Signal processing method and device, program product and second-order band-pass filter

Abstract

The invention discloses a signal processing method and device, a program product and a second-order band-pass filter, relates to the technical field of signal processing, is used for processing the distortion problem during signal integration and differential conversion, and aims to solve the problem that output distortion is caused due to the fact that low-frequency drift or a strong trend term cannot be avoided during integration and differential conversion at present. A signal processing method is provided, and the frequency response characteristic of a second-order band-pass filter is utilized: for a signal in a frequency response linear section, the attenuation of each frequency multiplication is 6.02 decibels, and the linear requirement required by integral transformation or differential transformation of the signal can be met; and large-error frequency points such as low-frequency noise and static acceleration of the second-order band-pass filter below the cut-off frequency can be effectively suppressed, so that the problem of signal distortion caused by the large-error frequency points is avoided, and the method is a flexible and efficient signal processing method.

Description

Technical Field

[0001] The present application relates to the field of signal processing technology, and in particular to a signal processing method, device, program product and second-order bandpass filter. Background Art

[0002] In the field of sensors, displacement and velocity are two widely used detection quantities. However, due to the limitations of sensor types or test environments, accelerometers are often used to obtain vibration signals, also known as acceleration signals, and then the velocity and displacement are indirectly obtained through the acceleration measurement.

[0003] The conversion of acceleration signals into velocity and displacement signals can be achieved theoretically through integration. Currently, there are two commonly used conversion methods: time domain integration and spectrum integration. Time domain integration uses the numerical integration method of trapezoidal quadrature, while frequency domain integration is mainly achieved by Fourier transform and inverse transform. However, both conversion methods will inevitably produce low-frequency drift or strong trend terms during the integration of signal samples. In addition, during the second integration, due to the influence of signal noise and the trend term of the first integration, the amplitude signal obtained after integration often has serious distortion.

[0004] Therefore, technicians in this field are in urgent need of a signal processing method to solve the problem that the amplitude signal obtained during the current signal processing process such as acceleration signal integration conversion often has serious distortion. Summary of the invention

[0005] The purpose of the present application is to provide a signal processing method, device, program product and second-order bandpass filter, which are used to solve the problem that the amplitude signal obtained in the current signal processing process such as acceleration signal integral conversion often has serious distortion.

[0006] In order to solve the above technical problems, the present application provides a signal processing method, comprising:

[0007] Construct a second-order bandpass filter;

[0008] Determine the cutoff frequency of the second-order bandpass filter according to the alternating frequency of the signal to be processed, so that the alternating frequency of the signal to be processed falls within the frequency response linear segment of the second-order bandpass filter;

[0009] Determining a transfer function of the second-order bandpass filter according to the cut-off frequency to complete parameter configuration of the second-order bandpass filter;

[0010] The signal to be processed is subjected to integral conversion or inverse integral conversion by the second-order bandpass filter.

[0011] In a possible embodiment, before determining the transfer function of the second-order bandpass filter, the method further includes:

[0012] Select any frequency within the frequency response linear segment and perform integral calibration on the second-order band-pass filter to determine an actual adjustment gain of the second-order band-pass filter;

[0013] Correspondingly, determining the transfer function of the second-order bandpass filter according to the cut-off frequency includes:

[0014] A transfer function of the second-order bandpass filter is determined according to the cut-off frequency and the actual adjustment gain.

[0015] In a possible embodiment, determining the transfer function of the second-order bandpass filter according to the cutoff frequency and the actual adjustment gain includes:

[0016] Constructing a transfer function of a second-order bandpass filter for implementing integral or differential filtering; wherein unknown parameters of the transfer function include: gain, center frequency and quality factor;

[0017] Taking the cut-off frequency as the system frequency of the transfer function, determining the corresponding angular frequency;

[0018] The transfer function is determined by taking the angular frequency as the center frequency of the transfer function, taking the actual adjustment gain as the gain of the transfer function, and taking the preset quality parameter value as the quality factor of the transfer function.

[0019] In a possible embodiment, selecting any frequency within the frequency response linear segment to perform integral calibration on the second-order bandpass filter to determine an actual adjustment gain of the second-order bandpass filter includes:

[0020] Constructing an integral calibrator and a calibration signal; wherein the alternating frequency of the calibration signal is the same as the system calibration frequency of the integral calibrator;

[0021] Performing an integral conversion on the calibration signal by the integral calibrator to obtain a calibrated signal;

[0022] The actual adjustment gain is determined according to the amplitude of the calibrated signal and the amplitude of the calibration signal.

[0023] In a possible embodiment, constructing the integral calibrator includes:

[0024] A second-order low-pass filter and a second-order high-pass filter are constructed, and the second-order low-pass filter and the second-order high-pass filter are connected in series to obtain the integral calibrator.

[0025] In a possible embodiment, determining the actual adjustment gain according to the amplitude of the calibrated signal and the amplitude of the calibration signal includes:

[0026] The actual gain of the integral calibrator is determined according to the ratio of the amplitude of the calibrated signal to the amplitude of the calibration signal, and the actual gain of the integral calibrator is used as the actual adjustment gain.

[0027] In a possible embodiment, the alternating frequency of the calibration signal is less than or equal to the cut-off frequency.

[0028] In a possible embodiment, determining the cutoff frequency of the second-order bandpass filter according to the alternating frequency of the signal to be processed includes:

[0029] Determine the provisional cutoff frequency of the second-order bandpass filter according to the alternating frequency of the signal to be processed; wherein the frequency value of the provisional cutoff frequency is less than the alternating frequency of the signal to be processed;

[0030] Based on the provisional cut-off frequency, determining whether the frequency value and the 2-fold frequency value of the alternating frequency of the signal to be processed fall within the frequency response linear segment;

[0031] If yes, determining the provisional cut-off frequency as the finally determined cut-off frequency;

[0032] If not, return to the step of determining the provisional cutoff frequency of the second-order bandpass filter according to the alternating frequency of the signal to be processed;

[0033] The frequency value of the newly determined provisional cut-off frequency is smaller than the provisional cut-off frequency determined last time.

[0034] In order to solve the above technical problems, the present application also provides a second-order bandpass filter, comprising: an integration circuit or an inverse integration circuit, an inverting output circuit and a feedback circuit;

[0035] The input end of the integration circuit / the inverse integration circuit serves as the input end of the second-order band-pass filter, and is used to access the signal to be processed; the output end of the integration circuit / the inverse integration circuit is connected to the input end of the inverting output circuit; the output end of the inverting output circuit serves as the output end of the second-order band-pass filter, and the output end of the inverting output circuit is connected to the input end of the feedback circuit; the output end of the feedback circuit is connected to the integration circuit / the inverse integration circuit;

[0036] The integration circuit / the inverse integration circuit is used to realize the integration conversion / inverse integration conversion of the signal to be processed;

[0037] The inverting output circuit is used to adjust the gain of the second-order bandpass filter;

[0038] The feedback circuit is used to adjust the cutoff frequency of the second-order bandpass filter so that the alternating frequency of the signal to be processed falls within the frequency response linear section of the second-order bandpass filter.

[0039] In a possible embodiment, the feedback circuit includes: a first resistor, a second resistor, a third resistor, a first capacitor and a first operational amplifier;

[0040] The first end of the first resistor serves as the input end of the feedback circuit, and the second end of the first resistor is connected to the inverting input end of the first operational amplifier; the non-inverting input end of the first operational amplifier is grounded through the second resistor; the output end of the first operational amplifier is connected to the inverting input end of the first operational amplifier through the first capacitor, and is connected to the first end of the third resistor; the second end of the third resistor serves as the output end of the feedback circuit;

[0041] Wherein, when the resistance value of the third resistor remains unchanged, the capacitance value of the first capacitor is negatively correlated with the cutoff frequency of the second-order bandpass filter;

[0042] The feedback circuit is used to adjust the capacitance of the first capacitor and the resistance of the third resistor so that the alternating frequency of the signal to be processed falls within the linear frequency response section of the second-order bandpass filter.

[0043] In a possible embodiment, the inverting output circuit includes: a fourth resistor, a fifth resistor, and a second operational amplifier;

[0044] The first end of the fourth resistor serves as the input end of the inverting output circuit, and the second end of the fourth resistor is connected to the inverting input end of the second operational amplifier; the non-inverting input end of the second operational amplifier is grounded; the output end of the second operational amplifier is connected to the inverting input end of the second operational amplifier through the fifth resistor, and serves as the output end of the inverting output circuit;

[0045] Wherein, the ratio of the resistance values ​​of the fifth resistor to the fourth resistor is positively correlated with the gain of the transfer function of the second-order bandpass filter;

[0046] Then the inverting output circuit is used to: adjust the resistance ratio of the fifth resistor and the fourth resistor so that the gain of the transfer function of the second-order bandpass filter is equal to the actual adjustment gain;

[0047] The process of determining the actual adjustment gain includes:

[0048] Any frequency within the frequency response linear segment is selected to perform integral calibration on the second-order band-pass filter to determine an actual adjustment gain of the second-order band-pass filter.

[0049] In a possible embodiment, the integration circuit includes: a sixth resistor, a seventh resistor, a second capacitor and a third operational amplifier;

[0050] The first end of the sixth resistor serves as the input end of the integration circuit, and the second end of the sixth resistor is connected to the inverting input end of the third operational amplifier and the output end of the feedback circuit; the non-inverting input end of the third operational amplifier is grounded; the output end of the third operational amplifier is connected to the inverting input end of the third operational amplifier through the seventh resistor and the second capacitor in parallel, and serves as the output end of the integration circuit.

[0051] In order to solve the above technical problem, the present application also provides a signal processing device, comprising N second-order bandpass filters as described above, where N is a positive integer greater than 1;

[0052] The N second-order bandpass filters are connected in series, and the N second-order bandpass filters all include an integration circuit or an inverse integration circuit.

[0053] In order to solve the above technical problems, the present application also provides a computer program product, including a computer program / instruction, which implements the steps of the signal processing method as described above when executed by a processor.

[0054] The present application provides a signal processing method, which utilizes the frequency response characteristics of a second-order bandpass filter: for signals located in the linear section of the frequency response, the attenuation per octave is 6.02 dB (i.e. -6.02 dB / oct), which can meet the linear requirements for integral or differential transformation of the signal, and can realize the function of suppressing signals below the cutoff frequency of the second-order bandpass filter. That is, for vibration signals or velocity signals that need to be integrally transformed, and velocity signals or displacement signals that need to be differentially transformed, the signal portion located in the linear section of the frequency response can be normally integrated or differentially transformed. And for low-frequency noise, static acceleration, and other frequency points below the cutoff frequency that cause large errors, they can be effectively suppressed. Therefore, this method designs a second-order bandpass filter transfer function whose frequency response linear segment above the cutoff frequency satisfies the -6.02dB / oct integral characteristic, and constructs an integrator or differentiator for signal processing based on this transfer function. Under the premise of meeting the linear requirements of normal integral or differential conversion of the signal, it can also effectively suppress the low-frequency noise, static acceleration and other frequency points that cause large errors below the cutoff frequency, avoid serious distortion of the processed signal, and thus improve the accuracy of signal integral or differential conversion. This method can not only solve the problem of severe distortion of amplitude signals that is currently faced in the sensor field when performing integral transformation of vibration signals, but also obtain the reverse differential transformation through inverse integral operation, and can also effectively suppress low-frequency noise, static acceleration and other large error frequency points below the cutoff frequency. It is a flexible and efficient signal processing method.

[0055] The second-order bandpass filter, signal processing device and computer program product provided in the present application correspond to the above method and have the same effects as above. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0057] Figure 1 A flow chart of a signal processing method provided by an embodiment of the present invention;

[0058] Figure 2 An integral characteristic curve diagram provided by an embodiment of the present invention;

[0059] Figure 3 A frequency response characteristic curve diagram of a second-order bandpass filter provided by an embodiment of the present invention;

[0060] Figure 4An amplitude-frequency characteristic curve diagram of a signal before calibration provided by an embodiment of the present invention;

[0061] Figure 5 An amplitude-frequency characteristic curve diagram of a calibrated signal provided by an embodiment of the present invention;

[0062] FIG6( a ) is a graph showing an amplitude-frequency characteristic curve of an acceleration signal provided by an embodiment of the present invention;

[0063] FIG6(b) is a graph showing the amplitude-frequency characteristic of a velocity signal obtained by integrating the acceleration signal of FIG6(a);

[0064] FIG6(c) is a graph showing the amplitude-frequency characteristic of a displacement signal obtained by performing a double integration process on the acceleration signal of FIG6(a);

[0065] Figure 7 A structural diagram of a second-order bandpass filter provided by an embodiment of the present invention;

[0066] Figure 8 A circuit diagram of a second-order bandpass filter provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0067] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0068] The core of this application is to provide a signal processing method, device, program product and second-order bandpass filter.

[0069] In order to enable those skilled in the art to better understand the present application, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0070] At present, the monitoring and control of motion are involved in many fields. Among them, displacement, velocity and acceleration are the basic physical quantities of object motion and are the most widely used. There is a connection between displacement, velocity and acceleration, which can be converted into each other through integration and differentiation.

[0071] In actual application scenarios, due to the limitations of sensor types or test environments, accelerometers are often used to obtain vibration signals, also known as acceleration signals, and then the velocity and displacement are indirectly obtained through the acceleration measurement. The acceleration signal can be converted into velocity and displacement signals theoretically through integration. Currently, the commonly used conversion methods are time domain integration and spectrum integration. The time domain integration uses the numerical integration method of trapezoidal quadrature, while the frequency domain integration is mainly achieved using Fourier transform and inverse transform.

[0072] However, both of the above conversion methods will inevitably produce low-frequency drift or strong trend terms in the process of signal sample integration. And in the second integration, due to the influence of signal noise and the first integration trend term, the amplitude signal obtained after integration often has serious distortion. Similarly, this problem also exists when the signal is inversely integrated (i.e., differentiated).

[0073] To solve the above problems, the present application provides a signal processing method, such as Figure 1 As shown, including:

[0074] S11: Construct a second-order bandpass filter.

[0075] S12: determining the cutoff frequency of the second-order bandpass filter according to the alternating frequency of the signal to be processed, so that the alternating frequency of the signal to be processed falls within the frequency response linear segment of the second-order bandpass filter.

[0076] S13: Determine the transfer function of the second-order band-pass filter according to the cut-off frequency to complete parameter configuration of the second-order band-pass filter.

[0077] S14: Performing integral conversion or inverse integral conversion on the signal to be processed through a second-order bandpass filter.

[0078] To better explain the method, before describing the specific embodiments of each step in detail, the principle of the method is first described: In kinematics, the acceleration a can be integrated once to obtain the velocity v, and the displacement x can be obtained by double integration. That is, the following relationship expression is obtained:

[0079] v = ∫a(t)dt (1);

[0080] x=∫v(t)dt=∫∫a(t)dtdt (2);

[0081] Where t is the amount of time.

[0082] For reciprocating alternating motion, the vibration expression is often related to the alternating frequency f, which indicates the number of alternations per second, in Hz. Taking sinusoidal vibration as an example, assuming that the sinusoidal vibration alternating frequency is f and the peak acceleration is A, then the vibration acceleration a, velocity v and displacement x are expressed as:

[0083] a(t) = Asin(2πft) (3);

[0084]

[0085] Therefore, when the peak acceleration of the sinusoidal vibration is A, the peak velocity V and peak displacement (amplitude) X of the vibration are:

[0086]

[0087]

[0088] According to the above two equations, the peak acceleration, peak velocity and peak displacement have a multiple relationship of 1 / (2πf) when integrated once. That is, for every octave increase in acceleration a(t) (i.e., frequency f doubles), the peak velocity V output drops to 1 / 2 (0.5 times), corresponding to a gain of -6.02dB. Among them, the relationship between the gain dB and the change multiple n is dB=20*log10(n). Similarly, for every octave increase in velocity v, the peak displacement X output drops to 1 / 2 (0.5 times), corresponding to a gain of about -6.02dB.

[0089] Assuming that the peak value of acceleration A=1, the acceleration of different alternating frequencies f is integrated according to formula (6), and the following equation can be obtained: Figure 2 The speed value and integral characteristic curve shown. Figure 2 It is not difficult to see that every time the alternating frequency f doubles on the original basis, the integrated value drops to 0.5 times the original value (about -6.02dB). Therefore, the integral characteristic curve shows an attenuation of 6.02dB per frequency doubling, that is, -6.02dB / oct.

[0090] Based on the above principle, this method constructs a second-order bandpass filter whose frequency response linear segment above the cutoff frequency satisfies the above-mentioned integral characteristic curve, and uses the second-order bandpass filter to perform integration or inverse integration processing on the signal, so that the frequency points that cause large integration errors such as low-frequency noise and static acceleration below the cutoff frequency can be effectively suppressed, thereby solving the problem that the signal obtained after integration or differentiation processing is prone to serious distortion.

[0091] Specifically, the method can be divided into three parts: construction of a second-order bandpass filter, parameter configuration of the second-order bandpass filter and use of the second-order bandpass filter, corresponding to step S11, step S12, step S13 and step S14 respectively.

[0092] Among them, step S11 is the process of constructing a second-order bandpass filter. The various parameters of the second-order bandpass filter constructed in this step need to be adjusted later so that the frequency response linear segment above the cutoff frequency satisfies the above integral characteristic curve. Therefore, this step only needs to construct a basic second-order bandpass filter. Since the second-order bandpass filter is a common signal processing device, its transfer function and construction method are well known to technicians. The transfer function H(s) can be expressed by the following formula:

[0093]

[0094] Where G is the gain of the second-order bandpass filter; s is the frequency domain of the system; ω is the center frequency, ω=2πf c , f c is the cut-off frequency of the second-order band-pass filter; Q is the quality factor of the second-order band-pass filter.

[0095] It can be seen from the above formula (7) that the second-order bandpass filter constructed in step S11 still has unknown parameters G, ω (ω can also be regarded as f c ), Q is to be determined. The process of determining these parameters is implemented by steps S12 and S13.

[0096] Among them, based on the principle of suppressing signal distortion of the above method, it can be known that the core of the method is to construct a second-order bandpass filter that satisfies the above integral characteristic curve to perform integration or differentiation processing on the processed signal. Therefore, the main purpose of step S12 is to adjust the cutoff frequency f of the second-order bandpass filter. c , so that the linear segment of the frequency response of the second-order bandpass filter satisfies the above-mentioned integral characteristic curve.

[0097] Furthermore, in this method, a second-order bandpass filter is constructed to realize the integration or differentiation of the signal to be processed to satisfy the above-mentioned integral characteristic curve, and the frequency response characteristics of the constructed second-order bandpass filter determine the frequency of the signal to be processed that is less than the cutoff frequency f c The frequency part is suppressed, which is greater than the cut-off frequency f c The frequency part of the second-order bandpass filter satisfies the integral characteristic of -6.02dB / oct to meet the above requirements. Therefore, step S12 requires the cutoff frequency f of the second-order bandpass filter to be c < the alternating frequency f1 of the signal to be processed, thereby ensuring that the alternating frequency f1 of the integrated or differentiated signal to be processed is within the linear frequency response section of the second-order bandpass filter -6.02dB / oct, so as to effectively suppress the frequency points of large integral errors caused by low-frequency noise, static acceleration, etc.

[0098] On the other hand, G is the adjustment gain of the system, and its purpose is to adjust the system input and output to an ideal relationship. The gain can be determined according to the actual control or signal processing needs, and this embodiment does not limit this. And considering that the main purpose of this method is to ensure that the frequency response linear segment above the cutoff frequency of the second-order bandpass filter satisfies the above-mentioned integral characteristic curve, there is no additional restriction on the gain part, so this embodiment will not be repeated here. There are currently many mature solutions for gain calibration of integration and differentiation processes, and a suitable gain determination solution can be selected according to actual needs.

[0099] This embodiment provides a possible solution for determining the gain of a second-order bandpass filter. Before determining the transfer function of the second-order bandpass filter in step S13, the method further includes:

[0100] S15: Select any frequency within the linear segment of the frequency response and perform integral calibration on the second-order band-pass filter to determine the actual adjustment gain of the second-order band-pass filter.

[0101] Correspondingly, "determining the transfer function of the second-order band-pass filter according to the cut-off frequency" in step S13 is specifically: determining the transfer function of the second-order band-pass filter according to the cut-off frequency and the actual adjustment gain.

[0102] A possible gain determination scheme provided in this embodiment is to perform integral calibration on the second-order bandpass filter by arbitrarily selecting a frequency within the linear segment of the frequency response of the second-order bandpass filter as the signal frequency of the calibration signal, thereby determining the actual adjustment gain of the second-order bandpass filter, and the actual adjustment gain can have higher accuracy in the linear segment of the frequency response.

[0103] Similarly, in practical applications, the quality factor generally has different empirical values ​​that can be selected according to the different applications of the second-order bandpass filter. As mentioned above, when the second-order bandpass filter is used as an integrator, a possible empirical value is Q = √2 / 2, and the specific value can be 0.707. Similarly, when the second-order bandpass filter is used as a differentiator, there is also a corresponding empirical value setting.

[0104] That is, in combination with the gain determination embodiment provided in the above embodiment, for the three unknown parameter items in the above formula (8), this embodiment provides a possible specific determination scheme for the transfer function of the second-order bandpass filter. The "determining the transfer function of the second-order bandpass filter according to the cutoff frequency and the actual adjustment gain" in step S13 of the above embodiment specifically includes:

[0105] S131: Construct a transfer function of a second-order bandpass filter for implementing integral or differential filtering.

[0106] Among them, the unknown parameters of the transfer function include: gain, center frequency and quality factor.

[0107] S132: Determine the corresponding angular frequency using the cut-off frequency as the system frequency of the transfer function.

[0108] S133: Determine the transfer function by using the angular frequency as the center frequency of the transfer function, the actual adjustment gain as the gain of the transfer function, and the preset quality parameter value as the quality factor of the transfer function.

[0109] Among them, step S132 is the process of determining the center frequency ω of the transfer function according to the cut-off frequency determined in step S12 and ω = 2πf. c To determine the center frequency ω of the transfer function. The gain of the transfer function has been obtained based on integral calibration in step S15 of the above embodiment. Then, in step S133, further using the preset quality parameter value as the quality factor of the transfer function can realize the determination of the three unknown parameter terms in Equation (8), obtain the transfer function of the final second-order band-pass filter, and complete the parameter configuration.

[0110] Specifically, the preset quality parameter value is also the empirical value of the quality factor commonly taken by the second-order band-pass filter in practical applications. As can be seen above, when the second-order band-pass filter is used for integral operation, the quality factor Q = √2 / 2, and the specific value can be taken as 0.707. Similarly, when the second-order band-pass filter is used as a differentiator, there are also corresponding empirical value settings.

[0111] Based on the above steps, the adjustment of the second-order band-pass filter can be realized, and the final transfer function can be determined. Among them, since the alternating frequencies of different signals to be processed are not necessarily the same, the alternating frequency of the signal to be processed is represented by a variable f1. Correspondingly, assuming there is a frequency value f2 that always satisfies f2 < f1, then the frequency value f2 can be used as the cut-off frequency of the second-order band-pass filter. If it is assumed that this second-order band-pass filter is used to perform integral processing on the signal to be processed, that is, the quality factor Q of the second-order band-pass filter takes 0.707, then there is the following transfer function:

[0112]

[0113] As can be seen from the above, the gain in Equation (9) needs to be calibrated separately and is therefore represented by G for now. When the second-order band-pass filter is used to perform differential processing on the signal to be processed, its transfer function only differs from the above Equation (9) in the empirical value of the quality factor Q taken. The key to determining the transfer function still lies in the determination of the cut-off frequency, so this embodiment will not be elaborated here.

[0114] In another possible embodiment, differential processing is the inverse of integral processing. The transfer function of the second-order band-pass filter can be taken as the inverse of the transfer function H(s) for integration corresponding to the above Equation (9), that is, H(s) -1That is, whether the second-order bandpass filter is used for integral processing or differential processing of the signal to be processed, it can be regarded as integral processing to determine the transfer function H(s) as described in the above formula (9). Finally, in step S14, if the second-order bandpass filter is used for integral processing, the integral processing is directly performed through H(s); if the second-order bandpass filter is used for differential processing, the differential processing can be realized by applying the inverse integral to H(s).

[0115] As can be seen from the above, a signal processing method provided by the present application is to construct a second-order bandpass filter for realizing integral processing or differential processing of a signal. Among them, by adjusting the cutoff frequency of the constructed second-order bandpass filter, the alternating frequency of the signal to be processed falls within the frequency response linear segment that satisfies the -6.02dB / oct integral characteristic, so that when the signal to be processed is integrated or differentiated by the second-order bandpass filter, the frequency points that cause large integral errors such as low-frequency noise and static acceleration below the cutoff frequency can be effectively suppressed, thereby alleviating the problem of signal distortion.

[0116] Furthermore, in the above embodiment, a solution for determining the actual adjustment gain of the second-order bandpass filter by using integral calibration is provided, but no limitation is imposed on the specific steps of the integral calibration. In a possible implementation, another second-order bandpass filter that is completely identical to the second-order bandpass filter to be calibrated can be constructed as a calibrator, and a calibration signal can be set. The calibration signal is processed by the calibrator, and the gain of the second-order bandpass filter can be determined according to the relationship between the input and output of the calibrator.

[0117] That is, this embodiment also provides a possible gain determination solution, and the above step S15 specifically includes:

[0118] S151: Construct an integral calibrator and a calibration signal.

[0119] The alternating frequency of the calibration signal is the same as the system calibration frequency of the integral calibrator.

[0120] S152: Performing an integral conversion on the calibration signal through an integral calibrator to obtain a calibrated signal.

[0121] S153: Determine the actual adjustment gain according to the amplitude of the calibrated signal and the amplitude of the calibration signal.

[0122] For step S151, if the constructed integral calibrator is the same as the second-order bandpass filter to be calibrated, then the actual adjustment gain of the second-order bandpass filter can be determined as in the above-mentioned integral calibration implementation scheme. This embodiment also provides another implementation scheme of the integral calibrator:

[0123] A second-order low-pass filter and a second-order high-pass filter are constructed, and the second-order low-pass filter and the second-order high-pass filter are connected in series to obtain an integral calibrator.

[0124] Among them, the transfer function of the second-order low-pass filter is H j1 (s) are as follows:

[0125]

[0126] The transfer function H of the second-order high-pass filter j2 (s) are as follows:

[0127]

[0128] Since the purpose of this solution is to calibrate the gain of the second-order bandpass filter, the quality factor Q can be set to 1 for ease of calculation. However, for the values ​​of the system frequency and the alternating frequency of the calibration signal in the second-order low-pass filter and the second-order high-pass filter, this embodiment provides a preferred implementation scheme:

[0129] The system frequency of the second-order low-pass filter, the second-order high-pass filter and the alternating frequency of the calibration signal are equal to the calibration frequency f j , and the calibration frequency f j Satisfy f j ≤f2.

[0130] In this embodiment, on the one hand, the frequencies of the calibrator and the calibration signal correspond to the same calibration frequency, and on the other hand, the calibration frequency is smaller than the cutoff frequency f2 of the second-order bandpass filter, so as to achieve the best calibration effect.

[0131] Furthermore, the second-order low-pass filter and the second-order high-pass filter constructed above are connected in series to obtain the final integral calibrator. The transfer function H of the integral calibrator is j (s) are as follows:

[0132] H j (s) = conv(H j1 (s),H j2 (s)) (12);

[0133] Where conv() represents the convolution operation.

[0134] The integral calibrator of this embodiment is simple to implement and can be realized by a simple second-order low-pass filter and a second-order high-pass filter in series, which simplifies the complexity of integral calibration to determine the actual adjustment gain of the second-order bandpass filter in terms of software calculation and hardware implementation.

[0135] On the other hand, the present embodiment does not limit the structure of the calibration signal. The amplitude of the calibration signal X(s) may be set to be A, and its alternating frequency may be the calibration frequency f as in the preferred solution provided in the above embodiment. j .

[0136] There is no need to elaborate on step S152, that is, the calibration signal is processed by the constructed integral calibrator to obtain a set of corresponding inputs and outputs of the integral calibrator for use in the gain determination in step S153. The input and output relationship corresponding to step S152 is as follows:

[0137] Y(s)= conv(X(s),H j (s)) (13);

[0138] Among them, Y(s) is the output of the integral calibrator, that is, the calibrated signal.

[0139] For step S153, the amplitude Y(f j ), and the amplitude A of the calibration signal X(s), to determine the gain of the integral calibrator. For the specific implementation of step S153, this embodiment also provides a corresponding optional solution:

[0140] According to the ratio of the amplitude of the calibrated signal to the amplitude of the calibration signal, the actual gain of the integration calibrator is determined, and the actual gain of the integration calibrator is used as the actual adjustment gain.

[0141] That is, based on the amplitude Y(f) of the calibrated signal Y(s) determined above j ), and the amplitude A of the calibration signal X(s), the gain of the integral calibrator G = Y(f j ) / A. At this time, the actual adjustment gain of the second-order bandpass filter = the gain of the integral calibrator G = Y(f j ) / A.

[0142] Based on this, the final transfer function of the second-order bandpass filter is determined as:

[0143]

[0144] In summary, this embodiment provides a complete set of solutions for determining the actual adjustment gain of a second-order bandpass filter by integral calibration. By constructing a corresponding integral calibrator and a calibration signal, the integral calibrator performs an integral process on the calibration signal, and then determines the gain of the second-order bandpass filter according to the input-output relationship of the integral calibrator. The entire calibration process is simple and convenient to implement, and the gain determination of the second-order bandpass filter can be completed quickly and accurately, thereby efficiently completing the parameter adjustment of the second-order bandpass filter in the above method.

[0145] On the other hand, as can be seen from the above embodiments, the frequency response characteristic of the second-order band-pass filter designed in this method determines that the frequency less than the cut-off frequency f c The frequency is suppressed, and the frequency greater than f c The frequency of can achieve integration satisfying -6.02 dB / oct. Therefore, it is required that f c < f1, so as to ensure that the signal frequency f1 to be integrated is within the linear frequency band of -6.02 dB / oct of the integrator.

[0146] However, the above is a theoretical situation. In actual applications, based on the adjustment of the above cut-off frequency, it is still necessary to further determine whether the signal to be processed really falls within the frequency response linear section of the second-order band-pass filter to ensure the reliability and accuracy of signal processing. Based on this, this embodiment also provides an optional implementation scheme. The "determining the cut-off frequency of the second-order band-pass filter according to the alternating frequency of the signal to be processed" in the above step S12 specifically includes:

[0147] S121: Determine a tentative cut-off frequency of the second-order band-pass filter according to the alternating frequency of the signal to be processed.

[0148] Among them, the frequency value of the tentative cut-off frequency is less than the alternating frequency of the signal to be processed.

[0149] S122: Based on the tentative cut-off frequency, determine whether the frequency value and the double frequency value of the alternating frequency of the signal to be processed fall within the frequency response linear section; if so, go to step S123; if not, return to step S121.

[0150] S123: Determine the tentative cut-off frequency as the finally determined cut-off frequency.

[0151] Among them, the frequency value of the newly determined tentative cut-off frequency is less than the previously determined tentative cut-off frequency.

[0152] That is, in this embodiment, by judging whether f1 and 2f1 satisfy the condition of -6.02 dB / oct to judge whether the adjustment of the cut-off frequency of the second-order band-pass filter meets the requirements. If not, in addition to the above f c < f1 condition, each newly set f c All need to be less than the previously set f c , so that the adjustment of the cut-off frequency f c Approaches the goal that the signal to be processed can fall within the frequency response linear section of the second-order band-pass filter.

[0153] On the other hand, based on the signal processing method provided by the above embodiments, this embodiment combines a computer program product example and simulation to illustrate the effect of this method in suppressing signal distortion, that is, to illustrate the software implementation manner of this method:

[0154] The above second-order bandpass filter is used to implement a peak acceleration of 1m / s 2 , the double integral operation of the sinusoidal vibration signal a(t) = 1*sin(2π*5*t) with an alternating frequency of 5Hz. According to the above design method, the design process and integral calculation results of the second-order bandpass filter are as follows:

[0155] 1. Determination of transfer function cutoff frequency

[0156] According to the requirements, the frequency of the integrated signal is 5Hz, so the cutoff frequency f of the second-order bandpass filter can be initially set c =3Hz, according to the above formula (9), the transfer function W1(s) of the second-order bandpass filter is preliminarily obtained as:

[0157]

[0158] In order to further confirm whether the frequency of the integrated signal is within the linear frequency response section of the second-order bandpass filter, it is necessary to analyze the frequency response characteristics of the second-order bandpass filter. Let G = 1 in W1(s), and the corresponding frequency response characteristic curve is obtained through simulation as follows: Figure 3 As shown in the figure above, 5Hz is within the linear frequency range of the integrator -6.02dB / oct, so the cutoff frequency point 3Hz meets the requirements, so the gain parameters of the second-order bandpass filter can be further determined.

[0159] 2. Determination of transfer function gain parameters

[0160] Based on the above embodiment, firstly, calibrator 1 and calibrator 2 are constructed, and their transfer functions are shown in the above equations (10) and (11) respectively. In order to simplify the calculation, G=1 and Q=1 are taken, then the transfer function of calibrator 1 is Transfer function of calibrator 2

[0161] Select the frequency within the linear segment of the frequency response for integral calibration, and construct an alternating frequency f0 = 3 Hz, amplitude A = 1 m / s 2 The sinusoidal calibration signal a0(t) = 1*sin(2π*3*t) has an amplitude-frequency characteristic curve as shown in Figure 4 The calibration signal is used as the input of the above two calibrators for calibration operation, and the amplitude-frequency characteristic curve of the calibrated signal is obtained as shown in Figure 5 As shown. According to Figure 4 and Figure 5 The amplitude relationship of the calibration signal before and after the calibrator is integrated can determine the actual adjustment gain G = 0.1126 of the second-order bandpass filter. In summary, the final transfer function of the second-order bandpass filter can be determined as

[0162] If we assume that there is an original acceleration signal a(t), the corresponding theoretical peak velocity Theoretical peak displacement Then the second-order bandpass filter based on the above structure integrates the acceleration signal to velocity, or re-integrates to displacement, as follows Figure 6(a) to Figure 6(c) The amplitude-frequency characteristic curves of the acceleration signal, velocity signal and displacement signal are shown in FIG6 . According to FIG6 , the velocity signal and displacement signal calculated by the second-order bandpass filter designed based on this method have a peak velocity of 0.032 m / s, an error of only 0.53%, and a peak displacement of 0.001024 m, an error of only 1%, a high accuracy of the integral result, and small signal distortion.

[0163] In the above embodiment, a signal processing method and its software implementation are described in detail. The above software implementation can be implemented by a programmable gate array such as a host computer or an FPGA. The present application also provides an embodiment corresponding to a second-order bandpass filter, which is a hardware implementation based on the present method. Figure 7 As shown, this embodiment provides a second-order bandpass filter including: an integration circuit or an inverse integration circuit 11 , an inverting output circuit 12 and a feedback circuit 13 .

[0164] Among them, the input end of the integration circuit / inverse integration circuit 11 serves as the input end of the second-order bandpass filter, which is used to access the signal to be processed; the output end of the integration circuit / inverse integration circuit 11 is connected to the input end of the inverting output circuit 12; the output end of the inverting output circuit 12 serves as the output end of the second-order bandpass filter, and the output end of the inverting output circuit 12 is connected to the input end of the feedback circuit 13; the output end of the feedback circuit 13 is connected to the integration circuit / inverse integration circuit 11.

[0165] The integration circuit / inverse integration circuit 11 is used to realize the integration conversion / inverse integration conversion of the signal to be processed; the inverting output circuit 12 is used to adjust the gain of the second-order bandpass filter; the feedback circuit 13 is used to adjust the cutoff frequency of the second-order bandpass filter so that the alternating frequency of the signal to be processed falls within the frequency response linear segment of the second-order bandpass filter.

[0166] Specifically, the second-order bandpass filter provided in this embodiment is also a hardware implementation scheme of the second-order bandpass filter designed in the above-mentioned signal processing method. By adjusting the parameters of the electrical components in the integration circuit or the inverse integration circuit, the inverting output circuit and the feedback circuit, the parameters of the second-order bandpass filter can be adjusted to meet the requirements of the above-mentioned signal processing method embodiment and achieve the effect of suppressing signal distortion during integration and differentiation processing.

[0167] Furthermore, this embodiment provides a specific structure of a feedback circuit 13 and a possible solution for adjusting the cutoff frequency of a second-order bandpass filter, such as Figure 8 As shown, the feedback circuit 13 includes: a first resistor R1, a second resistor R2, a third resistor R3, a first capacitor C1 and a first operational amplifier U1.

[0168] The first end of the first resistor R1 serves as the input end of the feedback circuit 13, and the second end of the first resistor R1 is connected to the inverting input end of the first operational amplifier U1; the non-inverting input end of the first operational amplifier U1 is grounded through the second resistor R2; the output end of the first operational amplifier U1 is connected to the inverting input end of the first operational amplifier U1 through the first capacitor C1, and is connected to the first end of the third resistor R3; the second end of the third resistor R3 serves as the output end of the feedback circuit 13.

[0169] Wherein, when the resistance value of the third resistor R3 remains unchanged, the capacitance value of the first capacitor C1 is negatively correlated with the cut-off frequency of the second-order band-pass filter. Then the feedback circuit 13 is used to adjust the capacitance value of the first capacitor C1 and the resistance value of the third resistor R3 so that the alternating frequency of the signal to be processed falls within the frequency response linear section of the second-order band-pass filter.

[0170] On the other hand, this embodiment also provides a specific structure of an inverting output circuit and a possible solution for adjusting the gain of a second-order bandpass filter, such as Figure 8 As shown, the inverting output circuit 12 includes: a fourth resistor R4, a fifth resistor R5 and a second operational amplifier U2.

[0171] The first end of the fourth resistor R4 serves as the input end of the inverting output circuit 12, and the second end of the fourth resistor R4 is connected to the inverting input end of the second operational amplifier U2; the non-inverting input end of the second operational amplifier U2 is grounded; the output end of the second operational amplifier U2 is connected to the inverting input end of the second operational amplifier U2 through the fifth resistor R5, and serves as the output end of the inverting output circuit 12.

[0172] The resistance ratio of the fifth resistor R5 to the fourth resistor R4 is positively correlated with the gain of the transfer function of the second-order bandpass filter.

[0173] The inverting output circuit 12 is used to adjust the resistance ratio of the fifth resistor R5 and the fourth resistor R4 so that the gain of the transfer function of the second-order bandpass filter is equal to the actual adjustment gain.

[0174] The process of determining the actual adjustment gain includes:

[0175] Select any frequency within the linear section of the frequency response to perform integral calibration on the second-order band-pass filter to determine the actual adjustment gain of the second-order band-pass filter.

[0176] On the other hand, when the second-order bandpass filter includes an integration circuit, this embodiment also provides a possible solution for the specific structure of the integration circuit, such as Figure 8 As shown, the integration circuit includes: a sixth resistor R6, a seventh resistor R7, a second capacitor C2 and a third operational amplifier U3.

[0177] The first end of the sixth resistor R6 serves as the input end of the integration circuit, and the second end of the sixth resistor R6 is connected to the inverting input end of the third operational amplifier U3 and the output end of the feedback circuit 13; the non-inverting input end of the third operational amplifier U3 is grounded; the output end of the third operational amplifier U3 is connected to the inverting input end of the third operational amplifier U3 through the seventh resistor R7 and the second capacitor C2 in parallel, and serves as the output end of the integration circuit.

[0178] Based on the hardware structure of the second-order bandpass filter provided in the above embodiment, the cutoff frequency, gain and other important parameters of the second-order bandpass filter can be adjusted by adjusting the parameters of some electrical components in the corresponding circuit, so that the alternating frequency of the signal to be processed falls within the linear segment of the frequency response of the second-order bandpass filter, thereby achieving the purpose of suppressing signal distortion.

[0179] Furthermore, based on the second-order bandpass filter provided in the above embodiment, this embodiment also provides an implementation scheme corresponding to a signal processing device. A signal processing device includes N second-order bandpass filters as described above, where N is a positive integer greater than 1.

[0180] Among them, N second-order bandpass filters are connected in series, and the N second-order bandpass filters all include an integration circuit or an inverse integration circuit. That is, in the above-mentioned embodiment of the second-order bandpass filter part, based on the different applications of integration or differentiation of the second-order bandpass filter, an integration circuit or an inverse integration (i.e., differentiation) circuit may be included. However, the present scheme provides a signal processing device for multiple integration or differentiation processing, so the signal processing device should only include a second-order bandpass filter for integration processing application or a second-order bandpass filter for differentiation processing application. Exemplarily, if N=2, then if the second-order bandpass filter includes an integration circuit, then the signal processing device is equivalent to a heavy integrator. Similarly, if N=2, and the second-order bandpass filter includes an inverse integration circuit, then the signal processing device is equivalent to a heavy differentiator.

[0181] Since the embodiments of the signal processing device part correspond to the embodiments of the second-order bandpass filter part, the embodiments of the signal processing device part refer to the description of the embodiments of the second-order bandpass filter part, which will not be described here.

[0182] Finally, in addition to the signal processing method, device, and second-order bandpass filter provided in the above embodiments, the present invention also provides an embodiment corresponding to a computer program product. A computer program product includes a computer program / instruction, and when the computer program / instruction is executed by a processor, the steps of the signal processing method described in any of the above embodiments can be implemented.

[0183] Since the embodiments of the computer program product part correspond to the embodiments of the method part, please refer to the description of the embodiments of the method part for the embodiments of the computer program product part, which will not be repeated here.

[0184] The above is a detailed introduction to a signal processing method, device, program product and second-order bandpass filter provided by the present application. The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same and similar parts between the various embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part description. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present application, several improvements and modifications can be made to the present application, and these improvements and modifications also fall within the scope of protection of the present application.

[0185] It should also be noted that, in this specification, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprise", "include" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the statement "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or device including the element.

Claims

1. A signal processing method, characterized in that: include: Construct a second-order bandpass filter; Determine the cutoff frequency of the second-order bandpass filter according to the alternating frequency of the signal to be processed, so that the alternating frequency of the signal to be processed falls within the frequency response linear segment of the second-order bandpass filter; Determining a transfer function of the second-order bandpass filter according to the cut-off frequency to complete parameter configuration of the second-order bandpass filter; The signal to be processed is subjected to integral conversion or inverse integral conversion by the second-order bandpass filter.

2. The signal processing method according to claim 1, characterized in that: Before determining the transfer function of the second-order bandpass filter, the method further includes: Select any frequency within the frequency response linear segment and perform integral calibration on the second-order band-pass filter to determine an actual adjustment gain of the second-order band-pass filter; Correspondingly, determining the transfer function of the second-order bandpass filter according to the cut-off frequency includes: A transfer function of the second-order bandpass filter is determined according to the cut-off frequency and the actual adjustment gain.

3. The signal processing method according to claim 2, characterized in that: Determining the transfer function of the second-order bandpass filter according to the cut-off frequency and the actual adjustment gain includes: Constructing a transfer function of a second-order bandpass filter for implementing integral or differential filtering; wherein unknown parameters of the transfer function include: gain, center frequency and quality factor; Taking the cut-off frequency as the system frequency of the transfer function, determining the corresponding angular frequency; The transfer function is determined by taking the angular frequency as the center frequency of the transfer function, taking the actual adjustment gain as the gain of the transfer function, and taking the preset quality parameter value as the quality factor of the transfer function.

4. The signal processing method according to claim 2, characterized in that: The step of selecting any frequency within the frequency response linear segment and performing integral calibration on the second-order bandpass filter to determine the actual adjustment gain of the second-order bandpass filter comprises: Constructing an integral calibrator and a calibration signal; wherein the alternating frequency of the calibration signal is the same as the system calibration frequency of the integral calibrator; Performing an integral conversion on the calibration signal by the integral calibrator to obtain a calibrated signal; The actual adjustment gain is determined according to the amplitude of the calibrated signal and the amplitude of the calibration signal.

5. The signal processing method according to claim 4, characterized in that: Constructing the integral calibrator includes: A second-order low-pass filter and a second-order high-pass filter are constructed, and the second-order low-pass filter and the second-order high-pass filter are connected in series to obtain the integral calibrator.

6. The signal processing method according to claim 5, characterized in that: Determining the actual adjustment gain according to the amplitude of the calibrated signal and the amplitude of the calibration signal includes: The actual gain of the integral calibrator is determined according to the ratio of the amplitude of the calibrated signal to the amplitude of the calibration signal, and the actual gain of the integral calibrator is used as the actual adjustment gain.

7. The signal processing method according to claim 4, characterized in that: The alternating frequency of the calibration signal is less than or equal to the cut-off frequency.

8. The signal processing method according to any one of claims 1 to 7, characterized in that: Determining the cutoff frequency of the second-order bandpass filter according to the alternating frequency of the signal to be processed comprises: Determine the provisional cutoff frequency of the second-order bandpass filter according to the alternating frequency of the signal to be processed; wherein the frequency value of the provisional cutoff frequency is less than the alternating frequency of the signal to be processed; Based on the provisional cut-off frequency, determining whether the frequency value and the 2-fold frequency value of the alternating frequency of the signal to be processed fall within the frequency response linear segment; If yes, determining the provisional cut-off frequency as the finally determined cut-off frequency; If not, return to the step of determining the provisional cutoff frequency of the second-order bandpass filter according to the alternating frequency of the signal to be processed; The frequency value of the newly determined provisional cut-off frequency is smaller than the provisional cut-off frequency determined last time.

9. A second-order bandpass filter, characterized in that: include: Integrator or inverse integrator, inverting output circuit and feedback circuit; The input end of the integration circuit / the inverse integration circuit serves as the input end of the second-order band-pass filter, and is used to access the signal to be processed; the output end of the integration circuit / the inverse integration circuit is connected to the input end of the inverting output circuit; the output end of the inverting output circuit serves as the output end of the second-order band-pass filter, and the output end of the inverting output circuit is connected to the input end of the feedback circuit; the output end of the feedback circuit is connected to the integration circuit / the inverse integration circuit; The integration circuit / the inverse integration circuit is used to realize the integration conversion / inverse integration conversion of the signal to be processed; The inverting output circuit is used to adjust the gain of the second-order bandpass filter; The feedback circuit is used to adjust the cutoff frequency of the second-order bandpass filter so that the alternating frequency of the signal to be processed falls within the frequency response linear section of the second-order bandpass filter.

10. The second-order bandpass filter according to claim 9, characterized in that: The feedback circuit comprises: a first resistor, a second resistor, a third resistor, a first capacitor and a first operational amplifier; The first end of the first resistor serves as the input end of the feedback circuit, and the second end of the first resistor is connected to the inverting input end of the first operational amplifier; the non-inverting input end of the first operational amplifier is grounded through the second resistor; the output end of the first operational amplifier is connected to the inverting input end of the first operational amplifier through the first capacitor, and is connected to the first end of the third resistor; the second end of the third resistor serves as the output end of the feedback circuit; Wherein, when the resistance value of the third resistor remains unchanged, the capacitance value of the first capacitor is negatively correlated with the cutoff frequency of the second-order bandpass filter; The feedback circuit is used to adjust the capacitance of the first capacitor and the resistance of the third resistor so that the alternating frequency of the signal to be processed falls within the linear frequency response section of the second-order bandpass filter.

11. The second-order bandpass filter according to claim 9, characterized in that: The inverting output circuit comprises: a fourth resistor, a fifth resistor and a second operational amplifier; The first end of the fourth resistor serves as the input end of the inverting output circuit, and the second end of the fourth resistor is connected to the inverting input end of the second operational amplifier; the non-inverting input end of the second operational amplifier is grounded; the output end of the second operational amplifier is connected to the inverting input end of the second operational amplifier through the fifth resistor, and serves as the output end of the inverting output circuit; Wherein, the ratio of the resistance values ​​of the fifth resistor to the fourth resistor is positively correlated with the gain of the transfer function of the second-order bandpass filter; Then the inverting output circuit is used to: adjust the resistance ratio of the fifth resistor and the fourth resistor so that the gain of the transfer function of the second-order bandpass filter is equal to the actual adjustment gain; The process of determining the actual adjustment gain includes: Any frequency within the frequency response linear segment is selected to perform integral calibration on the second-order band-pass filter to determine an actual adjustment gain of the second-order band-pass filter.

12. The second-order bandpass filter according to any one of claims 9 to 11, characterized in that: The integration circuit comprises: a sixth resistor, a seventh resistor, a second capacitor and a third operational amplifier; The first end of the sixth resistor serves as the input end of the integration circuit, and the second end of the sixth resistor is connected to the inverting input end of the third operational amplifier and the output end of the feedback circuit; the non-inverting input end of the third operational amplifier is grounded; the output end of the third operational amplifier is connected to the inverting input end of the third operational amplifier through the seventh resistor and the second capacitor in parallel, and serves as the output end of the integration circuit.

13. A signal processing device, characterized in that: comprising N second-order bandpass filters as claimed in any one of claims 9 to 12, wherein N is a positive integer greater than 1; The N second-order bandpass filters are connected in series, and the N second-order bandpass filters all include an integration circuit or an inverse integration circuit.

14. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the signal processing method according to any one of claims 1 to 8 are implemented.

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