Patent Publication Number: US-2023152345-A1

Title: Inertial sensor sensing of vibration frequency

Description:
BACKGROUND 
     Numerous items such as smartphones, smart watches, tablets, automobiles, aerial drones, appliances, aircraft, exercise aids, and game controllers utilize sensors during their operation (e.g., motion sensors, pressure sensors, temperature sensors, etc.). In commercial applications, microelectromechanical (MEMS) sensors such as accelerometers and gyroscopes capture complex movements and determine orientation or direction. For example, smartphones are equipped with accelerometers and gyroscopes to understand the movement of the smartphone, to augment navigation systems that rely on Global Position System (GPS) information, and to perform numerous other functions. Wearable devices and internet-of-things (IoT) devices constantly measure movement and other characteristics of a person, animal, or electronic device. In another example, drones and aircraft determine orientation based on gyroscope measurements (e.g., roll, pitch, and yaw), and vehicles of all types implement assisted driving to improve safety (e.g., to recognize skid or roll-over conditions). In these end-use applications, the MEMS sensor is exposed to a variety of vibration types from a variety of vibration sources. 
     SUMMARY 
     In an embodiment of the present disclosure, a method for identifying a frequency of an external vibration by a microelectromechanical system (MEMS) inertial sensor comprises generating, by processing circuitry of the MEMS inertial sensor, a frequency scan signal pattern comprising a plurality of periodic signal portions each having a test frequency, sensing, by one or more sense electrodes of the inertial sensor, a movement of a proof mass of the inertial sensor over a period of time, and generating, by the processing circuitry of the inertial sensor, a sense signal based on the sensed movement of the proof mass over the period of time. The method may further comprise correlating, by the processing circuitry, the sense signal with the frequency scan signal pattern, generating, by the processing circuitry, a plurality of correlation values based on the correlating, wherein each of the plurality of correlation values is based on a correlation of the sense signal with one of the plurality of periodic signal portions, and identifying, by the processing circuitry, a frequency associated with the sense signal based on one or more of the generated plurality of correlation values. 
     In an embodiment of the present disclosure, microelectromechanical system (MEMS) inertial sensor comprises a frequency scan generator that generates a frequency scan signal pattern, wherein the frequency scan signal pattern comprises a plurality of periodic signal portions each having a test frequency, a proof mass that responds to an inertial force, and one or more sense electrodes that sense a movement of the proof mass. The method may further comprises sense circuitry coupled to the proof mass, wherein the sense circuitry is configured to generate a sense signal based on the sensed movement of the proof mass detected by the one or more sense electrodes, and processing circuitry coupled to the sense circuitry; wherein the processing circuitry is configured to receive the sense signal generated by the sense circuitry, correlate the sense signal with the plurality of periodic signal portions to determine a plurality of correlation values, and identify a frequency associated with the sense signal based on one or more of the generated plurality of correlation values. 
     In an embodiment of the present disclosure, a method for monitoring a suspended spring-mass system and identifying a frequency of an external vibration by a microelectromechanical system (MEMS) inertial sensor may comprise generating, by processing circuitry of the MEMS inertial sensor, a frequency scan signal pattern comprising a plurality of periodic signal portions each having a test frequency, providing the frequency scan signal pattern to a self-test drive electrode of the MEMS inertial sensor, and driving, by the self-test drive electrode, a proof mass of the suspended spring-mass system based on the frequency scan signal pattern. The method may further comprise sensing, by one or more sense electrodes of the inertial sensor, a movement of a proof mass of the inertial sensor over a period of time during which the frequency scan pattern drives the proof mass, and generating, by the processing circuitry of the inertial sensor, a sense signal based on the sensed movement of the proof mass over the period of time. The method may further comprise correlating, by the processing circuitry, the sense signal with the frequency scan signal pattern, identifying, by the processing circuitry, a frequency associated with the external vibration based on the correlating, and identifying, by the processing circuitry, an error associated with the suspended spring-mass system based on the correlating. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       The above and other features of the present disclosure, its nature, and various advantages will be more apparent upon consideration of the following detailed description, taken in conjunction with the accompanying drawings in which: 
         FIG.  1    shows an illustrative MEMS system in accordance with an embodiment of the present disclosure; 
         FIG.  2    shows an illustrative MEMS accelerometer with vibration monitoring in accordance with an embodiment of the present disclosure; 
         FIG.  3    shows an example chart of correlation values corresponding to an example vibration signal monitored with the MEMS accelerometer of  FIG.  2    in accordance with an embodiment of the present disclosure; 
         FIG.  4    shows an illustrative MEMS accelerometer with vibration monitoring based on injected signal patterns driving the MEMS in accordance with an embodiment of the present disclosure; 
         FIG.  5    shows an example chart of correlation values corresponding to an example vibration signal monitored with the MEMS accelerometer of  FIG.  4    in accordance with an embodiment of the present disclosure; 
         FIG.  6 A  shows an example diagram depicting an out-of-phase sense signal compared to a square wave signal pattern having a frequency f k  in accordance with an embodiment of the present disclosure; 
         FIG.  6 B  shows an example diagram depicting an in-phase sense signal compared to a square wave signal pattern having a frequency f k  in accordance with an embodiment of the present disclosure; 
         FIG.  7    shows an example MEMS correlator design including a phase-shifted signal pattern in accordance with an embodiment of the present disclosure; 
         FIG.  8 A  shows an example diagram depicting a sense signal at a first frequency compared to a square wave signal pattern having a frequency in accordance with an embodiment of the present disclosure; 
         FIG.  8 B  shows an example diagram depicting a sense signal at a harmonic of the first frequency of  FIG.  8 A  compared to a square wave signal pattern having a frequency in accordance with an embodiment of the present disclosure; 
         FIG.  9 A  shows an example diagram depicting the sense signal of  FIG.  8 A  compared to a stairstep sinusoidal signal pattern having a frequency f k  in accordance with an embodiment of the present disclosure; 
         FIG.  9 B  shows an example diagram depicting the sense signal of  FIG.  8 B  compared to a stairstep sinusoidal signal pattern having a frequency f k  in accordance with an embodiment of the present disclosure; 
         FIG.  10 A  shows an example diagram depicting a high selectivity dot graph corresponding to use of the stairstep sinusoidal signal pattern in accordance with an embodiment of the present disclosure; 
         FIG.  10 B  shows an example diagram depicting a low selectivity dot graph in corresponding to use of the square wave sinusoidal signal pattern in accordance with an embodiment of the present disclosure; 
         FIG.  11    shows an illustrative MEMS gyroscope with vibration monitoring in accordance with an embodiment of the present disclosure; and 
         FIG.  12    shows an illustrative MEMS gyroscope with vibration monitoring based on injected signal patterns driving the MEMS in accordance with an embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION OF DRAWINGS 
     MEMS sensors such as MEMS inertial sensors include movable components that respond to a particular force of interest. In the context of MEMS accelerometers and gyroscopes, a suspended spring-mass system is configured to isolate and respond to a movement of interest, such as a linear acceleration along an axis for a MEMS accelerometer or a rotation about an axis for MEMS gyroscope. These sensors are utilized in a variety of devices under a multitude of operating conditions, and as such are subject to a variety of external vibrations depending on the end-use device and application. In some instances, it may be desirable to understand the external vibratory environment for the MEMS sensor. For example, it may be desirable to measure and characterize a background vibration experienced by the sensor, so as to allow processing circuitry to better distinguish the background vibration from a desired force or movement to be measured. As another example, it may be desirable to understand and characterize the vibration environment under particular conditions, such as device start-up or the entry of an active processing mode from a sleep mode. As yet another example, a user or application (e.g., running on a processing unit of an end-use device) may wish to understand and quantify the vibrations in a current environment. 
     A MEMS inertial sensor includes a frequency scan drive that generates periodic signals at a variety of frequencies. These frequencies in turn are compared to an output sense signal of the MEMS inertial sensor, such as by correlation, to identify the signal content of a vibration at various frequencies. The frequency scan and comparison may be performed via a frequency sweep, in an iterative fashion, and/or at multiple levels of precision. In some implementations, the frequency scan may also be provided to drive the suspended spring-mass system to drive a proof mass (or proof masses), allowing simultaneous monitoring of external vibration signals and of the frequency response of the suspended spring-mass system. A number of modifications may be applied in order to more accurately capture vibration frequency information, such as also providing phase-shifted versions of the frequency scan to mitigate issues that occur with phase alignment of sense signals and frequency scan signals. Another exemplary modification includes generating averaged correlation values based on the comparison of the sense signal to both the frequency scan signal and the phase-shifted frequency scan signal. Another exemplary modification includes providing more granularity within the frequency scan signal, such as by providing a simulated sinusoidal signal (e.g., a stepwise sinusoidal signal). 
       FIG.  1    depicts an exemplary MEMS system  100  in accordance with some embodiments of the present disclosure. Although particular components are depicted in  FIG.  1   , it will be understood that other suitable combinations of MEMS, processing components, memory, and other circuitry may be utilized as necessary for different applications and systems. In certain embodiments of the present disclosure, the circuitry, devices, systems, and methods described herein may be described in the context of a system including multiple MEMS inertial sensors including circuitry for identifying characteristics of an external vibration. However, it will be understood that that the circuitry, devices, systems, and methods described herein may be applied to other types of MEMS sensors and identification and analysis of a variety of noise sources. As non-limiting examples, the present disclosure may be utilized with low-cost seismic sensors for safety applications (e.g., emergency shutdown of household gas meter and appliances in case of earthquake) or with devices with custom software (e.g., a smartphone including inertial and/or pressure sensors, with customized sensor fusion software or embedded functionality) for identifying particular vibration frequency signals of interest or as a hazard. 
     In an embodiment as described herein, the MEMS system  100  may include at least a MEMS inertial sensor  102  (e.g., a single- or multi-axis inertial sensor for measuring motion along or about one or more axes) and supporting circuitry, such as processing circuitry  104  and memory  106 . In some embodiments, one or more additional sensors  108  (e.g., MEMS gyroscopes, MEMS accelerometers, MEMS microphones, MEMS pressure sensors, temperature sensors, and a compass) may be included within the motion processing system  100  to provide an integrated motion processing unit (“MPU”) (e.g., including 3 axes of MEMS gyroscope sensing, 3 axes of MEMS accelerometer sensing, microphone, pressure sensor, and compass). 
     Processing circuitry  104  may include one or more components providing necessary processing based on the requirements of the MEMS system  100 . In some embodiments, processing circuitry  104  may include hardware control logic that may be integrated within a chip of a sensor (e.g., on a substrate or capacitor of a MEMS sensor  102  or other sensor  108 , or on an adjacent portion of a chip to the MEMS sensor  102  or other sensor  108 ) to control the operation of the MEMS sensor  102  or other sensors  108  and perform aspects of processing for the MEMS sensor  102  or other sensors  108 . In some embodiments, the MEMS sensor  102  and other sensors  108  may include one or more registers that allow aspects of the operation of hardware control logic to be modified (e.g., by modifying a value of a register). In some embodiments, processing circuitry  104  may also include a processor such as microprocessor that executes software instructions, e.g., that are stored in memory  106 . The microprocessor may control the operation of the MEMS sensor  102  by interacting with the hardware control logic, and process signals received from MEMS sensor  102 . The microprocessor may interact with other sensors in a similar manner. In some embodiments, some or all of the functions of the processing circuitry  104 , and in some embodiments, of memory  106 , may be implemented on an application specific integrated circuit (“ASIC”) and/or a field programmable gate array (“FPGA”). 
     Although in some embodiments (not depicted in  FIG.  1   ), the MEMS sensor  102  or other sensors  108  may communicate directly with external circuitry (e.g., via a serial bus or direct connection to sensor outputs and control inputs), in an embodiment the processing circuitry  104  may process data received from the MEMS sensor  102  and other sensors  108  and communicate with external components via a communication interface  110  (e.g., a SPI or I2C bus, in automotive applications a controller area network (CAN) or Local Interconnect Network (LIN) bus, or in other applications suitable wired or wireless communications interfaces as is known in the art). The processing circuitry  104  may convert signals received from the MEMS sensor  102  and other sensors  108  into appropriate measurement units (e.g., based on settings provided by other computing units communicating over the communication bus  110 ) and perform more complex processing to determine measurements such as orientation or Euler angles, and in some embodiments, to determine from sensor data whether a particular activity (e.g., walking, running, braking, skidding, rolling, etc.) is taking place. In some embodiments, some or all of the conversions or calculations may take place on the hardware control logic or other on-chip processing of the MEMS sensor  102  or other MEMS sensors  108 . 
     In some embodiments, certain types of information may be determined based on data from multiple MEMS inertial sensors  102  and other sensors  108 , in a process that may be referred to as sensor fusion. By combining information from a variety of sensors it may be possible to accurately determine information that is useful in a variety of applications, such as image stabilization, navigation systems, automotive controls and safety, dead reckoning, remote control and gaming devices, activity sensors, 3-dimensional cameras, industrial automation, and numerous other applications. 
     In accordance with the present disclosure, a periodic signal pattern may be generated at a variety of frequencies and utilized to test for vibrations at the MEMS sensor  102 . An output sense signal of the MEMS sensor  102  is compared to a number of test signal patterns, for example, by correlating the sense signal with each of the signal patterns. The output correlation values for each of the tests can be compared to identify the frequency characteristics of the vibration pattern, based on the frequency content of the vibration at various frequencies. 
       FIG.  2    shows an illustrative MEMS accelerometer with vibration monitoring in accordance with an embodiment of the present disclosure. In the depicted embodiment, an exemplary MEMS accelerometer  200  has a particular configuration for sensing an amplitude and a frequency of an external vibration acceleration, including a frequency scan generator, a proof mass, a signal generator of processing circuitry, sense electrodes, a capacitance to voltage (C2V) amplifier, a frequency mixer, an analog-to-digital converter, a sense signal, s(t), periodic signal portions, shifted periodic signal portions, a correlator, an averaged correlation value, and a frequency circuitry of processing circuitry. It will be understood that the present invention is applicable to a variety of MEMS sensor types that are capable of outputting signals corresponding to a vibration source (e.g., MEMS accelerometer, MEMS gyroscope, MEMS pressure sensor, etc.) in a variety of physical and circuitry configuration, including modifications to any of the above or other features such as additional sense electrodes, varied locations and types of processing circuitry, and additional circuitry such as additional processing circuitry (e.g., gain/offset/scaling or compensation circuitry). 
     The exemplary MEMS accelerometer  200  includes a frequency scan generator  202 , which couples to correlator  222 . The frequency scan generator  202  generates a frequency scan signal pattern, wherein the frequency scan signal pattern includes a plurality of periodic signal portions  218  and a plurality of shifted periodic signal portions  220 , each having a test frequency, f k  (e.g., at a frequency ranging from a few Hertz to an upper Nyquist frequency of a sampled sensor signal, such as 2 kHz). The frequency scan generator  202  generates and delivers the plurality of periodic signal portions  218  and the plurality of shifted periodic signal portions  220  to correlator  222 . The shifted periodic signal portions  220  are shifted by T k /4 (e.g., 90 degrees), wherein T k  is the period of each sample of the frequency scan signal pattern (e.g., the time for one cycle of a waveform to complete). It will be understood that the shifted periodic signal portions  220  may be shifted by other suitable portions of the period of base periodic signal portion, in order to avoid signal correlation misalignment as described herein. In some embodiments, the frequency scan signal pattern, which includes the plurality of periodic signal portions  218  and the plurality of shifted periodic signal portions  220 , may implement a plurality of signal amplitudes. 
     Proof mass  204  is located adjacent to sense electrodes  208  and receives an accelerometer drive signal (e.g., a carrier signal for the sensed movement or vibration tuned to the C2V converter  210  and other processing circuitry) from drive signal generator  206 . It will be understood that in some embodiments the drive signal may be provided in other manners, such as via the proof mass. In some embodiments, the frequency scan generator  202  may drive proof mass  204  via an optional MEMS drive, as described herein for  FIG.  4   . As depicted in  FIG.  2   , in some embodiments, the MEMS accelerometer  200  may not include the optional MEMS drive, which results in the frequency scan signal pattern, including the periodic signal portions  218  and the shifted periodic signal portions  220 , not being injected into proof mass  204 . Accordingly, the respective frequencies, f k , of the periodic signal portions  218  and the shifted periodic signal portions  220  are not injected into proof mass  204 , so when the respective frequencies, f k , are far from the external vibration frequency, C k , an averaged correlation value  224 , C k , is close to zero. 
     Sense electrodes  208  form capacitors with proof mass  204  for sensing the proof mass&#39;s  204  movement, in accordance with the drive signal, relative to the sense electrodes  208 . The proof mass&#39;s  204  movement generates a capacitance between sense electrodes  208  (e.g., parallel capacitor plates with respect to proof mass  204 ) and proof mass  204 , which the proof mass  204  outputs to C2V converter  210  as capacitance signals. It will be understood that in other embodiments the sensing may be performed directly from the sense electrodes  208 . The C2V converter  210  receives the capacitance signals and outputs a suitable signal (e.g., voltage or current proportional to the capacitance) to additional processing circuitry such as frequency mixer  212 . The drive signal generator of processing circuitry  206  additionally couples to the frequency mixer  212 , which receives output voltage signals from C2V converter  210  and the drive signal from signal generator of processing circuitry  206 . Frequency mixer  212  cancels out the drive signal, implemented by signal generator of processing circuitry  206  at proof mass  204  via the sense electrodes  208 , from the received voltage signals and delivers the resulting analog signals representative of the baseband output due to movement of the proof mass to analog-to-digital converter  214 . Analog-to-digital converter  214  receives the analog signals from frequency mixer  212  and converts them into a digital signal (e.g., sense signal  216 , s(t)). Sense signal  216 , s(t), serves as an output signal of analog-to-digital converter  214  and is a digital representation of the movement of the proof mass, such as due to a linear acceleration along the sense axis due to a sensed force such as a vibration caused by the operating environment. 
     Periodic signal portions  218  partially composes the frequency scan signal pattern generated by frequency scan generator  202 , which delivers the periodic signal portions  218  to correlator  222 . As described herein, a variety of frequency patterns are provided to test the frequency of the sense signal  216 . In some instances, the sampling of the sense signal  216  based on the periodic signal pattern  218  may occur such that the alignment shows relatively little correlation despite a similar frequency. Shifted periodic signal portions  220  may provide a mechanism for correcting for this error, by sensing at time-shifted locations (e.g., 90 degree shifted) within the sense signal  216 . The signal patterns  218  and  220  may be provided in a variety of waveforms, such as square waves or stairstep sinusoidal pulse trains (e.g., a step-wise waveform approximating a sine wave). 
     Correlator  222  receives the periodic signal portions  218  from the frequency scan generator  202 , the shifted periodic signal portions  220  from the frequency scan generator  202 , and the sense signal  216 , s(t), from the analog-to-digital converter  214 . Correlator  222  correlates the sense signal  216 , s(t), with the plurality of periodic signal portions  218  and the plurality of shifted periodic signal portions  220  to determine a first plurality and a second plurality of correlation values, for example, with a first and second correlation values generated for each test pattern frequency. These values, in turn, are used to determine a frequency of the motion imparted on the proof mass  204 , as described herein. For example, in an embodiment correlator  222  generates an averaged correlation value  224  C k  for each pulse train at a particular frequency on, by averaging the first plurality of correlation values and the second plurality of correlation values, which includes squaring each of the first plurality of correlation values, squaring each of the second plurality of correlation values, adding associated squares of the first plurality of correlation values and the second plurality of correlation values, and taking the square root of each of the added associated squares. However the correlation is calculated for each test pattern frequency, correlator  222  delivers a plurality of averaged correlation values  224 , C k , to a frequency test circuitry  226  to determine which frequency or frequencies, f k , of the plurality of periodic signal portions  218  and shifted periodic signal portions  220  most closely corresponds to the frequency of the external vibration (e.g., sense signal  216 , s(t)), G. In some embodiments, the frequency of sense signal  216 , s(t), C k , and the frequency, f k , of the periodic signal portions  218  and the shifted periodic signal portions  220  may match but result in averaged correlation values, C k , equal to zero if the sense signal  216 , s(t), is 90 degrees out of phase with respect to the periodic signal portions  218  and the shifted periodic signal portions  220 . The averaged correlation value  224 , C k , overcomes phase invariance by the correlator  222  receiving periodic signal portions  218  and shifted periodic signal portions  220  so that the averaged correlation value  224 , C k , is insensitive to the phase of the sense signal  216 , s(t). 
       FIG.  3    shows an example chart of correlation values corresponding to an example vibration signal monitored with the MEMS accelerometer of  FIG.  2    in accordance with an embodiment of the present disclosure.  FIG.  3    conveys how a plurality of periodic signal portions (e.g., including combined values based on periodic signal portions and shifted periodic signal portions), correlate to a sense signal, s(t), based on their respective frequencies, f k , compared to the frequency of the sense signal, s(t), G. For example, a periodic signal portion with a frequency, f k , close to the frequency of the sense signal, s(t), f v , will show a high averaged correlation value, C k . Contrarily, a periodic signal portion with a frequency, f k , far from the frequency of the sense signal, s(t), f v , will show a low averaged correlation value, C k  (e.g., ˜0). Where the respective frequencies, f k , of the plurality of periodic signal portions approach the frequency of the sense signal, s(t), f v , the corresponding averaged correlation values C k  will peak as depicted in  FIG.  3   . By providing more periodic signal portions at a variety of frequencies, greater accuracy as to the vibration frequency f v  can be established. In some embodiments, an iterative testing methodology may be utilized in which a likely range for the frequency is first identified using a low resolution and additional periodic signal portions are used within that likely range. 
       FIG.  4    shows an illustrative MEMS accelerometer with vibration monitoring based on injected signal patterns driving the MEMS in accordance with an embodiment of the present disclosure. The components of the MEMS accelerometer  200  of  FIG.  2    are depicted in MEMS accelerometer  400  of  FIG.  4   , except that optional MEMS drive  402  delivers the frequency scan signal pattern to self-test drive  404 , which provides a drive signal based on the frequency scan to self-test drive electrodes  406  to drive proof mass  204 . Thus, the proof mass  204  is driven in accordance with the underlying periodic signals of the frequency scan as well as any external vibration. Accordingly, the output sense signal  216  includes a portion based on frequency scan periodic signals and a portion based on the external vibration. The combined sense signal is then processed by the correlator  222  in a similar manner as described with respect to  FIG.  2   , except that the sense signal being processed also includes a frequency scan signal portion (based on the frequency scan drive including periodic signal portions) that should be similar to the periodic signal portions  218  and phase-shifted periodic signal portions  220 . Thus, this portion of the sense signal should correlate consistently with the periodic signal portions  218  and phase-shifted periodic signal portions  220  throughout the entire frequency scan, with any differences corresponding to the electromechanical translation via proof mass  204  and associated processing circuitry (e.g., C2V converter  210 , mixer  212 , and A/D converter  214 ). In some embodiments, a delay element (not depicted in  FIG.  4   ) may be included between the frequency scan generator  202  and correlator  222  to match the delivery time of the periodic signal portions  218  to the correlator with the propagation delay of the applied frequency scan signal via the suspended spring-mass system and processing circuitry. 
     For the frequency scan signal portion of the sense signal, the resulting correlation values should be consistent throughout the entire frequency range of the frequency scan. The correlation values may be analyzed (e.g., by frequency test circuitry  226 ) to identify discrepancies that may correspond to errors or damage to the suspended spring-mass system or processing circuitry in the sense path. Example conditions indicative or damage or other errors may include an inconsistent baseline of correlation values (e.g., which is representative of a sense response that varies based on frequency), a frequency range where the correlation value differs from the baseline by more than a threshold (e.g., indicating an undesirable resonant frequency), changes in the frequency response baseline over time, rate of change in frequency response baseline over time, or other suitable analytics. The external vibration portion of the sense signal can also be analyzed simultaneously to determine the frequency of the vibration, as described with respect to  FIG.  2   . The principal difference is that in the embodiment of  FIG.  4   , the external vibration will be additive to the frequency scan contribution to the correlation values, as depicted and described with respect to  FIG.  5   . 
       FIG.  5    shows an example chart of correlation values corresponding to an example vibration signal monitored with the MEMS accelerometer of  FIG.  4    in accordance with an embodiment of the present disclosure.  FIG.  5    conveys how a plurality of periodic signal portions, including shifted periodic signal portions, correlate to a sense signal, s(t), based on their respective frequencies, f k , compared to the frequency of the sense signal, s(t), G. A baseline of “1” corresponds to a typical frequency scan portion of the sense signal, which should correlate well with the same signal that was used to excite the proof mass. As discussed above, a vibration portion of the sense signal will be additive to the frequency scan portion, such that a periodic signal portion with a frequency, f k , close to the frequency of the vibration portion of the sense signal, s(t), f v , will show a higher averaged correlation value C k . Contrarily, a periodic signal portion with a frequency, f k , far from the frequency of the vibration portion of the sense signal, s(t), f v , will have a correlation value C k  (e.g., ˜1) that is similar to the frequency scan signal baseline. The baseline correlation value is approximately equal to one because the sense signal, s(t), correlates with the plurality of periodic signal portions, including the plurality of shifted periodic signal portions, due to the plurality of periodic signal portions, including the plurality of shifted periodic signal portions, being injected into the proof mass of the MEMS via the optional MEMS drive. 
       FIG.  6 A  shows an example diagram depicting an out-of-phase sense signal compared to a square wave signal pattern having a frequency f k  in accordance with an embodiment of the present disclosure while  FIG.  6 B  shows an example diagram depicting an in-phase sense signal compared to a square wave signal pattern having a frequency f k  in accordance with an embodiment of the present disclosure. In  FIG.  6 A , the frequency, f k , of the periodic signal portion matches the frequency of the in-phase sense signal, s(t), f v , and the phases are lined up so that the square wave is associated with the positive portion of the ADC signal, which results in a relatively high correlation value, C k . Contrarily, in  FIG.  6 B , even though the frequency, f k , of the periodic signal portion matches the frequency of the out-of-phase sense signal, s(t), f v , the averaged correlation value, C k , equals zero because the sense signal, s(t), is 90 degrees out-of-phase with respect to the square pulse frequency, f k , such that the positive and negative portions of the ADC signal cancel. 
       FIG.  7    shows an example MEMS correlator design including a phase-shifted signal pattern in accordance with an embodiment of the present. Sense signal  216 , s(t), periodic signal portions  218 , shifted periodic signal portions  220 , correlator  222 , and averaged correlation value  224 , C k , of  FIG.  2    are depicted in  FIG.  7   . Correlation circuitry  702   a  receives a plurality of periodic signal portions  218  from the frequency scan generator  202  (e.g., via a delay element), correlation circuitry  702   b  receives a plurality of shifted periodic signal portions  220  from the frequency scan generator  202  (e.g., via a delay element), and each of correlation circuitry  702   a  and  702   b  receive sense signal  216  from the analog-to-digital converter  214 . Correlation circuitry  702   a  correlates the sense signal  216  with the plurality of periodic signal portions  218  to determine a first plurality of correlation values  704  while correlation circuitry  702   b  correlates the plurality of shifted periodic signal portions  220  to determine a second plurality of correlation values  706 . The first plurality of correlation values  704  are delivered by correlation circuitry  702  to squaring circuitry of processing circuitry  708   a , and the second plurality of correlation values  706  are delivered by correlation circuitry  702  to squaring circuitry of processing circuitry  708   b . Squaring circuitry of processing circuitry  708   a  squares each of the first plurality of correlation values  704  and delivers the resulting squares to sum circuitry of processing circuitry  710 , while squaring circuitry of processing circuitry  708   b  squares each of the second plurality of correlation values  706  and delivers the resulting squares to sum circuitry of processing circuitry  710 . The sum circuitry  710  adds associated squares of the first plurality of correlation values  704  and the second plurality of correlation values  706  and delivers the resulting sum to square root circuitry of processing circuitry  712 , which takes the square root of the added associated squares and produces the averaged correlation value  224 , C k . Accordingly, the averaged correlation value  224 , C k , proves to be robust to any vibration phase included in the sense signal  216 , s(t). Such a square root determination by square root circuitry  712  may only be required necessary when a proportional output is needed, such as direct determination of frequency. In embodiments where such a response is not needed, such as threshold crossing detection, linearity is not strictly necessary and block  712  might be removed. 
       FIG.  8 A  shows an example diagram depicting a sense signal at a first frequency compared to a square wave signal pattern having a frequency in accordance with an embodiment of the present disclosure while  FIG.  8 B  shows an example diagram depicting a sense signal at a harmonic of the first frequency of  FIG.  8 A  compared to a square wave signal pattern having the same frequency as in  FIG.  8 A  in accordance with an embodiment of the present disclosure. In  FIG.  8 A , the frequency, f k , of the periodic signal portion matches the frequency of the in-phase sense signal, s(t), f v , which results in a maximum averaged correlation value, C k . In  FIG.  8 B , the periodic signal portion aligns with an odd harmonic (e.g., third harmonic) of the sense signal, such that the correlation with the harmonic results in a partial correlation with the periodic signal at frequency f k . For example, the periodic signal portion aligns with a third harmonic of the sense signal, s(t), (e.g., f k =3*f v , wherein f v  is the frequency of the sense signal, s(t)) that results in the averaged correlation value, C k , decreasing by a factor of three (e.g., C k =max/3) versus a comparison to a f v  sense signal, but nonetheless resulting in a correlation value which is high enough to register as a possible match for an external vibration. Such an effect may occur at multiple odd harmonics (e.g., 5*f v , 7*f v , 9*f v ) of the periodic signal portion frequency, resulting in possible errors in identifying the frequency of vibration. In some embodiments, it may therefore be desirable to identify likely harmonics based on maximum correlation peaks and utilize the identification of those harmonics and the relative correlation values to more accurately identify the actual frequency. 
       FIG.  9 A  shows an example diagram depicting the sense signal of  FIG.  8 A  compared to a stairstep sinusoidal signal pattern having a frequency f k  in accordance with an embodiment of the present disclosure, while  FIG.  9 B  shows an example diagram depicting the sense signal of  FIG.  8 B  compared to a stairstep sinusoidal signal pattern having a frequency f k  in accordance with an embodiment of the present disclosure. Although the underlying periodic signal portions of the frequency scan have been depicted as square wave signals having different frequencies in certain figures and discussion herein, it will be understood that different waveform types, such as sinusoidal waveforms (e.g., a “filtered sinusoid” whereby the stairstep component is removed by a low-pass filter, a “wavelet,” or a “windowed sinusoid” that is a sinusoid multiplied by an suitable envelope function (window) to have a smooth beginning and ending), may be used. In an embodiment as depicted and described in  FIGS.  9 A and  9 B , a sinusoidal waveform may be approximated by a stairstep sinusoidal signal pattern, with the resolution of the stepwise sinusoidal signal pattern based on a number of available bits used to generate the stepwise pattern. In  FIG.  9 A , the frequency, f k , of the periodic signal portion matches the frequency of the in-phase sense signal, s(t), f v , which results in a maximum averaged correlation value, C k . In  FIG.  9 B , the periodic signal portion responds to a third harmonic (e.g., image frequency) of the sense signal, s(t), (e.g., f k =3*f v , wherein f v  is the frequency of the sense signal, s(t)), however, the stairstep sinusoidal pulse train (e.g., a step-wise waveform) mitigates the periodic signal portion&#39;s correlation to the third harmonic of sense signal, s(t), since measurements are taken at points where the stairstep sinusoidal pulse train is not at its maximum. Accordingly, the averaged correlation value, C k , decreases significantly (e.g., C k &lt;&lt;max/3) compared to the square-wave case depicted in  FIG.  8 B , resulting in lower correlation value for harmonics (e.g., 5*f v , 7*f v , 9*f v ) of sense signal, s(t). 
       FIG.  10 A  shows an example diagram depicting a high selectivity dot graph corresponding to use of the stairstep sinusoidal signal pattern in accordance with an embodiment of the present disclosure (e.g.,  FIGS.  9 A and  9 B ), while  FIG.  10 B  shows an example diagram depicting a low selectivity dot graph in corresponding to use of the square wave sinusoidal signal pattern in accordance with an embodiment of the present disclosure (e.g.,  FIGS.  8 A and  8 B ). Frequency selectivity corresponds by how much the averaged correlation value, C k , exceeds the next highest features in the f k -C k  spectrum. Accordingly, the high selectivity dot graph, shown in  FIG.  10 A , depicts a large difference between averaged correlation values, C k , with frequencies, f k , near the frequency of the sense signal, s(t), f v , as opposed to averaged correlation values, C k , with harmonic frequencies, f k , farther from the frequency of the sense signal, s(t), which contributes to determining a vibration from background noise. Contrarily, the low selectivity dot graph, shown in  FIG.  10 B , depicts a less pronounced difference between averaged correlation values, C k , with frequencies, f k , near the frequency of the sense signal, s(t), f v , as opposed to averaged correlation values, C k , with frequencies, f k , farther from the frequency of the sense signal, s(t), G. Frequency selectivity may improve as a function of a longer value of T, where T is the duration of a single periodic signal packet (e.g., corresponding to the number of “bits” of the periodic waveform). Frequency resolution is the difference in frequency (e.g., Δf) between two adjacent signal portions (e.g., f k  and f k+1 ) and improves linearly with the number of frequency samples recorded. In some embodiments, a hierarchical approach may be used to determine a background vibration, which includes a low resolution, low selectivity scan, as depicted in  FIG.  10 B  and  FIGS.  8 A- 8 B , to identify potential vibration sites based on bumps within the f k -C k  spectrum. For each identified bump, a high resolution, high selectivity scan, as depicted in  FIG.  10 A  and  FIGS.  9 A- 9 B , is used to determine whether a background vibration exists or not. Where there is no vibration the bump will disappear and if a vibration is present, the bump will become a peak and an accurate reading of its frequency and amplitude can be achieved. 
       FIG.  11    shows an illustrative MEMS gyroscope with vibration monitoring in accordance with an embodiment of the present disclosure. The principle of operation of the MEMS gyroscope is similar to that described herein for the MEMS accelerometer of  FIG.  2   , with appropriate modifications made in order to properly process an external rotational vibration signal. In the depicted embodiment, an exemplary MEMS gyroscope  1100  has a particular configuration for sensing an amplitude and a frequency of an external rotational vibration, including a frequency scan generator, drive electrodes, a proof mass, sense electrodes, a signal generator of processing circuitry, a 90-degree phase shift, a capacitance to voltage (C2V) amplifier, a frequency mixer, an analog-to-digital converter, a sense signal, s(t), periodic signal portions, shifted periodic signal portions, a correlator, an averaged correlation value, and a frequency circuitry of processing circuitry. It will be understood that the present invention is applicable to any suitable MEMS gyroscope configurations (e.g., for sensing angular velocity about any suitable axis or combination of axes, in any suitable sense plane), including modifications to any of the above or other features such as additional drive electrodes, additional sense electrodes, varied locations and types of processing circuitry, and additional circuitry such as additional processing. 
     The exemplary MEMS gyroscope  1100  includes a frequency scan generator  1102 , which couples to correlator  1126 . The frequency scan generator  1102  generates a frequency scan signal pattern, wherein the frequency scan signal pattern includes a plurality of periodic signal portions  1122  and a plurality of shifted periodic signal portions  1124 , each having a test frequency, f k  (e.g., at a frequency range associated with a range of interest for external vibrations). The frequency scan generator  1102  generates and delivers the plurality of periodic signal portions  1122  and the plurality of shifted periodic signal portions  1124  to correlator  1126 . The shifted periodic signal portions  1124  are shifted by T k /4 (e.g., 90 degrees), wherein T k  is the period of each sample of the frequency scan signal pattern (e.g., the time for once cycle of a waveform to complete). It will be understood that the shifted periodic signal portions  1124  may be shifted by any suitable time or degree. In some embodiments, the frequency scan signal pattern, which includes the plurality of periodic signal portions  1122  and the plurality of shifted periodic signal portions  1124 , may implement a plurality of signal amplitudes. 
     Drive signal generator  1110  provides a drive signal to drive electrodes  1104  which in turn cause a drive motion within components of the suspended spring-mass system (e.g., drive masses, springs, lever arms, Coriolis masses, etc.) to move at the drive frequency of the gyroscope. In the presence of a rotational vibration about the measurement axis of the MEMS gyroscope, a Coriolis force causes movement of the proof mass  1106  along an axis (e.g., depicted by the arrow of proof mass  1106  in  FIG.  11   ) perpendicular to the axis of the drive motion and the axis about which the rotation occurs. In some embodiments, the frequency scan generator  1102  may also apply a force directly or indirectly to the proof mass  1106  via an optional MEMS drive, as depicted and described with respect to  FIG.  12   . In the embodiment depicted in  FIG.  11   , the periodic signal portions  1122  and the shifted periodic signal portions  1124  are injected to cause movement of proof mass  1106 , such that an output signal sensed by sense electrodes  1108  corresponds only to the sensed external vibration. 
     Sense electrodes  1108  couple and form capacitors with proof mass  1106  for sensing the movement of proof mass  1106  relative to the sense electrodes  1108 , in accordance with the Coriolis forces generated by the external vibration and the drive signal delivered by drive electrodes  1104 . The proof mass&#39;s  1106  movement generates a change in capacitance between respective sense electrodes  1108  (e.g., parallel capacitor plates with respect to proof mass  1106 ) and proof mass  1106 , which the proof mass  1106  outputs to C2V converter  1114  via sense electrodes  1108  as capacitance signals. The C2V converter  1114  receives the capacitance signals from proof mass  1106  via sense electrodes  1108 , converts the capacitance signals into a suitable analog output signals (e.g., proportional voltage or current), and delivers the output to frequency mixer  1116 . Based on the sensed Coriolis force being 90 degrees out-of-phase from the drive motion, the output from C2V converter  1114  is 90 degrees out-of-phase from the original drive signal, which is operating as a carrier signal for the baseband Coriolis signal. Accordingly, the signal from the drive signal generator is phase shifted by 90-degree phase shift  1112  to be in phase with the output signal from C2V converter  1114 . Frequency mixer  1116  cancels out the carrier drive signal from the received signal from C2V converter  1114  and delivers the resulting analog signals to analog-to-digital converter  1118 . Analog-to-digital converter  1118  receives the analog signals from frequency mixer  1116  and converts them into a digital signal that corresponds to the baseband external vibration sensed by movement of proof mass  1106 . 
     Periodic signal portions  1122  and shifted periodic signal portions  1124  collectively compose the frequency scan signal pattern generated by frequency scan generator  1102 , which delivers the periodic signal portions  1122  and shifted periodic signal portions to correlator  1126 . As described herein, although square wave patterns are depicted in  FIG.  11   , in other embodiments other waveform patterns (e.g., a stepwise sinusoidal pattern) may be utilized for the periodic signal portions. Further, although the periodic signal portions are depicted as being provided in a particular order (e.g., increasing) and change in frequency (e.g., doubling), it will be understood that the frequency scan can be provided in different manners, such as via testing and interpolation in any of the embodiments described herein. 
     Correlator  1126  receives the periodic signal portions  1122  from the frequency scan generator  1102 , the shifted periodic signal portions  1124  from the frequency scan generator  1102 , and the sense signal  1120 , s(t), from the analog-to-digital converter  1118 . Correlator  1126  correlates the sense signal  1120 , s(t), with the plurality of periodic signal portions  1122  and the plurality of shifted periodic signal portions  1124  to determine a first plurality and a second plurality of correlation values. Correlator  1126  generates an overall correlation value  1128 , C k , as described herein, such as by averaging the first plurality of correlation values and the second plurality of correlation values (e.g., by squaring each of the first plurality of correlation values, squaring each of the second plurality of correlation values, adding associated squares of the first plurality of correlation values and the second plurality of correlation values, and taking the square root of each of the added associated squares). Correlator  1126  delivers a plurality of averaged correlation values  1128 , C k , to a frequency circuitry  1130  to determine which frequency, f k , of the plurality of periodic signal portions  1122  and shifted periodic signal portions  1124  most closely corresponds to the frequency of the external vibration (e.g., sense signal, s(t)), f v , as described herein. The averaged correlation value  1128 , C k , overcomes phase invariance by the correlator  1126  receiving periodic signal portions  1122  and shifted periodic signal portions  1124  so that the averaged correlation value  1128 , C k , is insensitive to the phase of the sense signal  1120 , s(t). Frequency circuitry  1130 , which receives the plurality of averaged correlation values  1128 , C k , from correlator  1126 , determines the frequency associated with the sense signal  1120 , s(t), based on the plurality of averaged correlation values  1128 , C k , as described herein. 
       FIG.  12    shows an illustrative MEMS gyroscope with vibration monitoring based on injected signal patterns driving the MEMS in accordance with an embodiment of the present disclosure. The principle of operation of the MEMS gyroscope is similar to that described herein for the MEMS accelerometer of  FIG.  4   , with appropriate modifications made in order to properly process an external rotational vibration signal. The components of the MEMS gyroscope  1100  of  FIG.  11    are depicted in MEMS gyroscope  1200  of  FIG.  12   , except that optional MEMS drive  1202  delivers the frequency scan signal pattern to self-test drive  1204 , self-test drive  1204  couples to frequency mixer  1206 , frequency mixer  1206  receives the frequency scan signal pattern from self-test drive  1204  and a 90-degree phase shifted  1210  drive signal from the drive signal generator  1110 , and self-test drive electrodes  1208  couple to proof mass  1106  via frequency mixer  1206 . In this manner, the periodic signal pattern of the frequency scan is applied to the drive mass directly via the self-test drive electrodes  1208 , including the appropriate and phase-aligned drive (physical carrier) signal. Thus, the proof mass  1106  is driven in accordance with the underlying periodic signals of the frequency scan as well as any external rotational vibration. Accordingly, the output sense signal  1120  includes a portion based on frequency scan periodic signals and a portion based on the external rotational vibration. The combined sense signal is then processed by the correlator  1126  in a similar manner as described with respect to  FIG.  11   , except that the sense signal being processed also includes a frequency scan signal portion (based on the frequency scan drive including periodic signal portions) that should be similar to the periodic signal portions  1122  and phase-shifted periodic signal portions  1124 . Thus, this portion of the sense signal should correlate consistently with the periodic signal portions  1122  and phase-shifted periodic signal portions  1124  throughout the entire frequency scan, with any differences corresponding to the electromechanical translation via proof mass  1106  and associated processing circuitry (e.g., C2V converter  1114 , mixer  1116 , and A/D converter  1118 ). In some embodiments, a delay element (not depicted in  FIG.  12   ) may be included between the frequency scan generator  1102  and correlator  1126  to match the delivery time of the periodic signal portions to the correlator with the propagation delay of the applied frequency scan signal via the suspended spring-mass system and processing circuitry. 
     For the frequency scan signal portion of the sense signal, the resulting correlation values should be consistent throughout the entire frequency range of the frequency scan. The correlation values may be analyzed (e.g., by frequency test circuitry  1130 ) to identify discrepancies that may correspond to errors or damage to the suspended spring-mass system or processing circuitry in the sense path. Example conditions indicative or damage or other errors may include an inconsistent baseline of correlation values (e.g., which is representative of a sense response that varies based on frequency), a frequency range where the correlation value differs from the baseline by more than a threshold (e.g., indicating an undesirable resonant frequency), changes in the frequency response baseline over time, rate of change in frequency response baseline over time, or other suitable analytics. The external vibration portion of the sense signal can also be analyzed simultaneously to determine the frequency of the vibration, as described with respect to  FIG.  11   . The principal difference is that in the embodiment of  FIG.  12   , the external vibration will be additive to the frequency scan contribution to the correlation values, as describe herein (e.g., in  FIG.  5    and the accompanying discussion). 
     The foregoing is merely illustrative of the principles of this disclosure and various modifications may be made by those skilled in the art without departing from the scope of this disclosure. The embodiments described herein are provided for purposes of illustration and not of limitation. Thus, this disclosure is not limited to the explicitly disclosed systems, devices, apparatuses, components, and methods, and instead includes variations to and modifications thereof, which are within the spirit of the attached claims. The systems, devices, apparatuses, components, and methods described herein may be modified or varied to optimize the systems, devices, apparatuses, components, and methods. Although the present disclosure has been described with respect to an exemplary sensor such as a MEMS accelerometer and a MEMS gyroscope, it will be understood that the inventions described in the present disclosure will apply equally to any sensor that may be exposed to a high vibration environment, such as MEMS pressure sensors and the like.