Target signal extraction method based on improved digital lock-in amplifier

Abstract

The invention relates to a target signal extraction method based on an improved digital lock-in amplifier. The method comprises the following steps: acquiring an input signal, an orthogonal reference signal and a cosine reference signal; obtaining a phase difference between the input signal and the orthogonal reference signal, a preset signal representation of a to-be-extracted target signal and noise, and constructing an input signal expression, an orthogonal reference signal expression and a cosine reference signal expression; the method comprises the following steps: respectively mixing an input signal expression with an orthogonal reference signal expression and a cosine reference signal expression by using a multiplier to obtain orthogonal and cosine component signals, respectively carrying out Kalman filtering, respectively obtaining orthogonal and cosine filtering component signals, respectively carrying out fast Fourier transform and inverse Fourier transform, and respectively obtaining the orthogonal and cosine component signals; after orthogonal and cosine time domain signals are obtained, adaptive filtering is carried out respectively, after orthogonal and cosine adaptive signals are obtained, averaging is carried out respectively, an orthogonal direct current component and a cosine direct current component are extracted from the orthogonal and cosine adaptive signals, and the amplitude and the phase of a target signal to be extracted are obtained through calculation.

Description

Technical Field

[0001] The invention relates to the technical field of digital signal processing, in particular to a target signal extraction method based on an improved digital lock-in amplifier. Background Art

[0002] The weak signal detection problem has always been a key research problem in the field of measurement, and it is also a cutting-edge problem in the current development of science and technology. Weak signal detection technology is an emerging science and technology involving information processing, electronic science and other technical fields, which is used to suppress noise and extract useful signals.

[0003] The existing weak signal detection methods mainly include narrowband filtering, synchronous accumulation, dual-channel noise elimination and correlation detection. The narrowband filtering method uses the characteristics of narrow power spectrum density of the signal and relatively wide power spectrum of the noise to improve the signal-to-noise ratio and thus extract the signal, but it can only be used in situations where the noise characteristics are very low. The synchronous accumulation method uses the repeatability of the signal and the randomness of the noise to repeatedly measure the signal multiple times to accumulate the signal in phase, but the operation cycle is long and the calculation in the controller is more complicated. The dual-channel noise elimination method uses two channels to process the input signal differently, then eliminates the common noise, and finally obtains the signal to be tested. The disadvantage of this method is that it can only be used to detect whether a weak sinusoidal signal exists, and cannot reproduce the waveform. The correlation detection method is a method of extracting periodic signals from strong noise based on the fact that the amplitudes of periodic signals are correlated at different times, while noise is random and uncorrelated. The correlation between periodic signals and the uncorrelation between noise and periodic signals are used to extract periodic signals. This method is divided into autocorrelation and cross-correlation. The cross-correlation method has the characteristic of being superior to autocorrelation in noise suppression ability because it can suppress various forms of noise that are uncorrelated with the reference signal.

[0004] Weak signal detection instruments have been evolving with the development of technology. Commonly used equipment includes low-noise preamplifiers, lock-in amplifiers, sampling integrators, and photon counters. Among these methods, the correlation detection method is widely used and is considered to be one of the most effective methods. In recent years, the lock-in amplifier developed based on the correlation method has become an effective tool for detecting weak signals. The lock-in amplifier is a device specially designed to extract signals of a specific frequency. It is widely used in scientific research and industry, especially when it is necessary to detect and extract weak signals from a noisy environment.

[0005] The original lock-in amplifier was completely implemented by analog circuits. With the development of digital technology and the maturity of large-scale integrated circuits, the advancement of high-speed digital signal processing technology has brought about various digital products. However, most lock-in amplifiers are still hybrid analog and digital devices. Although the analog lock-in amplifier has been improved over the years, its core circuit has not changed fundamentally. It has only partially adopted digital devices, such as digital filters for noise suppression, and analog-to-digital conversion (ADC) and digital-to-analog conversion (DAC) for auxiliary functions such as digital monitoring and display. However, its core phase-sensitive detector (PSD) still relies on analog electronic technology, so it is still an analog lock-in amplifier in essence.

[0006] With the emergence of microprocessors such as DSP and FPGA and the development of technology, the core phase-sensitive detector of the phase-locked amplifier has gradually been realized through the software of digital microprocessors, and finally a truly digital phase-locked amplifier was born. This marks a major shift of the phase-locked amplifier from traditional analog technology to full digitalization. Although traditional lock-in amplifiers perform well in many applications, their performance is greatly dependent on the effect of low-pass filters. In a low signal-to-noise ratio environment, the low-pass filter needs to have a very narrow bandwidth to effectively filter noise, which limits the dynamic response and adaptability of the system. In addition, too narrow a bandwidth will lead to increased signal processing delay, thereby reducing the system's ability to cope with rapidly changing signals. Summary of the invention

[0007] Therefore, the technical problem to be solved by the present invention is to overcome the problem that the lock-in amplifier in the prior art is highly dependent on the low-pass filter, which results in the inability to quickly and accurately detect and extract weak signals from a noisy environment.

[0008] In order to solve the above technical problems, the present invention provides a target signal extraction method based on an improved digital lock-in amplifier, comprising:

[0009] Acquire an input signal including noise and a target signal to be extracted, as well as an orthogonal reference signal and a cosine reference signal;

[0010] Based on phase sensitive detection, a phase difference between an input signal and an orthogonal reference signal is obtained;

[0011] Based on the preset signal representation of the target signal to be extracted, the noise, and the phase difference between the input signal and the orthogonal reference signal, construct an input signal expression, an orthogonal reference signal expression, and a cosine reference signal expression;

[0012] Using a multiplier, the input signal expression is mixed with the orthogonal reference signal expression and the cosine reference signal expression respectively, and the high frequency term is filtered out to obtain the orthogonal component signal and the cosine component signal;

[0013] Performing Kalman filtering on the orthogonal component signal and the cosine component signal respectively to filter out high frequency components and noise, and obtaining an orthogonal filtering component signal and a cosine filtering component signal;

[0014] Performing fast Fourier transform on the orthogonal filtering component signal and the cosine filtering component signal respectively, filtering out high-frequency noise, and then performing inverse Fourier transform to obtain an orthogonal time domain signal and a cosine time domain signal;

[0015] Adaptively filtering the orthogonal time domain signal and the cosine time domain signal respectively to suppress low-frequency noise and obtain an orthogonal adaptive signal and a cosine adaptive signal;

[0016] Averaging the quadrature adaptive signal and the cosine adaptive signal respectively, and extracting corresponding quadrature DC components and cosine DC components therefrom;

[0017] Based on the orthogonal DC component and the cosine DC component, the amplitude and phase of the target signal to be extracted are calculated.

[0018] Preferably, constructing the input signal expression, the orthogonal reference signal expression and the cosine reference signal expression based on the preset signal representation of the target signal to be extracted, the noise, and the phase difference between the input signal and the orthogonal reference signal includes:

[0019] The preset signal representation of the target signal to be extracted is: U0sin(ω0t+φ0);

[0020] Based on phase sensitive detection, a phase difference δ between the input signal and the orthogonal reference signal is obtained;

[0021] Construct the input signal expression: x(t) = U0sin(ω0t+φ0)+μ(t);

[0022] Construct the orthogonal reference signal expression as: rl (t) = U r *sin(ω0t+δ);

[0023] Construct the expression for the cosine reference signal as: r2 (t) = U r *cos(ω0t+δ);

[0024] Among them, U0, ω0 and φ0 represent the amplitude, angular frequency and phase of the target signal to be extracted, μ(t) represents the noise, U r Represents the amplitude of the quadrature reference signal and the cosine reference signal.

[0025] Preferably, the method of using a multiplier to mix the input signal expression with the orthogonal reference signal expression and the cosine reference signal expression respectively, filtering out high-frequency terms, and obtaining the orthogonal component signal and the cosine component signal comprises:

[0026] The quadrature component signal is expressed as:

[0027]

[0028] The cosine component signal is expressed as:

[0029]

[0030] in, and Represent the orthogonal DC component and cosine DC component respectively; and Respectively represent the orthogonal high-frequency component and cosine high-frequency component with a frequency of 2ω; U r μ(t)sin(ω0t+δ) and U r μ(t)cos(ω0t+δ) represent the orthogonal mixing component and cosine mixing component introduced by noise respectively.

[0031] Preferably, performing Kalman filtering on the orthogonal component signal and the cosine component signal respectively to filter out high frequency components and noise, and obtaining the orthogonal filter component signal and the cosine filter component signal comprises:

[0032] The orthogonal filtering component signal is expressed as:

[0033]

[0034] The cosine filtered component signal is expressed as:

[0035]

[0036] in, represents the target orthogonal state estimation value obtained based on Kalman filtering, Represents the target cosine state estimate obtained based on Kalman filtering.

[0037] Preferably, obtaining the target orthogonal state estimation value and the target cosine state estimation value both includes:

[0038] The predicted state estimate is expressed as:

[0039] The forecast error covariance is expressed as:

[0040] For each time instant k, the predicted state estimate is updated as:

[0041] For each time instant k, the prediction error covariance is updated and expressed as:

[0042] Initialize the predicted state estimate and the prediction error covariance as: Until the preset number of iterations is reached, the target state estimation value is obtained

[0043] Where, τ∈{I, Q}, when τ=I, the target orthogonal state estimate is calculated, and when τ=Q, the target cosine state estimate is calculated; A represents the state transfer matrix, represents the process noise covariance matrix; H represents the observation matrix, represents the identity matrix, represents the iterated covariance matrix; represents the Kalman gain, which is expressed as: R represents the measurement noise covariance matrix.

[0044] Preferably, the performing fast Fourier transform on the orthogonal filtering component signal and the cosine filtering component signal respectively, filtering out high-frequency noise, and then performing inverse Fourier transform to obtain an orthogonal time domain signal and a cosine time domain signal comprises:

[0045] Perform fast Fourier transform on the orthogonal filtering component signal and the cosine filtering component signal respectively to obtain the orthogonal FFT component and the cosine FFT component, including:

[0046] Orthogonal FFT components, expressed as:

[0047] Cosine FFT components, expressed as:

[0048] Convert the orthogonal FFT components and the cosine FFT components to frequency representation, including:

[0049] The orthogonal FFT component frequency domain representation is expressed as:

[0050]

[0051] The cosine FFT component frequency domain representation is expressed as:

[0052]

[0053] After filtering out high-frequency noise through frequency domain filtering, it is expressed as:

[0054] Orthogonal frequency domain filtering, expressed as:

[0055] Cosine frequency domain filtering, expressed as:

[0056] Perform inverse Fourier transform on orthogonal frequency domain filtering and cosine frequency domain filtering respectively, including:

[0057] Orthogonal I FFT signal, expressed as:

[0058] The cosine I FFT signal is expressed as:

[0059] Acquire orthogonal time domain signals and cosine time domain signals, including:

[0060] Orthogonal time domain signals:

[0061] Cosine time domain signal:

[0062] in, represents the complex exponential function, N represents the number of discrete Fourier transform points, k′ represents the frequency index, k′=0,1,2,…,N-1; n represents the time series sample point, j represents the imaginary unit, f cutoff Indicates the preset cutoff frequency.

[0063] Preferably, the adaptive filtering is performed on the orthogonal time domain signal and the cosine time domain signal respectively to suppress low-frequency noise and obtain the orthogonal adaptive signal and the cosine adaptive signal, including:

[0064] The preset filter length is M, the learning rate is μ, and the filter weight w is initialized i (0) = 0;

[0065] For each time instant n, the orthogonal adaptive signal I output by the filter is calculated adaptive (n) with cosine adaptive signal and Q adaptive (n), expressed as:

[0066]

[0067]

[0068] Calculate the filter's quadrature error e I (n) and cosine error e Q (n), expressed as:

[0069] e I (n) = d I (n)-I adaptive (n);

[0070] e Q (n) = dQ (n)-Q adaptive (n);

[0071] Update filter weights and It is expressed as:

[0072]

[0073] The orthogonal adaptive signal and the cosine adaptive signal after adaptive filtering are expressed as:

[0074] Orthogonal Adaptive Signal:

[0075] Cosine adaptive signal:

[0076] Among them, x(ni) is the historical sample of the input signal, w i (n) is the i-th filter weight; d(n) is the preset expected signal, the expected signal d I (n) and d Q (n) is set to zero signal.

[0077] Preferably, the averaging the quadrature adaptive signal and the cosine adaptive signal respectively and extracting corresponding quadrature DC components and cosine DC components therefrom comprises:

[0078] The orthogonal adaptive signal is averaged to eliminate the low-frequency noise residue and extract the DC component, which is expressed as:

[0079] The orthogonal adaptive signal I adaptive Substituting the expression of (t) into the equation and simplifying it, we get the orthogonal DC component, which is expressed as:

[0080] The cosine adaptive signal is averaged to eliminate the low-frequency noise residue and extract the DC component, which is expressed as:

[0081] The cosine adaptive signal Q adaptive Substituting the expression of (t) into the equation and simplifying it, we get the cosine DC component, which is expressed as:

[0082] Wherein, T represents the preset averaging time.

[0083] Preferably, the step of calculating and obtaining the amplitude and phase of the target signal to be extracted based on the orthogonal DC component and the cosine DC component includes:

[0084] The amplitude of the target signal to be extracted is expressed as:

[0085] The phase of the target signal to be extracted is expressed as:

[0086] The target signal to be extracted is expressed as:

[0087] Preferably, after obtaining the input signal containing noise and the target signal to be extracted, the input signal is also preprocessed, including: after amplifying and filtering the input signal, obtaining an input signal that meets a preset A / D resolution, and obtaining a discrete sequence of the input signal through A / D sampling.

[0088] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0089] The target signal extraction method based on the improved digital phase-locked amplifier described in the present invention designs a new digital phase-locked amplifier through Kalman filter, fast Fourier transform and adaptive filter; the adaptive filter can dynamically adjust the filtering parameters according to the real-time signal to optimize the filtering effect; FFT provides accurate spectrum analysis capability, can identify and remove noise of specific frequency, ensure the frequency component of the signal is purer, and then optimize the calculation of amplitude and phase; through the combination of Kalman filtering and adaptive filtering, it can maintain a stable noise suppression effect in different noise environments, and ensure the stability and accuracy of signal estimation; the present invention can extract the amplitude and phase of the signal more accurately through multi-stage processing in the frequency domain and time domain, especially in a low signal-to-noise ratio environment, the advantage is more obvious. The present invention directly processes the product of an input signal and a reference signal by adopting a method based on time analysis, and uses mathematical statistical methods and fast Fourier transform to stabilize and extract the DC component of the signal, thereby reducing dependence on a low-pass filter and not relying on a low-pass filter to obtain the DC component. The present invention can improve the performance of signal detection in a low signal-to-noise ratio environment and avoid the bandwidth limitation problem caused by a traditional low-pass filter, thereby reducing the complexity of system design, improving the speed and accuracy of signal processing, and providing higher real-time performance and noise suppression capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein

[0091] Figure 1 It is a flow chart of the steps of the target signal extraction method based on the improved digital lock-in amplifier provided by the present invention;

[0092] Figure 2 This is the main algorithm architecture diagram of the traditional lock-in amplifier;

[0093] Figure 3It is a schematic diagram of the working process of the optimized digital lock-in amplifier provided by the present invention;

[0094] Figure 4 It is a schematic diagram of the signal input channel provided by the present invention. DETAILED DESCRIPTION

[0095] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0096] Reference Figure 1 As shown, the step flow chart of the target signal extraction method based on the improved digital lock-in amplifier of the present invention comprises:

[0097] S101: acquiring an input signal including noise and a target signal to be extracted, as well as an orthogonal reference signal and a cosine reference signal;

[0098] S102: Acquire a phase difference between an input signal and an orthogonal reference signal based on phase sensitive detection;

[0099] S103: constructing an input signal expression, an orthogonal reference signal expression, and a cosine reference signal expression based on a preset signal representation of the target signal to be extracted, noise, and a phase difference between the input signal and the orthogonal reference signal;

[0100] S104: using a multiplier, mixing the input signal expression with the orthogonal reference signal expression and the cosine reference signal expression respectively, filtering out high-frequency terms, and obtaining an orthogonal component signal and a cosine component signal;

[0101] S105: performing Kalman filtering on the orthogonal component signal and the cosine component signal respectively to filter out high frequency components and noise, and obtaining an orthogonal filtering component signal and a cosine filtering component signal;

[0102] S106: performing fast Fourier transform on the orthogonal filtering component signal and the cosine filtering component signal respectively, filtering out high-frequency noise, and then performing inverse Fourier transform to obtain an orthogonal time domain signal and a cosine time domain signal;

[0103] S107: adaptively filter the orthogonal time domain signal and the cosine time domain signal respectively to suppress low-frequency noise, and obtain an orthogonal adaptive signal and a cosine adaptive signal;

[0104] S108: averaging the quadrature adaptive signal and the cosine adaptive signal respectively, and extracting corresponding quadrature DC components and cosine DC components therefrom;

[0105] S109: Based on the orthogonal DC component and the cosine DC component, the amplitude and phase of the target signal to be extracted are calculated and obtained.

[0106] Specifically, in step S103, constructing an input signal expression, an orthogonal reference signal expression and a cosine reference signal expression includes:

[0107] S103-1: The preset signal representation of the target signal to be extracted is: U0sin(ω0t+φ0);

[0108] S103-2: Acquire a phase difference δ between the input signal and the orthogonal reference signal based on phase sensitive detection;

[0109] S103-3: Construct an input signal expression: x(t)=U0sin(ω0t+φ0)+μ(t);

[0110] S103-4: Construct the orthogonal reference signal expression, which is: x rl (t) = U r *sin(ω0t+δ);

[0111] S103-5: Construct the expression for the cosine reference signal, which is: r2 (t) = U r *cos(ω0t+δ);

[0112] Among them, U0, ω0 and φ0 represent the amplitude, angular frequency and phase of the target signal to be extracted, μ(t) represents the noise, U r Represents the amplitude of the quadrature reference signal and the cosine reference signal.

[0113] Specifically, in step S104, the acquired quadrature component signal and cosine component signal include:

[0114] S104-1: quadrature component signal, expressed as:

[0115]

[0116]

[0117] S104-2: Cosine component signal, expressed as:

[0118]

[0119] in, and Represent the orthogonal DC component and cosine DC component respectively; and Respectively represent the orthogonal high-frequency component and cosine high-frequency component with a frequency of 2ω; U rμ(t)sin(ω0t+δ) and U r μ(t)cos(ω0t+δ) represent the orthogonal mixing component and cosine mixing component introduced by noise respectively.

[0120] Specifically, in step S105, obtaining the orthogonal filtering component signal and the cosine filtering component signal includes:

[0121] S105-1: Orthogonal filtering component signal, expressed as:

[0122]

[0123] S105-2: Cosine filter component signal, expressed as:

[0124]

[0125] in, represents the target orthogonal state estimation value obtained based on Kalman filtering, Represents the target cosine state estimate obtained based on Kalman filtering.

[0126] Specifically, the acquisition of the target orthogonal state estimation value and the target cosine state estimation value both include:

[0127] The predicted state estimate is expressed as:

[0128] The forecast error covariance is expressed as:

[0129] For each time instant k, the predicted state estimate is updated as:

[0130] For each time instant k, the prediction error covariance is updated and expressed as:

[0131] Initialize the predicted state estimate and the prediction error covariance as: Until the preset number of iterations is reached, the target state estimation value is obtained

[0132] Where, τ∈{I, Q}, when τ=I, the target orthogonal state estimate is calculated, and when τ=Q, the target cosine state estimate is calculated; A represents the state transfer matrix, represents the process noise covariance matrix; H represents the observation matrix, represents the identity matrix, represents the iterated covariance matrix; represents the Kalman gain, which is expressed as: R represents the measurement noise covariance matrix.

[0133] Specifically, in step S106, obtaining an orthogonal time domain signal and a cosine time domain signal includes:

[0134] S106-1: Performing fast Fourier transform on the orthogonal filtering component signal and the cosine filtering component signal respectively to obtain an orthogonal FFT component and a cosine FFT component, including:

[0135] Orthogonal FFT components, expressed as:

[0136] Cosine FFT components, expressed as:

[0137] S106-2: Convert the orthogonal FFT component and the cosine FFT component into frequency representation respectively, including:

[0138] The orthogonal FFT component frequency domain representation is expressed as:

[0139]

[0140] The cosine FFT component frequency domain representation is expressed as:

[0141]

[0142] S106-3: After filtering out high-frequency noise through frequency domain filtering, it is expressed as:

[0143] Orthogonal frequency domain filtering, expressed as:

[0144] Cosine frequency domain filtering, expressed as:

[0145] S106-4: performing inverse Fourier transform on the orthogonal frequency domain filtering and the cosine frequency domain filtering respectively, including:

[0146] Orthogonal I FFT signal, expressed as:

[0147] The cosine I FFT signal is expressed as:

[0148] S106-5: Acquiring an orthogonal time domain signal and a cosine time domain signal, including:

[0149] Orthogonal time domain signals:

[0150] Cosine time domain signal:

[0151] in, represents the complex exponential function, N represents the number of discrete Fourier transform points, k′ represents the frequency index, k′=0,1,2,…,N-1; n represents the time series sample point, j represents the imaginary unit, f cutoff Indicates the preset cutoff frequency.

[0152] The embodiment of the present invention sets an appropriate cut-off frequency f cutoff , which can effectively filter out frequencies higher than f cutoff The high-frequency noise and high-frequency signal components. time_filtered (n) and Q time_filtered The (n) signal mainly retains the DC component and low-frequency component of the target signal, reducing the impact of noise. The orthogonal components and cosine components after Kalman filtering can effectively separate the high-frequency and low-frequency components after fast Fourier transform FFT. The inverse Fourier transform IFFT converts the filtered signal back to the time domain to obtain the filtered time domain signal. This processing method can effectively improve the signal-to-noise ratio of the signal, so that the digital lock-in amplifier can reliably extract the target signal even in a low signal-to-noise ratio environment.

[0153] Specifically, in step S107, obtaining the orthogonal adaptive signal and the cosine adaptive signal includes:

[0154] S107-1: Preset the filter length to M, the learning rate to μ, and initialize the filter weight w i (0) = 0;

[0155] S107-2: For each time instant n, calculate the orthogonal adaptive signal I output by the filter adaptive (n) with cosine adaptive signal and Q adaptive (n), expressed as:

[0156]

[0157] S107-3: Calculate the orthogonal error e of the filter I (n) and cosine error e Q (n), expressed as:

[0158] e I (n) = d I (n)-I adaptive (n);

[0159] e Q (n) = d Q (n)-Q adaptive (n);

[0160] S107-4: Update filter weights and It is expressed as:

[0161]

[0162] S107-5: The orthogonal adaptive signal and the cosine adaptive signal after adaptive filtering are expressed as:

[0163] Orthogonal Adaptive Signal:

[0164] Cosine adaptive signal:

[0165] Among them, x(ni) is the historical sample of the input signal, w i (n) is the i-th filter weight; d(n) is the preset expected signal, the expected signal d I (n) and d Q (n) is set to zero signal.

[0166] Specifically, in step S108, the extraction of the orthogonal DC component and the cosine DC component includes:

[0167] S108-1: Averaging the orthogonal adaptive signal, eliminating the low-frequency noise residue, and extracting the DC component, which is expressed as:

[0168] S108-2: Orthogonal adaptive signal I adaptive Substituting the expression of (t) into the equation and simplifying it, we get the orthogonal DC component, which is expressed as:

[0169] S108-3: Averaging the cosine adaptive signal, eliminating the low-frequency noise residue, and extracting the DC component, which is expressed as:

[0170] S108-4: The cosine adaptive signal Q adaptive Substituting the expression of (t) into the equation and simplifying it, we get the cosine DC component, which is expressed as:

[0171] Wherein, T represents the preset averaging time.

[0172] Specifically, in step S109, the amplitude and phase of the target signal to be extracted are calculated and obtained, including:

[0173] S109-1: The amplitude of the target signal to be extracted is expressed as:

[0174] S109-2: The phase of the target signal to be extracted is expressed as:

[0175] S109-3: The target signal to be extracted is expressed as:

[0176] Specifically, after obtaining the input signal containing noise and the target signal to be extracted, the input signal is also preprocessed, including: after amplifying and filtering the input signal, an input signal that meets the preset A / D resolution is obtained, and a discrete sequence of the input signal is obtained through A / D sampling. The signal input channel of the digital phase-locked amplifier is constructed using analog devices to complete signal preprocessing such as amplification and filtering of the input signal to be measured. After obtaining the signal to be measured that meets the A / D resolution requirements, a discrete sequence is obtained through A / D sampling and input into the microprocessor; and the reference input channel and the correlator are both implemented internally, that is, they are implemented through internal programming of the microprocessor. After the internal correlation operation is implemented, the amplitude and initial phase are calculated to obtain the useful signal to be measured.

[0177] The present invention reduces the reliance on low-pass filters, not only reduces the complexity of system design, but also improves the speed and accuracy of signal processing. And the present invention can more accurately extract the amplitude and phase of the signal through multi-stage processing in the frequency domain and time domain, especially in a low signal-to-noise ratio environment, the advantage is more obvious. Compared with the traditional fixed low-pass filter, the adaptive filter in the present invention can dynamically adjust the filtering parameters according to the real-time signal to optimize the filtering effect. FFT provides accurate spectrum analysis capabilities, can identify and remove noise of specific frequencies, ensure that the frequency components of the signal are purer, and then optimize the calculation of amplitude and phase; through the combination of Kalman filtering and adaptive filtering, it can maintain a stable noise suppression effect in different noise environments, ensuring the stability and accuracy of signal estimation. The present invention can improve the calculation efficiency while maintaining high-precision signal estimation through multi-stage filtering and optimization algorithms, and is suitable for real-time signal processing scenarios. In summary, the present invention has significant advantages in signal processing accuracy, real-time and adaptability, solves some key technical problems faced by traditional digital lock-in amplifiers, and has good application prospects.

[0178] Reference Figure 2 As shown in the figure, the main algorithm architecture diagram of the traditional phase-locked amplifier includes an input signal channel, two reference signal channels (sine and cosine) with a phase difference of 90 degrees, two low-pass filters, and a phase sensitive detector (PSD). This structural framework explains how to multiply the input signal with the reference signal to extract a signal of a specific frequency, which is the key to the signal preparation stage. Based on this algorithm structure, the present invention optimizes the extraction of the amplitude and phase of the subsequent target to be extracted.

[0179] Based on the above embodiments, in the embodiments of the present invention, referring to Figure 3As shown, it is a schematic diagram of the workflow of the optimized digital lock-in amplifier. After Kalman filtering, fast Fourier transform (FFT) and adaptive filter processing, the high-frequency noise and low-frequency noise in the signal are effectively suppressed. By extracting the DC component and calculating the amplitude and phase, the amplitude and phase information of the target signal can be accurately obtained. This combined algorithm can effectively extract the amplitude and phase of the target signal in a low signal-to-noise ratio environment, improve the signal-to-noise ratio and processing accuracy of the signal, and significantly improve the performance of the digital lock-in amplifier. Specifically, the workflow of the optimized digital lock-in amplifier used in the present invention includes:

[0180] S201: preprocessing the input signal and the reference signal;

[0181] The input signal x(t) contains the signal to be measured and noise, and the goal is to distinguish the two through processing. The sine wave is chosen as the signal to be measured because its mathematical model is simple and easy to analyze. Two orthogonal reference signals (sine and cosine) are used in order to extract amplitude and phase information from the input signal. This method is based on the basic principle of Fourier transform, in which the signal can be decomposed into sine and cosine components.

[0182] Reference Figure 4 The following is a schematic diagram of the signal input channel. The signal input channel of the digital lock-in amplifier is constructed using analog devices to complete signal preprocessing such as amplification of the input signal to be measured. Figure 4 As shown, after obtaining the signal to be measured that meets the A / D resolution requirement, the discrete sequence is obtained through A / D sampling and input into the microprocessor; the reference input channel and the correlator are both implemented internally, that is, they are implemented by internal programming of the microprocessor. After the internal correlation operation is implemented, the amplitude and initial phase are calculated to obtain the useful signal to be measured.

[0183] The input signal selects or generates a composite signal x(t) containing the signal to be measured and background noise. The target signal is usually a simple sine wave in the form of U0sin(ω0t+φ0), where U0, ω0, φ0 represent the amplitude, angular frequency and phase of the signal respectively, and the background noise μ(t) can be Gaussian white noise to simulate the interference in the actual environment.

[0184] x(t)=U0sin(ω0t+φ0)+μ(t)=U0sin(2πf0t+θ)+μ(t);

[0185] After being phase-shifted by 90° by the phase shifter, the orthogonal reference signal xr1(t)=Ursin(ω0t) and the cosine reference signal xr2(t)=Urcos(ω0t) are formed for subsequent phase-sensitive detection, where Ur represents the amplitude of the reference signal.

[0186] S202: Perform PSD processing on the signal to obtain I and Q components;

[0187] In PSD (Phase Sensitive Detection), the phase difference between the input signal and the reference signal is measured, and then the input signal x(t) is multiplied by two reference signals xr1(t) and xr2(t) respectively using a multiplier. The two generated signals I(t) and Q(t) contain mixed information of the target signal and noise, in this way, the useful signal components can be separated in the subsequent steps. This is the key to eliminating noise by using the orthogonal property. The two signals contain the amplitude and phase information of the original signal;

[0188]

[0189] First item: and Represents the DC component, reflecting the amplitude and phase of the signal.

[0190] Second item: and It indicates the high frequency component with a frequency of 2ω, which needs to be filtered out.

[0191] The third item: U r μ(t)sin(ω0t+δ) and U r μ(t)cos(ω0t+δ) indicates that the mixing component introduced by the noise is the product of the noise and the reference signal. Since the sinusoidal signal is periodic and has no correlation with the noise signal, this integral is 0.

[0192] The input signal is mixed with the reference signal by multiplication, and the two generated signals I(t) and Q(t) contain mixed information of the target signal and noise. This process is equivalent to moving the input signal to the DC component, which facilitates subsequent low-frequency filtering and processing. In this way, useful signal components can be separated in subsequent steps.

[0193] S203: Perform Kalman filtering on the I and Q components to estimate the signal state;

[0194] Kalman filtering calculates the optimal estimate of the current state by calculating the previous state prediction value, the current state observation value, and the prediction error, and then predicts the next state. The I(t) and Q(t) signals of PSD are:

[0195]

[0196] The Kalman filter gradually suppresses the high-frequency component with a frequency of 2ω through prediction and update steps, so that the high-frequency components in the signal are filtered out. By continuously adjusting the state estimation and error covariance, the Kalman filter can effectively suppress noise, making the filtered signal closer to the DC component of the real signal.

[0197] The specific steps of Kalman filtering include:

[0198] ① Initialization:

[0199] ② Submission step (for each time k):

[0200] For I mixed :Status prediction:

[0201] represents the predicted state estimate at time k, A represents the state transfer matrix, which describes the state transfer relationship of the system from time k-1 to k. For the simple case of a constant signal, A=1.

[0202] Error covariance prediction:

[0203] represents the process noise covariance matrix, which describes the process noise in the system.

[0204] Status Update:

[0205] H represents the observation matrix, which maps the state to the measurement space; for direct measurement, H = 1.

[0206] Error covariance update:

[0207] P k|k is the iterated covariance matrix; K k is the Kalman gain; is the identity matrix.

[0208] Kalman gain calculation:

[0209] R represents the measurement noise covariance matrix, which describes the measurement noise.

[0210] The I component after the Kalman filter becomes:

[0211]

[0212] The above calculation process is similarly applied to the reference signal Q after having a phase shift of 90 degrees mixed (cosine wave) channel output, Q after Kalman filtering filteredThe signal is:

[0213]

[0214] Processing I through Kalman filtering mixcd and Q mixcd The Kalman filter can provide high-precision signal estimation in a noisy environment through state prediction and measurement update. It can adapt to dynamically changing signal and noise environments and is more flexible and adaptable than a low-pass filter with fixed parameters. Traditional digital lock-in amplifiers rely on low-pass filters to filter out high-frequency noise. The performance of the low-pass filter directly affects the signal-to-noise ratio (SNR) and bandwidth of the lock-in amplifier.

[0215] This processing method can effectively suppress noise, improve signal accuracy and stability, and enable the digital lock-in amplifier to reliably extract the target signal even in a low signal-to-noise ratio environment.

[0216] S204: performing FFT on the I and Q components after the Kalman filter. The purpose of FFT is to convert the time domain signal into the frequency domain and perform frequency domain filtering to more easily separate and filter out high frequency noise;

[0217] FFT of the I component:

[0218] Among them, I filtered (n) represents the I component after Kalman filtering, and k represents the frequency index.

[0219] FFT of the Q component:

[0220] Among them, Q filtercd (n) represents the Q component after Kalman filtering, and k′ represents the frequency index.

[0221] Applying Fast Fourier Transform (FFT) for frequency domain analysis can effectively convert signals from the time domain to the frequency domain, making component separation and analysis easier. By converting time domain signals to the frequency domain through FFT, specific frequency components can be accurately selected and filtered out. Frequency domain filtering provides high-resolution spectrum analysis, which can more effectively separate signals and noise and improve the accuracy of signal processing.

[0222] In the frequency domain, it is easier to observe the spectral content of a signal:

[0223] Frequency domain representation of the I component:

[0224]

[0225] k=0,1,2,…,N-1;

[0226] Frequency domain representation of the Q component:

[0227]

[0228] k=0,1,2,…,N-1;

[0229] In the frequency domain, the high-frequency components of the signal and the noise residue will appear as high-frequency spectral components, while the DC component of the target signal will be concentrated at low frequencies.

[0230] By filtering in the frequency domain, high-frequency noise can be filtered out and low-frequency signals can be retained:

[0231] Frequency domain filtering of the I component:

[0232]

[0233] Frequency domain filtering of the Q component:

[0234]

[0235] By setting the cutoff frequency f cutoff , high-frequency noise can be removed, and only the low-frequency part of the signal is retained to filter out the high-frequency part. However, when the cut-off frequency gradually increases, the DC component of the output signal is gradually submerged by the noise, resulting in a locked situation. The digital low-pass filter is indispensable in the entire algorithm of the traditional lock-in amplifier, and its performance directly affects the improvement of the signal-to-noise ratio of the lock-in amplifier. The equivalent noise bandwidth of the lock-in amplifier depends on the bandwidth of the low-pass filter. This means that overcoming the dependence on the low-pass filter can reduce the design difficulty of the lock-in amplifier and improve the anti-noise performance.

[0236] Then perform an inverse Fourier transform (IFFT) to convert the filtered frequency domain signal back to the time domain to obtain the filtered time domain signal:

[0237] Inverse Fourier transform of the I component:

[0238]

[0239] Inverse Fourier transform of the Q component:

[0240]

[0241] The filtered signal is converted back to the time domain through the inverse Fourier transform IFFT to obtain the filtered time domain signal. This processing method can effectively improve the signal-to-noise ratio of the signal, so that the digital lock-in amplifier can reliably extract the target signal even in a low signal-to-noise ratio environment.

[0242] After inverse Fourier transform, I time_filtercd (n) and Qtime_filtercd (n) The signal will mainly contain the DC component and low-frequency components of the target signal, and the high-frequency noise has been filtered out.

[0243] After these steps, the signal I and Q expressions are:

[0244]

[0245] After frequency domain filtering and inverse Fourier transform, these signals retain the main components of the target signal, filter out high-frequency noise, and improve the accuracy and stability of the signal.

[0246] S205: Adaptively filter the I and Q components after frequency domain filtering to further suppress noise;

[0247] Before adaptive filtering, the time domain signal I that mainly retains the DC component and low-frequency component of the target signal has been obtained through Kalman filtering, FFT frequency domain filtering and inverse Fourier transformation. time_filtered (t) and Q time_filtered (t).

[0248]

[0249] Adaptive filters can better adapt to different signal and noise environments by dynamically adjusting filter parameters, further suppress low-frequency noise, and improve the signal-to-noise ratio of the signal. Adaptive filters can provide better performance when dealing with non-stationary noise and changing signal environments. The low-pass filter parameters of traditional lock-in amplifiers are fixed and cannot dynamically adapt to different signal and noise characteristics.

[0250] Apply to I time_filtered and Q time_filtered For component I time_filtered (t) and Q component Q time_filtered (t), apply adaptive filter for processing. Set the filter length M and learning rate μ, initialize the filter weight w i (0) = 0. For each time instant n, the filter output I is calculated. adaptive (n) and Q adaptive (n).

[0251] Calculate the filter output:

[0252]

[0253] Among them, x(ni) is the historical sample of the input signal, w i (n) is the i-th filter weight.

[0254] Calculate the filter error e I (n) and e Q(n):

[0255] e I (n) = d I (n)-I adaptive (n);

[0256] e Q (n) = d Q (n)-Q adaptive (n);

[0257] Where d(n) is the desired signal (usually a zero signal or a reference signal), and e(n) is the filter error. Usually, the desired signal d I (n) and d Q (n) can be set to a zero signal so that the filter only suppresses noise.

[0258] Update filter weights and

[0259]

[0260] Among them, μ is the learning rate.

[0261] After adaptive filtering, the signal I adaptive (t) and Q adaptive (t) is:

[0262]

[0263] S206: extracting a DC component from the I and Q components after adaptive filtering, and calculating the amplitude and phase of the target signal according to the DC component;

[0264] The filtered signal is averaged to eliminate the residual low-frequency noise and extract the DC component. adaptive (t) and Q adaptive (t) to extract the DC component:

[0265]

[0266] Will I adaptive Substituting the expression of (t) into the equation, we get:

[0267]

[0268] Since the average value of the low-frequency noise residual is zero, it can be simplified to:

[0269]

[0270] because is a constant and can be mentioned outside the integral sign:

[0271]

[0272] The Q component process is similar

[0273] Calculate the amplitude and phase of the input signal based on the DC component:

[0274] Amplitude:

[0275] Phase:

[0276] The target signal extraction method based on the improved digital phase-locked amplifier described in the present invention designs a new digital phase-locked amplifier through Kalman filter, fast Fourier transform and adaptive filter; the adaptive filter can dynamically adjust the filtering parameters according to the real-time signal to optimize the filtering effect; FFT provides accurate spectrum analysis capability, can identify and remove noise of specific frequency, ensure the frequency component of the signal is purer, and then optimize the calculation of amplitude and phase; through the combination of Kalman filtering and adaptive filtering, it can maintain a stable noise suppression effect in different noise environments, and ensure the stability and accuracy of signal estimation; the present invention can extract the amplitude and phase of the signal more accurately through multi-stage processing in the frequency domain and time domain, especially in a low signal-to-noise ratio environment, the advantage is more obvious. The present invention directly processes the product of an input signal and a reference signal by adopting a method based on time analysis, and uses mathematical statistical methods and fast Fourier transform to stabilize and extract the DC component of the signal, thereby reducing dependence on a low-pass filter and not relying on a low-pass filter to obtain the DC component. The present invention can improve the performance of signal detection in a low signal-to-noise ratio environment and avoid the bandwidth limitation problem caused by a traditional low-pass filter, thereby reducing the complexity of system design, improving the speed and accuracy of signal processing, and providing higher real-time performance and noise suppression capabilities.

[0277] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0278] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0279] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0280] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0281] Obviously, the above embodiments are merely examples for the purpose of clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the present invention.

Claims

1. A target signal extraction method based on an improved digital lock-in amplifier, characterized in that: include: Acquire an input signal including noise and a target signal to be extracted, as well as an orthogonal reference signal and a cosine reference signal; Based on phase sensitive detection, a phase difference between an input signal and an orthogonal reference signal is obtained; Based on the preset signal representation of the target signal to be extracted, the noise, and the phase difference between the input signal and the orthogonal reference signal, construct an input signal expression, an orthogonal reference signal expression, and a cosine reference signal expression; Using a multiplier, the input signal expression is mixed with the orthogonal reference signal expression and the cosine reference signal expression respectively, and the high frequency term is filtered out to obtain the orthogonal component signal and the cosine component signal; Performing Kalman filtering on the orthogonal component signal and the cosine component signal respectively to filter out high frequency components and noise, and obtaining an orthogonal filtering component signal and a cosine filtering component signal; Performing fast Fourier transform on the orthogonal filtering component signal and the cosine filtering component signal respectively, filtering out high-frequency noise, and then performing inverse Fourier transform to obtain an orthogonal time domain signal and a cosine time domain signal; Adaptively filtering the orthogonal time domain signal and the cosine time domain signal respectively to suppress low-frequency noise and obtain an orthogonal adaptive signal and a cosine adaptive signal; Averaging the quadrature adaptive signal and the cosine adaptive signal respectively, and extracting corresponding quadrature DC components and cosine DC components therefrom; Based on the orthogonal DC component and the cosine DC component, the amplitude and phase of the target signal to be extracted are calculated.

2. The target signal extraction method based on the improved digital lock-in amplifier according to claim 1 is characterized in that: The method constructs an input signal expression, an orthogonal reference signal expression and a cosine reference signal expression based on a preset signal representation of the target signal to be extracted, noise, and a phase difference between the input signal and the orthogonal reference signal, including: The preset signal representation of the target signal to be extracted is: U0sin(ω0t+φ0); Based on phase sensitive detection, a phase difference δ between the input signal and the orthogonal reference signal is obtained; Construct the input signal expression: x(t) = U0sin(ω0t+φ0)+μ(t); Construct the orthogonal reference signal expression as: rl (t) = U r *sin(ω0t+δ); Construct the expression for the cosine reference signal as: r2 (t) = U r *cos(ω0t+δ); Among them, U0, ω0 and φ0 represent the amplitude, angular frequency and phase of the target signal to be extracted, μ(t) represents the noise, U r Represents the amplitude of the quadrature reference signal and the cosine reference signal.

3. The target signal extraction method based on the improved digital lock-in amplifier according to claim 2 is characterized in that: The method of using a multiplier to mix the input signal expression with the orthogonal reference signal expression and the cosine reference signal expression, filtering out high-frequency terms, and obtaining the orthogonal component signal and the cosine component signal includes: The quadrature component signal is expressed as: The cosine component signal is expressed as: in, and Represent the orthogonal DC component and cosine DC component respectively; and Respectively represent the orthogonal high-frequency component and cosine high-frequency component with a frequency of 2ω; U r μ(t)sin(ω0t+δ) and U r μ(t)cos(ω0t+δ) represent the orthogonal mixing component and cosine mixing component introduced by noise respectively.

4. The target signal extraction method based on the improved digital lock-in amplifier according to claim 3 is characterized in that: The step of performing Kalman filtering on the orthogonal component signal and the cosine component signal respectively to filter out high frequency components and noise, and obtaining the orthogonal filter component signal and the cosine filter component signal comprises: The orthogonal filtering component signal is expressed as: The cosine filtered component signal is expressed as: in, represents the target orthogonal state estimation value obtained based on Kalman filtering, Represents the target cosine state estimate obtained based on Kalman filtering.

5. The target signal extraction method based on the improved digital lock-in amplifier according to claim 4 is characterized in that: The acquisition of the target orthogonal state estimation value and the target cosine state estimation value includes: The predicted state estimate is expressed as: The forecast error covariance is expressed as: For each time instant k, the predicted state estimate is updated as: For each time instant k, the prediction error covariance is updated and expressed as: Initialize the predicted state estimate and the prediction error covariance as: Until the preset number of iterations is reached, the target state estimation value is obtained Where, τ∈{I, Q}, when τ=I, the target orthogonal state estimate is calculated, and when τ=Q, the target cosine state estimate is calculated; A represents the state transfer matrix, represents the process noise covariance matrix; H represents the observation matrix, represents the identity matrix, represents the iterated covariance matrix; represents the Kalman gain, which is expressed as: R represents the measurement noise covariance matrix.

6. The target signal extraction method based on the improved digital lock-in amplifier according to claim 4 is characterized in that: The method of performing fast Fourier transform on the orthogonal filtering component signal and the cosine filtering component signal respectively, filtering out high frequency noise, and then performing inverse Fourier transform to obtain an orthogonal time domain signal and a cosine time domain signal comprises: Perform fast Fourier transform on the orthogonal filtering component signal and the cosine filtering component signal respectively to obtain the orthogonal FFT component and the cosine FFT component, including: Orthogonal FFT components, expressed as: Cosine FFT components, expressed as: Convert the orthogonal FFT components and the cosine FFT components to frequency representation, including: The orthogonal FFT component frequency domain representation is expressed as: The cosine FFT component frequency domain representation is expressed as: After filtering out high-frequency noise through frequency domain filtering, it is expressed as: Orthogonal frequency domain filtering, expressed as: Cosine frequency domain filtering, expressed as: Perform inverse Fourier transform on orthogonal frequency domain filtering and cosine frequency domain filtering respectively, including: Orthogonal IFFT signal, expressed as: The cosine IFFT signal is expressed as: Acquire orthogonal time domain signals and cosine time domain signals, including: Orthogonal time domain signals: Cosine time domain signal: in, represents the complex exponential function, N represents the number of discrete Fourier transform points, k′ represents the frequency index, k′=0,1,2,…,N-1; n represents the time series sample point, j represents the imaginary unit, f cutoff Indicates the preset cutoff frequency.

7. The target signal extraction method based on the improved digital lock-in amplifier according to claim 6 is characterized in that: The method of adaptively filtering the orthogonal time domain signal and the cosine time domain signal respectively to suppress low-frequency noise and obtain an orthogonal adaptive signal and a cosine adaptive signal includes: The preset filter length is M, the learning rate is μ, and the filter weight w is initialized i (0) = 0; For each time instant n, the orthogonal adaptive signal I of the filter output is calculated adaptive (n) with cosine adaptive signal and Q adaptive (n), expressed as: Calculate the filter's quadrature error e I (n) and cosine error e Q (n), expressed as: e I (n)=d I (n)-I adaptive (n); e Q (n)=d Q (n)-Q adaptive (n); Update filter weights and It is expressed as: The orthogonal adaptive signal and the cosine adaptive signal after adaptive filtering are expressed as: Orthogonal Adaptive Signal: Cosine adaptive signal: Among them, x(ni) is the historical sample of the input signal, w i (n) is the i-th filter weight; d(n) is the preset expected signal, the expected signal d I (n) and d Q (n) is set to zero signal.

8. The target signal extraction method based on the improved digital lock-in amplifier according to claim 7 is characterized in that: The step of averaging the quadrature adaptive signal and the cosine adaptive signal respectively and extracting corresponding quadrature DC components and cosine DC components therefrom comprises: The orthogonal adaptive signal is averaged to eliminate the low-frequency noise residue and extract the DC component, which is expressed as: The orthogonal adaptive signal I adaptive Substituting the expression of (t) into the equation and simplifying it, we get the orthogonal DC component, which is expressed as: The cosine adaptive signal is averaged to eliminate the low-frequency noise residue and extract the DC component, which is expressed as: The cosine adaptive signal Q adaptive Substituting the expression of (t) into the equation and simplifying it, we get the cosine DC component, which is expressed as: Wherein, T represents the preset averaging time.

9. The target signal extraction method based on the improved digital lock-in amplifier according to claim 1 is characterized in that: The step of calculating and obtaining the amplitude and phase of the target signal to be extracted based on the orthogonal DC component and the cosine DC component includes: The amplitude of the target signal to be extracted is expressed as: The phase of the target signal to be extracted is expressed as: The target signal to be extracted is expressed as:

10. The target signal extraction method based on the improved digital lock-in amplifier according to claim 1 is characterized in that: After obtaining the input signal containing noise and the target signal to be extracted, the input signal is also preprocessed, including: after amplifying and filtering the input signal, obtaining the input signal that meets the preset A / D resolution, and obtaining a discrete sequence of the input signal through A / D sampling.

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