Also, in some examples, Δ is set based on available reliability/aging test data for a given speaker type or speaker lot. 
     In some examples, operations of the filter parameter selection block  324  and/or related adaptive speaker parameter estimation is performed using voltage and current measurements from the speaker  124 A. As desired, a voice coil resistance related to the voice coil  310  is determined from the voltage and current measurements, and is used for adaptive speaker parameter estimation. In  FIG. 3 , the voltage measurements, current measurements, and/or voice coil resistance measurements are represented by arrow  320 . 
     The output of the filter parameter selection block  324  (e.g., b0, a1, a2 or a previous copy of b0, a1, a2) is used to produce an audio signal represented by arrow  322  for the speaker  124 A. The audio signal results in current passing through the voice coil  310 , which causes displacement  318  of the voice coil  310  in presence of a magnetic field. The displacement  318  of the voice coil  310  results in movement of the diaphragm  308 , which produces audible sound. With the operations of the filter parameter selection block  324 , the current to the voice coil  310  is based on adaptive speaker parameter estimation while accounting for issues related to narrowband audio signals as described herein. 
       FIG. 4  shows another block diagram of an audio system  400  in accordance with various examples. As shown, the audio system  400  comprises the amplifier  122  and the speaker  124  introduced in  FIG. 1 . In addition, the audio system  400  comprises a controller  402  that adjusts an input audio signal before it is amplified by the amplifier  122  (e.g., outputting AS 3  based on AS 2 ). More specifically, the controller  402  includes a feedforward processor  404 , a speaker model block  406 , and a compare node  410 . In at least some examples, the speaker model block  406  includes a filter parameter selection block  408 . In some examples, the filter parameter selection block  408  corresponds to the filter parameter selection circuit  104  of  FIG. 1 , the filter parameter selection instructions  104 A of  FIG. 2 , and/or the filter parameter selection block  324  of  FIG. 3 . Also, in some examples, the feedforward processor  404  corresponds to or includes the filter circuit  102  of  FIG. 1  and/or the filter instructions  102 A of  FIG. 2 . 
     In operation, the feedforward processor  404  performs a filter or power compression operation on the input audio data (e.g., AS 2 ) based on parameters provided by the speaker model block  406 . The parameters provided by the speaker model block  406  are based on adaptive speaker parameter estimations operations and filter parameter selection operations. In at least some examples, the speaker model block  406  performs adaptive speaker parameter estimation and selects a set of filter parameters (e.g., a current version of b0, a1, a2, or a previous copy of b0, a1, a2) as described herein. Also, it should be understood that the speaker model block  406  continues to adapt even in a narrowband audio signal scenario by using a previous copy of the filter parameters with the adaptation algorithm. By using a previous copy of the filter parameters in a narrowband audio signal scenario, the adaptive speaker parameter estimation is more constrained. 
     In at least some examples, adaptive speaker parameter estimation during narrowband audio signal scenarios involves fixing the value of less sensitive parameters (e.g., Rms) and tracking the value of more sensitive parameters (e.g., Cms). This is accomplished by using a previous copy of the filter parameters b0, a1, a2 during a narrowband audio signal scenario, where the b0, a1 and a2 values implicitly contain the speaker parameters Cms, Rms, etc. Accordingly, speaker parameter estimation in a narrowband audio signal scenario becomes constrained (i.e. the range of Bl 2 /Rms is narrowed down to +/−Δ). This process constrains Rms to a fixed value while allowing Cms to still be adapted or “tracked.” In a broadband audio signal scenario (i.e. when Bl 2 /Rms is within +/−Δ), there is no previous copy of b0, a1 and a2, so all parameters are adapted with equal weightage or sensitivity. 
     As previously noted, the feedforward processor  404  performs a filter or power compression operation on the input audio data (e.g., AS 2 ) based on the parameters from the speaker model block  406 . The output of the feedforward processor  404  is an audio signal (e.g., AS 3 ) to be amplified. The amplifier  122  receives an analog audio signal (e.g., a DAC converts AS 3  to an analog audio signal) based on the output from the feedforward processor  404  and amplifies the analog audio signal for input to the speaker  124 . During speaker operations, measurements of the voltage and current along the conductive path between the amplifier  122  and the speaker  124  are obtained, and digitized versions of these measurements are provided to the speaker model block  406 . In some examples, the speaker model block  406  receives a voltage error value from the compare node  410  (relative to an expected voltage value determined by the speaker model block  406 ) and a current value as represented in  FIG. 4 . In some examples, the voltage error value and the current value are used by the speaker model block  406  to select filter parameters for the feedforward processor  404 . 
     More specifically, filter parameters for the feedforward processor  404  are determined by the filter parameter selection block  408  using an audio signal bandwidth estimate obtained from back-EMF analysis. In some examples, the back-EMF analysis uses the frequency of the back-EMF value and/or the current value to determine the audio signal bandwidth estimate (e.g., based on Equations 2 and 3). In some examples, the audio signal bandwidth estimate corresponds to a back-EMF impedance transfer function peak magnitude. When compared to a threshold the 
     
       
         
           
             ( 
             
               
                 e 
                 . 
                 g 
                 . 
               
               , 
               
                 
                   
                     
                       Bl 
                       
                         
                             
                         
                          
                         2 
                       
                     
                     
                       R 
                       ms 
                     
                   
                    
                   
                     ( 
                     
                       1 
                       - 
                       Δ 
                     
                     ) 
                   
                 
                 ≤ 
                 
                   
                     2 
                      
                     
                         
                     
                      
                     b 
                      
                     
                         
                     
                      
                     0 
                   
                   
                     ( 
                     
                       1 
                       - 
                       
                         a 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     ) 
                   
                 
                 ≤ 
                 
                   
                     
                       Bl 
                       
                         
                             
                         
                          
                         2 
                       
                     
                     
                       R 
                       ms 
                     
                   
                    
                   
                     ( 
                     
                       1 
                       + 
                       Δ 
                     
                     ) 
                   
                 
               
               , 
             
           
         
       
     
     audio signal bandwidth estimate indicated whether an audio signal is a narrowband audio signal or wideband audio signal. If the audio signal bandwidth estimate indicates a wideband audio signal 
     
       
         
           
             
               ( 
               
                 
                   e 
                   . 
                   g 
                   . 
                 
                 , 
                 
                   
                     if 
                      
                     
                         
                     
                      
                     
                       
                         Bl 
                         
                           
                               
                           
                            
                           2 
                         
                       
                       
                         R 
                         ms 
                       
                     
                      
                     
                       ( 
                       
                         1 
                         - 
                         Δ 
                       
                       ) 
                     
                   
                   ≤ 
                   
                     
                       2 
                        
                       
                           
                       
                        
                       b 
                        
                       
                           
                       
                        
                       0 
                     
                     
                       ( 
                       
                         1 
                         - 
                         
                           a 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       ) 
                     
                   
                   ≤ 
                   
                     
                       
                         Bl 
                         
                           
                               
                           
                            
                           2 
                         
                       
                       
                         R 
                         ms 
                       
                     
                      
                     
                       ( 
                       
                         1 
                         + 
                         Δ 
                       
                       ) 
                     
                      
                     
                         
                     
                      
                     is 
                      
                     
                         
                     
                      
                     true 
                   
                 
               
               ) 
             
             , 
           
         
       
     
     the speaker model block  406  provides a current set of filter parameters (e.g., b0, b1, b2) to the feedforward processor  404 . On the other hand, if the audio signal bandwidth estimate indicates a narrowband audio signal 
     
       
         
           
             
               ( 
               
                 
                   e 
                   . 
                   g 
                   . 
                 
                 , 
                 
                   
                     if 
                      
                     
                         
                     
                      
                     
                       
                         Bl 
                         
                           
                               
                           
                            
                           2 
                         
                       
                       
                         R 
                         ms 
                       
                     
                      
                     
                       ( 
                       
                         1 
                         - 
                         Δ 
                       
                       ) 
                     
                   
                   ≤ 
                   
                     
                       2 
                        
                       
                           
                       
                        
                       b 
                        
                       
                           
                       
                        
                       0 
                     
                     
                       ( 
                       
                         1 
                         - 
                         
                           a 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       ) 
                     
                   
                   ≤ 
                   
                     
                       
                         Bl 
                         
                           
                               
                           
                            
                           2 
                         
                       
                       
                         R 
                         ms 
                       
                     
                      
                     
                       ( 
                       
                         1 
                         + 
                         Δ 
                       
                       ) 
                     
                      
                     
                         
                     
                      
                     is 
                      
                     
                         
                     
                      
                     not 
                      
                     
                         
                     
                      
                     true 
                   
                 
               
               ) 
             
             , 
           
         
       
     
     the speaker model block  406  provides a previous set of filter parameters (e.g., a previous copy of b0, a1, a2) to the feedforward processor  404 . For the audio system  400 , the current set and previous set of filter parameters are determined by the speaker model block  406  using adaptive speaker parameter estimation, where each set of filter parameters associated with a wideband audio signal is stored for later use (e.g., one or more previous sets of filter parameters associated with a wideband audio signal are stored by the speaker model block  406 ). 
       FIG. 5  shows a flowchart of an excursion control method  500  in accordance with various examples. As shown, the method  500  comprises estimating a back-EMF impedance transfer function or filter at block  502 . In at least some examples, the back-EMF filter is estimated using Equation 2. At block  503 , 
     
       
         
           
             
               2 
                
               
                   
               
                
               b 
                
               
                   
               
                
               0 
             
             
               ( 
               
                 1 
                 - 
                 
                   a 
                    
                   
                       
                   
                    
                   2 
                 
               
               ) 
             
           
         
       
     
     is computed. At decision block  504 , a determination is made regarding whether 
     
       
         
           
             
               
                 2 
                  
                 
                     
                 
                  
                 b 
                  
                 
                     
                 
                  
                 0 
               
               
                 ( 
                 
                   1 
                   - 
                   
                     a 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 ) 
               
             
             ≤ 
             
               
                 
                   Bl 
                   
                     
                         
                     
                      
                     2 
                   
                 
                 
                   R 
                   ms 
                 
               
                
               
                 
                   ( 
                   
                     1 
                     + 
                     Δ 
                   
                   ) 
                 
                 . 
               
             
           
         
       
     
     If so, a determination is made regarding whether 
     
       
         
           
             
               
                 
                   Bl 
                   
                     
                         
                     
                      
                     2 
                   
                 
                 
                   R 
                   ms 
                 
               
                
               
                 ( 
                 
                   1 
                   - 
                   Δ 
                 
                 ) 
               
             
             ≤ 
             
               
                 2 
                  
                 
                     
                 
                  
                 b 
                  
                 
                     
                 
                  
                 0 
               
               
                 ( 
                 
                   1 
                   - 
                   
                     a 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 ) 
               
             
           
         
       
     
     at decision block  506 . If so, the back-EMF filter of block  502  is updated using a default adaptation for wideband audio signals. If either of the decision blocks  504  and  506  have a negative result 
     
       
         
           
             
               ( 
               
                 
                   e 
                   . 
                   g 
                   . 
                 
                 , 
                 
                   
                     if 
                      
                     
                         
                     
                      
                     
                       
                         2 
                          
                         
                             
                         
                          
                         b 
                          
                         
                             
                         
                          
                         0 
                       
                       
                         ( 
                         
                           1 
                           - 
                           
                             a 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         ) 
                       
                     
                   
                   ≤ 
                   
                     
                       
                         Bl 
                         
                           
                               
                           
                            
                           2 
                         
                       
                       
                         R 
                         ms 
                       
                     
                      
                     
                       ( 
                       
                         1 
                         + 
                         Δ 
                       
                       ) 
                     
                      
                     
                         
                     
                      
                     is 
                      
                     
                         
                     
                      
                     not 
                      
                     
                         
                     
                      
                     true 
                   
                 
                 , 
                 
                   
                     or 
                      
                     
                         
                     
                      
                     
                       
                         Bl 
                         
                           
                               
                           
                            
                           2 
                         
                       
                       
                         R 
                         ms 
                       
                     
                      
                     
                       ( 
                       
                         1 
                         - 
                         Δ 
                       
                       ) 
                     
                   
                   ≤ 
                   
                     
                       
                         2 
                          
                         
                             
                         
                          
                         b 
                          
                         
                             
                         
                          
                         0 
                       
                       
                         ( 
                         
                           1 
                           - 
                           
                             a 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         ) 
                       
                     
                      
                     
                         
                     
                      
                     is 
                      
                     
                         
                     
                      
                     not 
                      
                     
                         
                     
                      
                     true 
                   
                 
               
               ) 
             
             , 
           
         
       
     
     the back-EMF filter of block  502  is updated using a narrowband stabilization adaptation based on a previous set of filter parameters (e.g., the back-EMF filter of block  502  is updated based on the most recent set of filter parameters obtained from a wideband audio signal). 
     At block  508 , a Q-factor is determined using Equation 4. The Q-factor determined at block  508  is used to select a tunable scaling factor at block  510 . At block  512 , excursion control is performed based on the back-EMF filter of block  502  and the scaling factor of block  510 . The excursion control operations of block  512  prevent mechanical damage to a speaker (e.g., the speaker  124  of  FIGS. 1 and 4 , or the speaker  124 A of  FIG. 3 ). 
       FIG. 6  shows an audio amplification system  600  in accordance with various examples. As shown, the audio amplification system  600  includes the amplifier  122 , the speaker  124 , and the voltage/current sensor  126 , and the DAC  128  introduced in  FIG. 1 . The audio amplification system  600  also includes an excursion control block  602  that receives an input audio signal (e.g., AS 2 ) and provides an output audio signal (e.g., AS 3 ). In at least some examples, the excursion control block  602  is an example of the filter circuit  102  introduced in  FIG. 1 , the filter instructions  102 A in  FIG. 2 , and/or the feedforward processor  404  of  FIG. 4 , where the operations of the excursion control block  602  are based on the filter parameters (e.g., b0, a1, a2, or a previous copy of b0, a1, a2). During operations of the speaker  124 , updated values for the filter parameters are provided to the excursion control block  602 , which performs excursion control by adjusting the input audio signal. In different examples, the excursion control block  602  adjusts the input audio signal to balance speaker loudness and speaker protection, where the specific balance employed for different audio amplification systems varies. Also, in some examples, the excursion control block  602  adjusts this balance to account for changes to the speaker  124  over time. 
     In the audio amplification system  600 , the filter parameters are determined using various components including the voltage/current sensor  126 , an adaptive speaker parameter estimation block  604 , and a calculation block  606 . These components and/or others represented in  FIG. 6  are an example of the filter parameter selection circuit  104  of  FIG. 1 , the filter parameter selection instructions  104 A of  FIG. 2 , the filter parameter selection block  324  of  FIG. 3 , and/or the speaker model block  406  of  FIG. 4 . More specifically, the voltage/current sensor  126  obtains voltage and current measurements from a conductive path between the amplifier  122  and the speaker  124 . The voltage and current measurements are provided to the calculation block  606 , which uses the voltage and current measurements and a base resistance (RO) for the speaker  124  to determine a voice coil resistance, R(t). More specifically, in some examples, R(t) is a function of an estimated voice coil temperature obtained from the voltage and current measurements and RO. In some examples, RO is provided to the calculation block  606  by a calibration block  624  (e.g., RO is determined by a calibration process for the speaker  124  or a related speaker). 
     The voltage measurements, the current measurements, and R(t) values are provided to an adaptive speaker parameter estimation block  604 , which determines a current set of filter parameters (b0, a1, a2) for the current audio signal represented by the voltage and current measurements. If the audio signal represented by the voltage and current measurements is determined to be a wideband audio signal, the current set of filter parameters (b0, a1, a2) are selected by selection block  612 , and are provided to the excursion control block  602 . Otherwise, if the audio signal represented by the voltage and current measurements is determined to be a narrowband audio signal, a previous set of filter parameters (a previous copy of b0, a1, a2 related to the most recent wideband audio signal) is selected by the selection block  612 , and are provided to the excursion control block  602 . 
     In some examples, an audio signal bandwidth estimate and thresholds are obtained using back-EMF analysis as described herein. In the audio amplification system  600 , a value for 
     
       
         
           
             
               2 
                
               
                   
               
                
               b 
                
               
                   
               
                
               0 
             
             
               ( 
               
                 1 
                 - 
                 
                   a 
                    
                   
                       
                   
                    
                   2 
                 
               
               ) 
             
           
         
       
     
     is determined at block  608 , where the values for b0 and a2 are provided by the adaptive speaker parameter estimation block  604 . Also, a previous copy of values for b0, a1, and a2 are stored at block  610 , where the values for b0, a1, and a2 are provided by the adaptive speaker parameter estimation block  604 . In some examples, the value for 
     
       
         
           
             
               
                 2 
                  
                 
                     
                 
                  
                 b 
                  
                 
                     
                 
                  
                 0 
               
               
                 ( 
                 
                   1 
                   - 
                   
                     a 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 ) 
               
             
             , 
           
         
       
     
     obtained at block  608 , is also used to determine whether to overwrite a previous copy of b0, a1, and a2 with a current copy of b0, a1, and a2. More specifically, if 
     
       
         
           
             
               2 
                
               
                   
               
                
               b 
                
               
                   
               
                
               0 
             
             
               ( 
               
                 1 
                 - 
                 
                   a 
                    
                   
                       
                   
                    
                   2 
                 
               
               ) 
             
           
         
       
     
     is within a threshold 
     
       
         
           
             
               ( 
               
                 
                   e 
                   . 
                   g 
                   . 
                 
                 , 
                 
                   
                     
                       
                         Bl 
                         
                           
                               
                           
                            
                           2 
                         
                       
                       
                         R 
                         ms 
                       
                     
                      
                     
                       ( 
                       
                         1 
                         - 
                         Δ 
                       
                       ) 
                     
                   
                   ≤ 
                   
                     
                       2 
                        
                       
                           
                       
                        
                       b 
                        
                       
                           
                       
                        
                       0 
                     
                     
                       ( 
                       
                         1 
                         - 
                         
                           a 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       ) 
                     
                   
                   ≤ 
                   
                     
                       
                         Bl 
                         
                           
                               
                           
                            
                           2 
                         
                       
                       
                         R 
                         ms 
                       
                     
                      
                     
                       ( 
                       
                         1 
                         + 
                         Δ 
                       
                       ) 
                     
                   
                 
               
               ) 
             
             , 
           
         
       
     
     the current audio signal is designated as a wideband signal, and the current values for b0, a1, and a2 determined by block  604  are selected by the selection block  612 , and are provided to block  610  for later use as needed (the current values for b0, a1, and a2 become the previous copy of b0, a1, and a2 in the next iteration). Otherwise, if 
     
       
         
           
             
               2 
                
               
                   
               
                
               b 
                
               
                   
               
                
               0 
             
             
               ( 
               
                 1 
                 - 
                 
                   a 
                    
                   
                       
                   
                    
                   2 
                 
               
               ) 
             
           
         
       
     
     is not within the threshold, the current audio signal is designated as a narrowband signal, and the current values for b0, a1, and a2 determined by block  604  are not selected by the selection block  612 , and are not provided to block  610 . In such case, the previous copy of b0, a1, and a2 stored by block  610  (corresponding to the latest filter parameters for a wideband audio signal) are selected by the selection block  612 . In some examples, the threshold used to determine if an audio signal is narrowband or wideband is stored at block  622 . As needed, the threshold value is updated using speaker characterization block  620 . In some examples, the speaker characterization block  620  determines the threshold based on reliability/aging test results and statistical data. 
     The output of the selection block  612  is selectively scaled using a scaling block  614  and selection block  616 . In some examples, the scaling block  614  applies a Q-factor scaling value (e.g., see Equation 4) to the output of the selection block  612 . Also, the selection block  616  operates based on a control signal from a test block  618 , where the control signal from the test block  618  is based on previous test results for the speaker  124  or a related speaker. 
     In some examples, the operations represented by blocks  604 ,  608 ,  610 , and  612  correspond to Equations 3 and 5 described previously. Also, in some examples, the operations represented by block  614  correspond to Equation 4 described previously. In different examples, the various operational or value blocks (e.g., blocks  602 ,  604 ,  606 ,  608 ,  610 ,  612 ,  614 ,  616 ,  618 ,  620 ,  622 ,  624 ) represented for the audio amplification system  600  correspond to hardware implementation components (e.g., circuitry to perform specific operations and/or to store specific values) and/or a software implementation components (e.g., a processor coupled to a memory with stored values and/or instructions). 
       FIG. 7  shows an amplifier device  700  in accordance with various examples. As shown, the amplifier device  700  includes a DSP  702 . In some examples, the DSP  702  corresponds to or performs the operations of the filter circuit  102  and the filter parameter selection circuit  104  of  FIG. 1 . In some examples, the DSP  702  corresponds to or performs the operations of the DSP  202  of  FIG. 2 . In some examples, the DSP  702  performs the filter parameter selection algorithm represented in the filter parameter selection block  324  of  FIG. 3 . In some examples, the DSP  702  corresponds to or performs the operations of at least the feedforward processor  404  and the speaker model block  406  of  FIG. 4 . In some examples, the DSP  702  corresponds to or performs the operations of at least the excursion control block  602 , the adaptive speaker parameter estimation block  602 , the calculation block  606 , the selection block  612 , and the selection block  616  of  FIG. 6 . 
     In  FIG. 7 , the DSP  702  is powered by one or more voltage supply signals (e.g., VS 1  and VS 2 ) and couples to ground. In operation, the DSP  702  receives an input data stream (DIN) corresponding to an audio signal (e.g., AS 2 ) and provides an output signal to an amplifier  122 A (e.g., an example of amplifier  122 ), where the amplifier  122 A includes voltage/current sensing. In some examples, the DSP  702  also provides an output data stream (DOUT) to communicate with other components outside the amplifier device  700 . In different examples, the DSP  702  includes other inputs such as clock signals and control signals. As shown, the amplifier device  700  of  FIG. 7  includes other components such as ADCs, DACs, voltage supply circuitry, a multiplexer, a temperature sensor, a boost circuit, a charge pump, and an overcurrent/overtemp protection circuit. In other amplifier device examples, one or more of these other components are omitted. Also, in some amplifier device examples, other components are used. In  FIG. 7 , the amplifier  122 A provides differential output signals (OUT_P and OUT_N) to the speaker  124 . Also, differential sense inputs are received by the amplifier  122 A from the conductive paths between the amplifier  122 A and the speaker  124 . The differential sense inputs are used to determine voltage and current measurements. As desired, amplifier devices such as the amplifier device  700  of  FIG. 7  are included with a mobile device with a speaker (e.g., a cellular phone or tablet) to balance excursion control and loudness of the speaker as described herein. 
       FIG. 8  shows graphs comparing broadband and narrowband portions of an audio signal and related filter parameter tracking with and without narrowband stabilization in accordance with various examples. As used herein, “narrowband stabilization” refers to the filter parameter selection process described herein (e.g., operations related to the filter parameter selection circuit  104  of  FIG. 1 , the filter parameter selection instructions  104 A of  FIG. 2 , the filter parameter selection block  324  of  FIG. 3 , the speaker model block  406  of  FIG. 4 , the method  500  of  FIG. 5 , various components of  FIG. 6 , and/or the DSP  702  of  FIG. 7 ). More specifically, graph  800  shows an audio signal  801  as a function of time, where the audio signal  801  has a wideband portion  802  (from approximately 0-40 seconds) and a narrowband board  804  (starting after 40 seconds). In graph  810 , a resonant frequency (f0) for a speaker is tracked over the same time period as represented in graph  800  with narrowband stabilization being used. In graph  820 , another speaker parameter (Qts) is tracked over the same time period as represented in graph  800  with narrowband stabilization being used. In graph  830 , f0 is tracked over the same time period as represented in graph  800  without narrowband stabilization being used. In graph  840 , Qts is tracked over the same time period as represented in graph  800  without narrowband stabilization being used. As represented in graphs  810  and  820 , use of narrowband stabilization results in f0 and Qts being sufficiently stable even during the narrowband portion  804  of the audio signal  801  (e.g., all values for f0 are within approximately 60 Hz of each other). When the stability and accuracy of f0 and Qts are sufficient as represented in graphs  810  and  820 , excursion control operations (e.g., performed by the excursion control block  602 ) prevent over excursion of a speaker (e.g., the speaker  124 ). Without narrowband stabilization, f0 and Qts are not sufficiently stable during the narrowband portion  804  of the audio signal  801  as represented in graphs  830  and  840  (e.g., some values for f0 vary by as much as 200 Hz). In such situations, excursion control operations do not work properly. 
       FIG. 9  shows a graph  900  representing adaptation behavior without narrowband stabilization. In graph  900 , curves  902 ,  904 ,  906 ,  908 , and  910  represent a target back-EMF impedance transfer function and back-EMF impedance transfer functions for audio signals with different bandwidths. More specifically, curve  902  shows a target back-EMF impedance transfer function, curve  904  shows back-EMF impedance magnitude as a function of frequency for a wideband audio signal, curve  906  shows back-EMF impedance magnitude as a function of frequency for a first narrowband audio signal (e.g., less than 800 Hz), curve  908  shows back-EMF impedance magnitude as a function of frequency for a second narrowband audio signal (e.g., less than 700 Hz), and curve  910  shows back-EMF impedance magnitude as a function of frequency for a third narrowband audio signal (e.g., less than 500 Hz). As represented in graph  900 , without narrowband stabilization, the back-EMF impedance transfer functions for the narrowband audio signals corresponding to curves  906 ,  908 , and  910  significantly vary from the target back-EMF impedance transfer function corresponding to curve  902  (only the curve  904  corresponding to a wideband audio signal closely resembles the target back-EMF impedance transfer function). 
       FIG. 10  shows a graph  1000  representing adaptation behavior with narrowband stabilization. In graph  1000 , curves  1002 ,  1004 , and  1006  represent a target back-EMF impedance transfer function and back-EMF impedance transfer functions for audio signals with different bandwidths. More specifically, curve  1006  shows a target back-EMF impedance transfer function, curve  1004  shows back-EMF impedance magnitude as a function of frequency for a wideband audio signal, curve  1002  shows back-EMF impedance magnitude as a function of frequency for a narrowband audio signal. As represented in graph  1000 , with narrowband stabilization, the back-EMF impedance transfer functions for a wideband audio signal corresponding to curve  1004  and for a narrowband audio signal corresponding to curve  1002  closely resemble the target back-EMF impedance transfer function corresponding to curve  1006 . With narrowband stabilization, the peak magnitudes of curves  1004  and  1002  are within a threshold offset from the peak magnitude of curve  1006 . 
       FIG. 11  shows a flowchart of an audio signal amplification method  1100  in accordance with various examples. As shown, the method  1100  comprises receiving a digitized audio signal at block  1102 . At block  1104 , a bandwidth for the audio signal is estimated based on back-EMF analysis. If the estimated bandwidth indicates wideband audio signal (decision block  1106 ), a current set of filter parameters are selected at block  1108 . On the other hand, if the estimated bandwidth does not indicate a wideband audio signal (decision block  1106 ), a previous set of filter parameters are selected at block  1110 . At block  1112 , the digitized audio signal is filtered based on the selected set of filter parameters (from either block  1108  or block  1110 ). At block  1114 , a result of the filtering is converted into an analog audio signal. At block  1116 , the analog audio signal is amplified. 
     In some examples, the method  1100  comprises calculating the current set of filter parameters and the previous set of filter parameters based on voltage measurements for a speaker, current measurements for the speaker, and estimated resistance values for a voice coil of the speaker. In some examples, the method  1100  comprises obtaining the voltage measurements and the current measurements from a voltage/current sensor as a function of time, and estimating resistance values for the voice coil of the speaker as a function of time. In some examples, the method  1100  comprises comprising scaling the selected set of filter parameters, wherein the filtering is performed using a scaled set of filter parameters. In some examples, the block  1104  comprises determining a back-EMF impedance transfer function, and block  1106  comprises comparing a back-EMF impedance transfer function peak magnitude to a target back-EMF impedance transfer function peak magnitude, where an offset relative to the target back-EMF impedance transfer function peak corresponds to the predetermined threshold. 
     Certain terms have been used throughout this description and claims to refer to particular system components. As one skilled in the art will appreciate, different parties may refer to a component by different names. This document does not intend to distinguish between components that differ in name but not function. In this disclosure and claims, the terms “including” and “comprising” are used in an open-ended fashion, and thus should be interpreted to mean “including, but not limited to . . . .” Also, the term “couple” or “couples” is intended to mean either an indirect or direct wired or wireless connection. Thus, if a first device couples to a second device, that connection may be through a direct connection or through an indirect connection via other devices and connections. The recitation “based on” is intended to mean “based at least in part on.” Therefore, if X is based on Y, X may be a function of Y and any number of other factors. 
     The above discussion is meant to be illustrative of the principles and various embodiments of the present invention. Numerous variations and modifications will become apparent to those skilled in the art once the above disclosure is fully appreciated. It is intended that the following claims be interpreted to embrace all such variations and modifications.