Design method of anti-pre-whitening filter circuit and filter circuit

Abstract

The invention discloses a design method of an anti-pre-whitening filter circuit and the filter circuit. The design method comprises the following steps: decomposing the anti-pre-whitening filter circuit into two sub-modules, namely a low-pass filter circuit with low cut-off frequency and gain and a low-pass filter circuit with high cut-off frequency and no gain; performing independent analysis and calculation on each sub-module to obtain a transfer function of each sub-module; according to the transfer function, calculating to obtain an expression of gain, cut-off frequency and quality factor of the sub-module; a resistor and a capacitor are further configured; and superposing the output signals of the two sub-modules through an anti-phase adder to complete the design of the anti-pre-whitening filter circuit. The anti-pre-whitening filter circuit designed based on the design method can effectively enhance and amplify the low-frequency part in the underwater acoustic signal, so that non-flat amplitude-frequency response is generated in a passband, the target identification range is expanded, and the target identification accuracy is improved. And the method has the characteristic of low noise coefficient, and the overall signal-to-noise ratio of the system can be improved.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater acoustic signal processing, and in particular relates to a design method of an anti-pre-whitening filter circuit and a filter circuit. Background Art

[0002] With the advancement of science and technology, the development of marine resources and the construction of maritime military forces have become core areas of concern for countries around the world. In recent years, countries around the world have strengthened the research and development of hydroacoustic detection technology, and are committed to improving the collection, processing and analysis capabilities of hydroacoustic signals to expand the coverage of underwater signal detection and improve the accuracy and sensitivity of detection. my country has also continued to make efforts in this regard, strengthening its naval strength by adopting advanced underwater target detection, positioning and identification technologies. Today, hydroacoustic detection technology has been widely used in many fields such as hydroacoustic communications, marine environmental monitoring, seabed resource exploration and marine military, and has achieved remarkable technological progress and achievements.

[0003] In the field of underwater acoustic detection technology, effectively conditioning and amplifying weak underwater acoustic signals has always been a major challenge. Since the underwater acoustic signal itself has low power and faces high background noise interference, the technical difficulty of signal processing is significantly increased. The traditional active low-pass filter only has a flat amplitude-frequency response characteristic in the passband, which can be considered as a pre-whitening treatment of the signal. However, given that most of the underwater acoustic target signals of interest are concentrated in the low-frequency band, it is necessary to perform targeted enhancement and amplification of these specific frequency signals during the filtering process to achieve an anti-pre-whitening effect.

[0004] This patent proposes an innovative anti-pre-whitening filter circuit design that focuses on enhancing specific low-frequency components in underwater acoustic signals. This technical solution is original and there is no similar solution to refer to in the existing technical system. Summary of the invention

[0005] In view of this, the present invention proposes a design method and a filter circuit for an anti-pre-whitening filter circuit, which is used to enhance and amplify the low-frequency part of the underwater acoustic signal, thereby generating a non-flat amplitude-frequency response in the passband, thereby expanding the target recognition range and improving the accuracy of target recognition. In addition, the filter circuit has the characteristics of a low noise coefficient, which can improve the overall signal-to-noise ratio of the system.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] In a first aspect, a design method for an anti-pre-whitening filter circuit is provided, comprising the following steps:

[0008] S0: Decompose the anti-pre-whitening filter circuit into two sub-modules: a low-pass filter circuit with a low cut-off frequency and a gain, and a low-pass filter circuit with a high cut-off frequency and no gain;

[0009] S1: Analyze and calculate each submodule separately to obtain the transfer function of each submodule;

[0010] S2: according to the transfer function of the submodule, calculating the expression of the gain, cutoff frequency and quality factor of the submodule;

[0011] S3: configuring the resistor and capacitor according to the expression of the gain, cutoff frequency and quality factor of the submodule;

[0012] S4: superimposing the output signals of the two submodules through an inverting adder to complete the design of the anti-pre-whitening filter circuit.

[0013] Furthermore, the low-cutoff frequency low-pass filter circuit submodule with gain adopts a first-order Butterworth active low-pass filter, and the high-cutoff frequency low-pass filter circuit submodule without gain adopts a fourth-order Butterworth active low-pass filter, which is composed of two second-order Sallen-Key structure Butterworth active low-pass filters in cascade.

[0014] Furthermore, the theoretical formula of the transfer function of the first-order Butterworth active low-pass filter with gain is:

[0015]

[0016] Where A0 is the circuit gain of the first-order filter, ω 10 is the cutoff frequency of the first-order filter, s is a complex frequency domain variable;

[0017] The gain-free fourth-order Butterworth active low-pass filter is composed of two second-order Sallen-Key structure active low-pass filters in cascade connection. The transfer function theoretical formula of the second-order active low-pass filter is:

[0018]

[0019] where ω 20 is the cutoff frequency of the second-order filter, Q is the quality factor of the second-order filter, and s is a complex frequency domain variable.

[0020] Furthermore, the step of calculating the transfer function of the inverse pre-whitening filter circuit submodule is specifically as follows:

[0021] According to Kirchhoff's voltage-current law and the voltage-current relationship between the in-phase terminal and the inverting terminal of the integrated operational amplifier, the node equations for the submodule circuit nodes are listed respectively;

[0022] The ratio of the output voltage to the input voltage is calculated according to the node equation to obtain the transfer function of the circuit.

[0023] Furthermore, the transfer function of the first-order low-pass filter circuit submodule with low cutoff frequency and gain in the inverse pre-whitening filter circuit is obtained as follows:

[0024]

[0025] Where s is a complex frequency domain variable, C1 is the capacitance of the capacitor at the non-inverting input of the integrated operational amplifier, R1 is the resistance of the resistor at the non-inverting input of the integrated operational amplifier, and R f is the feedback resistor value of the integrated operational amplifier, R g is the resistance value of the inverting input terminal of the integrated operational amplifier, This is the circuit gain of the filter.

[0026] Furthermore, the transfer functions of the first-stage second-order filter and the second-stage second-order filter of the high cut-off frequency and no-gain fourth-order low-pass filter circuit submodule in the inverse pre-whitening filter circuit are obtained as follows:

[0027]

[0028] Where s is a complex frequency domain variable, C2 and C3 are the capacitance values ​​of the first-stage second-order filter in the low-pass filter circuit with high cutoff frequency and no gain, and R2 and R3 are the resistance values ​​of the first-stage second-order filter in the low-pass filter circuit with high cutoff frequency and no gain;

[0029] Among them, C4 and C5 are the capacitance values ​​of the second-stage second-order filter in the low-pass filter circuit with high cut-off frequency and no gain, and R4 and R5 are the resistance values ​​of the second-stage second-order filter in the low-pass filter circuit with high cut-off frequency and no gain.

[0030] Further, according to the transfer function of the submodule, the expression of the gain, cutoff frequency and quality factor of the submodule is calculated, and the specific steps are:

[0031] The transfer function of the low cut-off frequency band gain first-order low-pass filter in the anti-pre-whitening filter circuit is made equal to its transfer function theoretical formula, and the simultaneous formula of the first-order low-pass filter transfer function is obtained as follows:

[0032] H1′(s)=H1(s)

[0033] Right now

[0034]

[0035] By comparing the left and right sides of the equal sign of the simultaneous formula of the transfer function of the first-order low-pass filter, the gain A0 of the first-order low-pass filter in the anti-pre-whitening filter circuit can be obtained as follows:

[0036]

[0037] Cut-off frequencyω 10 for:

[0038]

[0039] The transfer function of the high cut-off frequency gain-free second-order low-pass filter in the anti-pre-whitening filter circuit is made equal to its transfer function theoretical formula, and the simultaneous formulas of the transfer functions of the two-stage second-order low-pass filters are obtained as follows:

[0040]

[0041] By comparing the left and right sides of the equal sign of the simultaneous formula of the transfer function of the second-order low-pass filter, it can be obtained that the cutoff frequencies of the two-stage second-order low-pass filters in the anti-pre-whitening filter circuit are:

[0042]

[0043] The quality factors of the two-stage second-order low-pass filters in the anti-pre-whitening filtering circuit are respectively:

[0044]

[0045] By consulting the coefficient table of the cascaded high-order Butterworth low-pass filter, it can be known that the quality factors of the first-order and second-order second-order low-pass filters should be Q′=0.5412 and Q″=1.3065, respectively, and the following relationship can be obtained:

[0046]

[0047] Furthermore, according to the gain and cut-off frequency of the first-order low-pass filter submodule, the required resistance value and capacitance value can be determined, and the specific steps are as follows:

[0048] First, specify the value of the resistor to be between a few hundred ohms and tens of kiloohms. For simplicity, R1 can usually be set to 10kΩ. The value of the capacitor can be calculated based on the cutoff frequency expression of the first-order low-pass filter in the anti-pre-whitening filter circuit:

[0049]

[0050] Setting resistance R g The value is 1kΩ, and the feedback resistance R can be calculated according to the following expression f The values ​​are:

[0051] R f =(A0-1)R g

[0052] According to the cutoff frequency and quality factor of the first-stage second-order low-pass filter in the fourth-order low-pass filter submodule, the required resistance and capacitance values ​​can be determined. The specific steps are:

[0053] First, let the resistor R2 = R3, and specify the resistance value to be between several hundred ohms and several tens of kiloohms. For simplicity, it can usually be set to 10kΩ. According to the cutoff frequency expression of the second-order low-pass filter in the anti-pre-whitening filter circuit, the value of the capacitor can be obtained as follows:

[0054]

[0055] According to the quality factor expression of the first-order second-order low-pass filter in the anti-pre-whitening filter circuit

[0056]

[0057] have to

[0058]

[0059] but

[0060]

[0061] According to the above steps, the resistor values ​​R4 and R5, and the capacitor values ​​C4 and C5 of the second-order low-pass filter in the fourth-order low-pass filter are configured, and their values ​​are:

[0062] R4=R5=10kΩ

[0063]

[0064] Furthermore, the output signals of the two submodules are superimposed through an inverting adder to obtain a specific non-flat amplitude-frequency response characteristic, and the low-frequency signal components of a specific frequency are enhanced and amplified in a targeted manner, thereby completing the design of the anti-pre-whitening filter circuit.

[0065] On the other hand, the present invention also provides an anti-pre-whitening filter circuit, comprising: a low-pass filter and an inverting adder, wherein:

[0066] The low-pass filter includes a low-pass filter circuit with a gain at a low cut-off frequency and a low-pass filter circuit with no gain at a high cut-off frequency;

[0067] The low-pass filter circuit with low cut-off frequency and gain is used to perform targeted enhancement and amplification on low-frequency signal components of a specific frequency;

[0068] The high cut-off frequency and gain-free low-pass filter circuit is used to remove high-frequency noise in the signal;

[0069] The inverting adder is used to realize the superposition of the output signals of two low-pass filters.

[0070] In summary, the present invention can solve the problem of difficulty in extracting low-frequency target signals due to low signal power and high environmental noise in the current underwater acoustic detection technology. The advantages and specific beneficial effects of the present invention are as follows:

[0071] (1) Since the filter circuit of the present invention is designed with a non-flat amplitude-frequency response characteristic within the passband, it can specifically enhance and amplify specific low-frequency components in the underwater acoustic signal, thereby obtaining a higher signal-to-noise ratio, expanding the target recognition range and improving the accuracy of target recognition;

[0072] (2) The filter circuit designed by the present invention adopts the Sallen-Key active low-pass filter architecture, is insensitive to changes in the values ​​of components in the circuit, and has the characteristics of low noise coefficient, which can significantly reduce the interference of background noise on useful signals, thereby improving the overall signal-to-noise ratio of the system;

[0073] (3) The filter circuit designed by the present invention also has the advantages of simple structure, small number of components used, and small circuit size. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the prior art description are briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0075] Figure 1 A block diagram of the circuit structure of the anti-pre-whitening filter provided by the present invention;

[0076] Figure 2 Schematic diagram of the structure of a low-cutoff frequency band gain low-pass filter circuit in Embodiment 1 of the present invention;

[0077] Figure 3 Schematic diagram of the structure of a high cut-off frequency gain-free low-pass filter circuit in Embodiment 1 of the present invention;

[0078] Figure 4 Schematic diagram of the structure of the inverting adder circuit in Embodiment 1 of the present invention;

[0079] Figure 5 Schematic diagram of the structure of the anti-pre-whitening filter circuit in Embodiment 1 of the present invention;

[0080] Figure 6 The first-order low-pass filter circuit diagram with a cutoff frequency of 10 Hz and a gain of 20 dB in Embodiment 2 of the present invention;

[0081] Figure 7 The simulation result of the amplitude-frequency characteristic of the first-order low-pass filter circuit in Example 2 of the present invention;

[0082] Figure 8 The fourth-order low-pass filter circuit diagram with a cut-off frequency of 11kHz and a gain of 0dB in Embodiment 2 of the present invention;

[0083] Fig. 9 The simulation result of the amplitude-frequency characteristic of the fourth-order low-pass filter circuit in Example 2 of the present invention;

[0084] Fig.10 The amplitude-frequency characteristic curve test result of the anti-pre-whitening filter circuit designed in Example 2 of the present invention. DETAILED DESCRIPTION

[0085] In order to make the purpose, technical scheme and beneficial effect of the present invention clearer, the present invention is further described and illustrated in detail below in conjunction with the embodiments and the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Those skilled in the art may make various changes or modifications to the present invention, and these equivalent forms are also within the scope of the claims listed in the present application.

[0086] To facilitate understanding of the anti-pre-whitening filter circuit design method and filter circuit provided by the embodiment of the present invention, the application scenario is first explained. In the field of underwater acoustic detection technology, effectively conditioning and amplifying weak underwater acoustic signals has always been a major challenge. Since the underwater acoustic signal itself has low power and faces high background noise interference, the technical difficulty of signal processing is significantly increased. The traditional active low-pass filter only has a flat amplitude-frequency response characteristic within the passband, which can be considered as a pre-whitening treatment of the signal. However, in view of the fact that most of the underwater acoustic target signals of interest are concentrated in the low-frequency band, it is necessary to perform targeted enhancement and amplification of these specific frequency signals during the filtering process to achieve the anti-pre-whitening effect.

[0087] The present invention proposes an innovative anti-pre-whitening filter circuit design method and filter circuit, focusing on strengthening specific low-frequency components in underwater acoustic signals. The following is a detailed description of the method in conjunction with specific drawings and embodiments.

[0088] Embodiment 1:

[0089] refer to Figure 1 to Figure 5 , this embodiment provides a design method for an anti-pre-whitening filter circuit, comprising the following steps:

[0090] S0: Decompose the anti-pre-whitening filter circuit into two sub-modules: a low-pass filter circuit with a low cut-off frequency and a gain, and a low-pass filter circuit with a high cut-off frequency and no gain;

[0091] S1: Analyze and calculate each submodule separately to obtain the transfer function of each submodule;

[0092] S2: according to the transfer function of the submodule, calculating the expression of the gain, cutoff frequency and quality factor of the submodule;

[0093] S3: configuring the resistor and capacitor according to the expression of the gain, cutoff frequency and quality factor of the submodule;

[0094] S4: superimposing the output signals of the two submodules through an inverting adder to complete the design of the anti-pre-whitening filter circuit.

[0095] In a specific implementation scheme, the anti-pre-whitening filter circuit is decomposed into two sub-modules: a low-pass filter circuit with a low cut-off frequency and a gain, and a low-pass filter circuit with a high cut-off frequency and no gain. Figure 2 As shown, the low-cutoff frequency band gain low-pass filter circuit submodule adopts a first-order Butterworth active low-pass filter; Figure 3 As shown, the high cut-off frequency gain-free low-pass filter circuit submodule adopts a fourth-order Butterworth active low-pass filter, and the fourth-order active low-pass filter is composed of two second-order Sallen-Key structure Butterworth active low-pass filters in cascade connection.

[0096] The attenuation characteristics of the first-order Butterworth active low-pass filter are -6dB / octave and -20dB / decade; the attenuation characteristics of the fourth-order Butterworth active low-pass filter are -24dB / octave and -80dB / decade. The first-order low-pass filter with low cutoff frequency and gain can enhance and amplify the low-frequency signal in a targeted manner. At the same time, due to its relatively gentle attenuation characteristics, it can achieve a smooth transition between the low-frequency band and the high-frequency band in the entire signal passband of the anti-pre-whitening filter circuit; the fourth-order low-pass filter with high cutoff frequency and no gain has a faster out-of-band attenuation characteristic, which can more effectively filter out high-frequency interference and noise signals.

[0097] In a specific implementation scheme, the theoretical formula of the transfer function of the first-order Butterworth active low-pass filter with gain is:

[0098]

[0099] Where A0 is the circuit gain of the first-order filter, ω 10 is the cutoff frequency of the first-order filter, s is a complex frequency domain variable;

[0100] The gain-free fourth-order Butterworth active low-pass filter is composed of two second-order Sallen-Key structure active low-pass filters in cascade connection. The transfer function theoretical formula of the second-order active low-pass filter is:

[0101]

[0102] where ω 20 is the cutoff frequency of the second-order filter, Q is the quality factor of the second-order filter, and s is a complex frequency domain variable.

[0103] In a specific implementation scheme, the step of calculating the transfer function of the inverse pre-whitening filter circuit submodule is specifically:

[0104] According to Kirchhoff's voltage-current law and the voltage-current relationship between the in-phase terminal and the inverting terminal of the integrated operational amplifier, the node equations for the submodule circuit nodes are listed respectively;

[0105] The ratio of the output voltage to the input voltage is calculated according to the node equation to obtain the transfer function of the circuit.

[0106] In a specific implementation scheme, the transfer function of the first-order low-pass filter circuit submodule with low cutoff frequency and gain in the inverse pre-whitening filter circuit is obtained as follows:

[0107]

[0108] Where s is a complex frequency domain variable, C1 is the capacitance of the capacitor at the non-inverting input of the integrated operational amplifier, R1 is the resistance of the resistor at the non-inverting input of the integrated operational amplifier, and R f is the feedback resistor value of the integrated operational amplifier, R g is the resistance value of the inverting input terminal of the integrated operational amplifier, This is the circuit gain of the filter.

[0109] The transfer functions of the first-stage second-order filter and the second-stage second-order filter of the high cut-off frequency and no-gain fourth-order low-pass filter circuit submodule in the inverse pre-whitening filter circuit are obtained as follows:

[0110]

[0111] Wherein C2 and C3 are the capacitance values ​​of the first-stage second-order filter in the low-pass filter circuit with high cut-off frequency and no gain, and R2 and R3 are the resistance values ​​of the first-stage second-order filter in the low-pass filter circuit with high cut-off frequency and no gain;

[0112] Among them, C4 and C5 are the capacitance values ​​of the second-stage second-order filter in the low-pass filter circuit with high cut-off frequency and no gain, and R4 and R5 are the resistance values ​​of the second-stage second-order filter in the low-pass filter circuit with high cut-off frequency and no gain.

[0113] In a specific implementation scheme, based on the transfer function of the submodule, the expression of the gain, cutoff frequency and quality factor of the submodule is calculated, and the specific steps are:

[0114] The transfer function of the low cut-off frequency band gain first-order low-pass filter in the anti-pre-whitening filter circuit is made equal to its transfer function theoretical formula, and the simultaneous formula of the first-order low-pass filter transfer function is obtained as follows:

[0115] H1′(s)=H1(s)

[0116] Right now

[0117]

[0118] By comparing the left and right sides of the equal sign of the simultaneous formula of the transfer function of the first-order low-pass filter, the gain A0 of the first-order low-pass filter in the anti-pre-whitening filter circuit can be obtained as follows:

[0119]

[0120] Cut-off frequencyω 10 for:

[0121]

[0122] The transfer function of the high cut-off frequency gain-free second-order low-pass filter in the anti-pre-whitening filter circuit is made equal to its transfer function theoretical formula, and the simultaneous formulas of the transfer functions of the two-stage second-order low-pass filters are obtained as follows:

[0123]

[0124] By comparing the left and right sides of the equal sign of the simultaneous formula of the transfer function of the second-order low-pass filter, it can be obtained that the cutoff frequencies of the two-stage second-order low-pass filters in the anti-pre-whitening filter circuit are:

[0125]

[0126] The quality factors of the two-stage second-order low-pass filters in the anti-pre-whitening filtering circuit are respectively:

[0127]

[0128] By consulting the coefficient table of the cascaded high-order Butterworth low-pass filter, it can be known that the quality factors of the first-order and second-order second-order low-pass filters should be Q′=0.5412 and Q″=1.3065, respectively, and the following relationship can be obtained:

[0129]

[0130] In a specific implementation scheme, the required resistance and capacitance values ​​can be determined according to the gain and cutoff frequency of the first-order low-pass filter submodule, and the specific steps are as follows:

[0131] First, specify the value of the resistor to be between a few hundred ohms and tens of kiloohms. For simplicity, R1 can usually be set to 10kΩ. The value of the capacitor can be calculated based on the cutoff frequency expression of the first-order low-pass filter in the anti-pre-whitening filter circuit:

[0132]

[0133] Setting resistance R g The value is 10kΩ, and the feedback resistance R can be calculated according to the following expression f The values ​​are:

[0134] R f =(A0-1)R g

[0135] According to the cutoff frequency and quality factor of the first-stage second-order low-pass filter in the fourth-order low-pass filter submodule, the required resistance and capacitance values ​​can be determined. The specific steps are:

[0136] First, let the resistor R2 = R3, and specify the resistance value to be between several hundred ohms and several tens of kiloohms. For simplicity, it can usually be set to 10kΩ. According to the cutoff frequency expression of the second-order low-pass filter in the anti-pre-whitening filter circuit, the value of the capacitor can be obtained as follows:

[0137]

[0138] According to the quality factor expression of the first-order second-order low-pass filter in the anti-pre-whitening filter circuit

[0139]

[0140] have to

[0141]

[0142] but

[0143]

[0144] According to the above steps, the resistor values ​​R4 and R5, and the capacitor values ​​C4 and C5 of the second-order low-pass filter in the fourth-order low-pass filter are configured, and their values ​​are:

[0145] R4=R5=10kΩ

[0146]

[0147] In a specific implementation scheme, the output signals of the two submodules are transmitted as follows: Figure 4 The inverting adder shown in FIG. 1 is superimposed to obtain a specific non-flat amplitude-frequency response characteristic, and the low-frequency signal component of a specific frequency is enhanced and amplified in a targeted manner, thereby completing the following steps: Figure 5 The design of the anti-pre-whitening filter circuit is shown.

[0148] Embodiment 2:

[0149] The embodiment of the present application provides an anti-pre-whitening filter circuit for underwater acoustic signal processing, and the technical indicator parameters of the circuit are as follows: 1) filter type: low-pass filter; 2) passband: 0~11kHz; 3) amplitude-frequency characteristics within the passband: stepped non-flat amplitude-frequency response, where the gain in the 0~10Hz interval is 20dB, the gain in the 100Hz~11kHz interval is 0dB, and the gain in the 10~100Hz interval has a smooth transition.

[0150] The specific design steps and parameter calculation of the anti-pre-whitening filter circuit that meets the above technical indicators are as follows:

[0151] 1) The anti-pre-whitening filter circuit is decomposed into two sub-modules: a first-order Butterworth low-pass filter circuit with a cutoff frequency of 10 Hz and a gain of 20 dB, and a fourth-order Butterworth low-pass filter circuit with a cutoff frequency of 11 kHz and a gain of 0 dB.

[0152] 2) Design a first-order Butterworth low-pass filter circuit with a cutoff frequency of 10Hz and a gain of 20dB. First, write out the theoretical formula of its transfer function:

[0153]

[0154] Where A0 = 10 (i.e. 20 dB), ω 10 =2πf 10 =2π×10=62.8, is the cutoff frequency of the first-order filter, s is a complex frequency domain variable;

[0155] Then find Figure 2 The transfer function of the first-order low-pass filter circuit submodule is:

[0156]

[0157] Where s is a complex frequency domain variable, C1 is the capacitance of the capacitor at the non-inverting input of the integrated operational amplifier, R1 is the resistance of the resistor at the non-inverting input of the integrated operational amplifier, and R f is the feedback resistor value of the integrated operational amplifier, R g is the resistance value of the inverting input terminal of the integrated operational amplifier, This is the circuit gain of the filter.

[0158] Then, the transfer function of the first-order low-pass filter is made equal to its theoretical transfer function formula, and the simultaneous formula of the transfer function of the first-order low-pass filter is obtained as follows:

[0159] H1′(s)=H1(s)

[0160] Right now

[0161]

[0162] By comparing the left and right sides of the equal sign of the simultaneous formula of the transfer function of the first-order low-pass filter, the gain A0 of the first-order low-pass filter in the anti-pre-whitening filter circuit can be obtained as follows:

[0163]

[0164] Cut-off frequencyω 10 for:

[0165]

[0166] The value of the resistor in the active filter circuit is usually in the range of several hundred ohms to several tens of kiloohms. For simplicity, R1 and R g All are set to 10kΩ, so we can get:

[0167] R f =(A0-1)R g =(10-1)×10=90kΩ

[0168]

[0169] Finally, we can get Figure 6 The cut-off frequency is 10Hz and the gain is 20dB. The simulation results of the amplitude-frequency characteristics are shown in the following figure. Figure 7 shown.

[0170] 3) Design a fourth-order Butterworth low-pass filter circuit with a cutoff frequency of 11kHz and a gain of 0dB. Since the fourth-order active low-pass filter is composed of two second-order Sallen-Key structure Butterworth active low-pass filters in cascade, the transfer function theoretical formula of the second-order active low-pass filter is first written as:

[0171]

[0172] where ω 20 =2πf 20=2π×11000=69080, which is the cutoff frequency of the second-order low-pass filter and also the cutoff frequency of the cascaded fourth-order low-pass filter; Q is the quality factor of the second-order filter, and the first and second stages should take different parameter values; s is a complex frequency domain variable.

[0173] Then find Figure 3 The transfer functions of the first-order second-order filter and the second-order second-order filter are:

[0174]

[0175]

[0176] Wherein C2 and C3 are the capacitance values ​​of the first-stage second-order filter in the low-pass filter circuit with high cut-off frequency and no gain, and R2 and R3 are the resistance values ​​of the first-stage second-order filter in the low-pass filter circuit with high cut-off frequency and no gain;

[0177] Among them, C4 and C5 are the capacitance values ​​of the second-stage second-order filter in the low-pass filter circuit with high cut-off frequency and no gain, and R4 and R5 are the resistance values ​​of the second-stage second-order filter in the low-pass filter circuit with high cut-off frequency and no gain.

[0178] Then, the transfer function of the second-order low-pass filter is made equal to its theoretical transfer function formula, and the simultaneous formulas of the transfer functions of the two-stage second-order low-pass filters are obtained as follows:

[0179]

[0180] By comparing the left and right sides of the equal sign of the simultaneous formula of the transfer function of the second-order low-pass filter, it can be obtained that the cutoff frequencies of the two-stage second-order low-pass filters in the anti-pre-whitening filter circuit are:

[0181]

[0182] By consulting the coefficient table of the cascaded high-order Butterworth low-pass filter, it can be known that the quality factors of the first-order and second-order second-order low-pass filters should be Q′=0.5412 and Q″=1.3065, respectively, and the following relationship can be obtained:

[0183]

[0184] The value of the resistor in the active filter circuit is usually in the range of several hundred ohms to several tens of kiloohms. For simplicity, let the resistor R2 = R3 = R4 = R5 = 10kΩ, so we can get:

[0185]

[0186] Also because

[0187]

[0188] therefore

[0189]

[0190] Finally, we can get Figure 8 The cut-off frequency is 11kHz and the gain is 0dB. The simulation results of the amplitude-frequency characteristics are as follows: Fig. 9 shown.

[0191] 4) The output signals of the two low-pass filter submodules designed above are superimposed through an inverting adder to obtain a specific non-flat amplitude-frequency response characteristic, and the low-frequency signal components of a specific frequency are enhanced and amplified in a targeted manner, thereby completing the design of the anti-pre-whitening filter circuit. Fig.10 The figure shows the actual test results of the designed anti-pre-whitening filter circuit, which shows that the technical index requirements are met.

[0192] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A design method for an anti-pre-whitening filter circuit, characterized in that: The following steps are involved: S0: Decompose the anti-pre-whitening filter circuit into two sub-modules: a low-pass filter circuit with a low cut-off frequency and a gain, and a low-pass filter circuit with a high cut-off frequency and no gain; S1: Analyze and calculate each submodule separately to obtain the transfer function of each submodule; S2: according to the transfer function of the submodule, calculating the expression of the gain, cutoff frequency and quality factor of the submodule; S3: configuring the resistor and capacitor according to the expression of the gain, cutoff frequency and quality factor of the submodule; S4: superimposing the output signals of the two submodules through an inverting adder to complete the design of the anti-pre-whitening filter circuit.

2. The design method of the anti-pre-whitening filter circuit according to claim 1, characterized in that: The low-cutoff frequency low-pass filter circuit submodule with gain adopts a first-order Butterworth active low-pass filter, and the high-cutoff frequency low-pass filter circuit submodule without gain adopts a fourth-order Butterworth active low-pass filter, which is composed of two second-order Sallen-Key structure Butterworth active low-pass filters in cascade.

3. The design method of the anti-pre-whitening filter circuit according to claim 2, characterized in that: The theoretical formula of the transfer function of the first-order Butterworth active low-pass filter with gain is: Where A0 is the circuit gain of the first-order filter, ω 10 is the cutoff frequency of the first-order filter, s is a complex frequency domain variable; The gain-free fourth-order Butterworth active low-pass filter is composed of two second-order Sallen-Key structure active low-pass filters in cascade connection. The transfer function theoretical formula of the second-order active low-pass filter is: where ω 20 is the cutoff frequency of the second-order filter, Q is the quality factor of the second-order filter, and s is a complex frequency domain variable.

4. The design method of the anti-pre-whitening filter circuit according to claim 1, characterized in that: The step of calculating the transfer function of the inverse pre-whitening filter circuit submodule is specifically: According to Kirchhoff's voltage-current law and the voltage-current relationship between the in-phase terminal and the inverting terminal of the integrated operational amplifier, the node equations for the submodule circuit nodes are listed respectively; The ratio of the output voltage to the input voltage is calculated according to the node equation to obtain the transfer function of the circuit.

5. The design method of the anti-pre-whitening filter circuit according to claim 3, characterized in that: The transfer function of the first-order low-pass filter circuit submodule with low cutoff frequency and gain in the anti-pre-whitening filter circuit is obtained as follows: Where s is a complex frequency domain variable, C1 is the capacitance of the capacitor at the non-inverting input of the integrated operational amplifier, R1 is the resistance of the resistor at the non-inverting input of the integrated operational amplifier, and R f is the feedback resistor value of the integrated operational amplifier, R g is the resistance value of the inverting input terminal of the integrated operational amplifier, This is the circuit gain of the filter.

6. The design method of the anti-pre-whitening filter circuit according to claim 3, characterized in that: The transfer functions of the first-stage second-order filter and the second-stage second-order filter of the high cut-off frequency and no-gain fourth-order low-pass filter circuit submodule in the inverse pre-whitening filter circuit are obtained as follows: Where s is a complex frequency domain variable, C2 and C3 are the capacitance values ​​of the first-stage second-order filter in the low-pass filter circuit with high cutoff frequency and no gain, and R2 and R3 are the resistance values ​​of the first-stage second-order filter in the low-pass filter circuit with high cutoff frequency and no gain; Among them, C4 and C5 are the capacitance values ​​of the second-stage second-order filter in the low-pass filter circuit with high cut-off frequency and no gain, and R4 and R5 are the resistance values ​​of the second-stage second-order filter in the low-pass filter circuit with high cut-off frequency and no gain.

7. The design method of the anti-pre-whitening filter circuit according to claim 5 or 6, characterized in that: According to the transfer function of the submodule, the expression of the gain, cutoff frequency and quality factor of the submodule is calculated, and the specific steps are: The transfer function of the low cut-off frequency band gain first-order low-pass filter in the anti-pre-whitening filter circuit is set equal to its transfer function theoretical formula, and the simultaneous formula of the first-order low-pass filter transfer function is obtained as follows: H1′(s)=H1(s) Right now By comparing the left and right sides of the equal sign of the simultaneous formula of the transfer function of the first-order low-pass filter, the gain A0 of the first-order low-pass filter in the anti-pre-whitening filter circuit can be obtained as follows: Cut-off frequencyω 10 for: The transfer function of the high cut-off frequency gain-free second-order low-pass filter in the anti-pre-whitening filter circuit is made equal to its transfer function theoretical formula, and the simultaneous formulas of the transfer functions of the two-stage second-order low-pass filters are obtained as follows: By comparing the left and right sides of the equal sign of the simultaneous formula of the transfer function of the second-order low-pass filter, it can be obtained that the cutoff frequencies of the two-stage second-order low-pass filters in the anti-pre-whitening filter circuit are: The quality factors of the two-stage second-order low-pass filters in the anti-pre-whitening filtering circuit are respectively: By consulting the coefficient table of the cascaded high-order Butterworth low-pass filter, it can be known that the quality factors of the first-order and second-order second-order low-pass filters should be Q′=0.5412 and Q″=1.3065, respectively, and the following relationship can be obtained:

8. The design method of the anti-pre-whitening filter circuit according to claim 7, characterized in that: According to the gain and cutoff frequency of the first-order low-pass filter submodule, the required resistance and capacitance values ​​can be determined. The specific steps are as follows: First, specify the value of the resistor to be between a few hundred ohms and tens of kiloohms. For simplicity, R1 can usually be set to 10kΩ. The value of the capacitor can be calculated based on the cutoff frequency expression of the first-order low-pass filter in the anti-pre-whitening filter circuit: Setting resistance R g The value is 1kΩ, and the feedback resistance R can be calculated according to the following expression f The values ​​are: R f =(A0-1)R g According to the cutoff frequency and quality factor of the first-stage second-order low-pass filter in the fourth-order low-pass filter submodule, the required resistance and capacitance values ​​can be determined. The specific steps are: First, let the resistor R2 = R3, and specify the resistance value to be between several hundred ohms and several tens of kiloohms. For simplicity, it can usually be set to 10kΩ. According to the cutoff frequency expression of the second-order low-pass filter in the anti-pre-whitening filter circuit, the value of the capacitor can be obtained as follows: According to the quality factor expression of the first-order second-order low-pass filter in the anti-pre-whitening filter circuit have to but According to the above steps, the resistor values ​​R4 and R5, and the capacitor values ​​C4 and C5 of the second-order low-pass filter in the fourth-order low-pass filter are configured, and their values ​​are: R4=R5=10kΩ 9. The design method of the anti-pre-whitening filter circuit according to claim 8, characterized in that: The output signals of the two submodules are superimposed through an inverting adder to obtain a specific non-flat amplitude-frequency response characteristic, and the low-frequency signal component of a specific frequency is enhanced and amplified in a targeted manner, thereby completing the design of the anti-pre-whitening filter circuit.

10. An anti-pre-whitening filter circuit, characterized in that: According to the design method as claimed in any one of claims 1 to 6 or 8 to 9, the anti-pre-whitening filter circuit comprises a low-pass filter and an inverting adder, wherein: The low-pass filter includes a low-pass filter circuit with a gain at a low cut-off frequency and a low-pass filter circuit with no gain at a high cut-off frequency; The low-pass filter circuit with low cut-off frequency and gain is used to perform targeted enhancement and amplification on low-frequency signal components of a specific frequency; The high cut-off frequency and gain-free low-pass filter circuit is used to remove high-frequency noise in the signal; The inverting adder is used to realize the superposition of the output signals of two low-pass filters.

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