A target signal extraction method based on an improved digital lock-in amplifier

Abstract

The present invention relates to a method for extracting a target signal based on an improved digital lock-in amplifier, which includes obtaining an input signal, a quadrature reference signal, and a cosine reference signal; obtaining the phase difference between the input signal and the quadrature reference signal, and constructing an input signal expression, a quadrature reference signal expression, and a cosine reference signal expression in combination with the preset signal representation and noise of the target signal to be extracted; using a multiplier to mix the input signal expression with the quadrature reference signal expression and the cosine reference signal expression respectively to obtain quadrature and cosine component signals, performing Kalman filtering on them respectively, obtaining quadrature and cosine filtered component signals, then performing fast Fourier transform respectively, and then performing inverse Fourier transform to obtain quadrature and cosine time-domain signals, performing adaptive filtering on them respectively, obtaining quadrature and cosine adaptive signals, and then performing averaging respectively, and extracting the quadrature DC component and the cosine DC component therefrom to calculate and obtain the amplitude and phase of the target signal to be extracted.

Description

Technical Field

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

[0002] The problem of weak signal detection has always been a key research issue in the field of measurement, and it is also a frontier issue in the development of science and technology at the present stage. The weak signal detection technology is a new science and technology involving technical fields such as information processing and electronic science, and is used to achieve the purpose of suppressing noise and extracting useful signals.

[0003] The existing weak signal detection methods mainly include narrowband filtering method, synchronous accumulation method, dual-channel noise cancellation method and correlation detection method. The narrowband filtering method uses the characteristics that the power spectral density of the signal is relatively narrow while the power spectrum of the noise is relatively wide to improve the signal-to-noise ratio and thus extract the signal, but it can only be applied to occasions with very low requirements for noise characteristics. The synchronous accumulation method applies the repeatability of the signal and the randomness of the noise, measures the signal repeatedly for multiple times, and accumulates the signals in phase, but the operation period is long and the calculation in the controller is relatively complex. The dual-channel noise cancellation method uses two channels to process the input signal differently, then cancels the common noise, and finally obtains the signal to be measured. The disadvantage of this method is that it can only be used to detect whether a weak sine wave signal exists and cannot reproduce the waveform. The correlation detection method is a method of extracting a periodic signal from strong noise based on the fact that the amplitude of a periodic signal has correlation at different times, while the noise is random and has no correlation. This method is divided into two types: autocorrelation and cross-correlation. The cross-correlation method shows its superiority over autocorrelation in noise suppression ability because it can suppress various forms of noise that are not correlated with the reference signal.

[0004] Weak signal detection instruments have evolved continuously with the development of technology. Commonly used devices include low-noise preamplifiers, lock-in amplifiers, sampling integrators, and photon counters, etc. 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. A lock-in amplifier is a device specifically used to extract signals of a specific frequency and is widely used in scientific research and industrial fields, especially in cases where it is necessary to detect and extract weak signals from a noisy environment.

[0005] The original lock-in amplifier was fully implemented by analog circuits. With the development of digital technology and the maturity of large-scale integrated circuits, the progress of high-speed digital signal processing technology has brought various digital products. However, most lock-in amplifiers are still analog-digital hybrid devices. Although analog lock-in amplifiers have been improved over the years, their core circuits have not undergone fundamental changes. Only digital devices are used locally, 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 and development of microprocessors such as DSP and FPGA, the core phase-sensitive detector of the lock-in amplifier has gradually been implemented through the software of digital microprocessors, and finally a truly digital lock-in amplifier was born. This marks a major transformation of the lock-in amplifier from traditional analog technology to full digitalization. Although traditional lock-in amplifiers perform well in many applications, their performance highly depends 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, an overly narrow bandwidth will cause an increase in signal processing delay, thereby reducing the system's ability to respond to rapidly changing signals. Summary of the Invention

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

[0008] To solve the above technical problem, the present invention provides a method for extracting a target signal based on an improved digital lock-in amplifier, including:

[0009] Obtain an input signal containing noise and the target signal to be extracted, as well as a quadrature reference signal and a cosine reference signal;

[0010] Based on phase-sensitive detection, obtain the phase difference between the input signal and the quadrature reference signal;

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

[0012] Use a multiplier to mix the input signal expression with the quadrature reference signal expression and the cosine reference signal expression respectively, filter out the high-frequency terms, and obtain a quadrature component signal and a cosine component signal;

[0013] Perform Kalman filtering on the orthogonal component signal and the cosine component signal respectively to filter out high-frequency components and noise, and obtain the orthogonal filtered component signal and the cosine filtered component signal;

[0014] Perform fast Fourier transform on the orthogonal filtered component signal and the cosine filtered component signal respectively. After filtering out high-frequency noise, perform inverse Fourier transform to obtain the orthogonal time-domain signal and the cosine time-domain signal;

[0015] Perform adaptive filtering 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;

[0016] Average the orthogonal adaptive signal and the cosine adaptive signal respectively, and extract the corresponding orthogonal DC component and cosine DC component from them;

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

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

[0019] The preset signal representation of the target signal to be extracted is: U 0 sin(ω 0 t + φ 0 );

[0020] Based on phase-sensitive detection, obtain the phase difference δ between the input signal and the orthogonal reference signal;

[0021] Construct the input signal expression as: x(t) = U 0 sin(ω 0 t + φ 0 ) + μ(t);

[0022] Construct the orthogonal reference signal expression as: x rl (t) = U r *sin(ω 0 t + δ);

[0023] Construct the cosine reference signal expression as: x r2 (t) = U r *cos(ω 0 t + δ);

[0024] Among them, U 0 , ω 0 and φ 0respectively represent the amplitude, angular frequency, and phase of the target signal to be extracted, μ(t) represents noise, and U r represents the amplitudes of the quadrature reference signal and the cosine reference signal.

[0025] Preferably, the mixer is used to mix the input signal expression with the quadrature reference signal expression and the cosine reference signal expression respectively, filter out the high-frequency terms, and obtain the quadrature component signal and the cosine component signal, including:

[0026] The quadrature component signal is expressed as:

[0027]

[0028] The cosine component signal is expressed as:

[0029]

[0030] Where and respectively represent the quadrature DC component and the cosine DC component; and respectively represent the quadrature high-frequency component and the cosine high-frequency component with a frequency of 2ω; U r μ(t)sin(ω 0 t + δ) and U r μ(t)cos(ω 0 t + δ) respectively represent the quadrature mixing component and the cosine mixing component introduced by noise.

[0031] Preferably, the Kalman filter is respectively applied to the quadrature component signal and the cosine component signal to filter out the high-frequency components and noise, and obtain the quadrature filtered component signal and the cosine filtered component signal, including:

[0032] The quadrature filtered component signal is expressed as:

[0033]

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

[0035]

[0036] Where represents the target quadrature state estimate value obtained based on the Kalman filter, represents the target cosine state estimate value obtained based on the Kalman filter.

[0037] Preferably, the acquisition of the target quadrature state estimate value and the target cosine state estimate value both include:

[0038] The predicted state estimate value is expressed as:

[0039] The prediction error covariance, denoted as:

[0040] For each time instant k, update the predicted state estimate, denoted as:

[0041] For each time instant k, update the prediction error covariance, denoted as:

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

[0043] where τ ∈ {I, Q}, when τ = I, calculate and obtain the target quadrature state estimate, and when τ = Q, calculate and obtain the target cosine state estimate; A represents the state transition matrix, represents the process noise covariance matrix; H represents the observation matrix, represents the identity matrix, represents the iteration covariance matrix; represents the Kalman gain, and the expression is: R represents the measurement noise covariance matrix.

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

[0045] Performing fast Fourier transform on the quadrature filter component signal and the cosine filter component signal respectively to obtain the quadrature FFT component and the cosine FFT component, includes:

[0046] The quadrature FFT component, denoted as:

[0047] The cosine FFT component, denoted as:

[0048] Converting the quadrature FFT component and the cosine FFT component into frequency representations respectively, includes:

[0049] The frequency-domain representation of the quadrature FFT component, denoted as:

[0050]

[0051] The frequency-domain representation of the cosine FFT component, denoted as:

[0052]

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

[0054] Orthogonal frequency-domain filtering is expressed as:

[0055] Cosine frequency-domain filtering is expressed as:

[0056] Performing inverse Fourier transforms on the orthogonal frequency-domain filtering and the cosine frequency-domain filtering respectively, including:

[0057] The orthogonal IFFT signal is expressed as:

[0058] The cosine IFFT signal is expressed as:

[0059] Obtaining the orthogonal time-domain signal and the cosine time-domain signal, including:

[0060] Orthogonal time-domain signal:

[0061] Cosine time-domain signal:

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

[0063] Preferably, performing adaptive filtering 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] Presetting the filter length as M and the learning rate as μ, and initializing the filter weight w i (0) = 0;

[0065] For each moment n, calculating the orthogonal adaptive signal I adaptive (n) and the cosine adaptive signal Q adaptive (n), which is expressed as:

[0066]

[0067]

[0068] Calculating the orthogonal error e I (n) and the cosine error e Q (n), which is expressed as:

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

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

[0071] Update filter weights and is expressed as:

[0072]

[0073] Express the quadrature adaptive signal and the cosine adaptive signal after adaptive filtering as:

[0074] Quadrature adaptive signal:

[0075] Cosine adaptive signal:

[0076] where x(n - i) is the historical sample of the input signal, and w i (n) is the i-th filter weight; d(n) is the preset desired signal, and the desired signals d I (n) and d Q (n) are set to zero signals.

[0077] Preferably, respectively averaging the quadrature adaptive signal and the cosine adaptive signal, and extracting the corresponding quadrature DC component and cosine DC component, includes:

[0078] Averaging the quadrature adaptive signal, eliminating the low-frequency noise residue, and extracting the DC component, which is expressed as:

[0079] Substitute the expression of the quadrature adaptive signal I adaptive (t) and simplify to obtain the quadrature DC component, which is expressed as:

[0080] Averaging the cosine adaptive signal, eliminating the low-frequency noise residue, and extracting the DC component, which is expressed as:

[0081] Substitute the expression of the cosine adaptive signal Q adaptive (t) and simplify to obtain the cosine DC component, which is expressed as:

[0082] where T represents the preset average time.

[0083] Preferably, 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, preprocessing the input signal is further included, including: after amplifying and filtering the input signal, obtaining the input signal that meets the preset A / D resolution, and obtaining the 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 lock-in amplifier of the present invention designs a new digital lock-in amplifier through a Kalman filter, a fast Fourier transform, and an adaptive filter; the adaptive filter can dynamically adjust the filtering parameters according to the real-time signal to optimize the filtering effect; the FFT provides accurate spectrum analysis capabilities, can identify and remove noise at 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, stable noise suppression effects can be maintained in different noise environments to 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, and the advantages are more obvious. The present invention directly processes the product of the input signal and the reference signal by adopting a time-analysis-based method, uses mathematical statistical methods and fast Fourier transforms to stabilize and extract the DC component of the signal, reduces the dependence on the low-pass filter, does not rely on the low-pass filter to obtain the DC component, can improve the performance of signal detection in a low signal-to-noise ratio environment, and avoids the bandwidth limitation problem brought by the traditional low-pass filter, not only reducing the complexity of system design, but also improving the speed and accuracy of signal processing, 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 easier to be clearly understood, the following further details the present invention according to specific embodiments of the present invention in combination with the drawings, wherein

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

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

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

[0094] Figure 4 It is the schematic diagram of the signal input channel provided by the present invention. Specific embodiments

[0095] The present invention will be 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 be able to implement it, but the specific embodiments cited are not intended to limit the present invention.

[0096] Refer to Figure 1 As shown, the flowchart of the steps of the target signal extraction method based on an improved digital lock-in amplifier of the present invention, the specific steps include:

[0097] S101: Obtain an input signal containing noise and the target signal to be extracted, as well as a quadrature reference signal and a cosine reference signal;

[0098] S102: Based on phase-sensitive detection, obtain the phase difference between the input signal and the quadrature reference signal;

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

[0100] S104: Use a multiplier to mix the input signal expression with the quadrature reference signal expression and the cosine reference signal expression respectively, filter out the high-frequency terms, and obtain a quadrature component signal and a cosine component signal;

[0101] S105: Perform Kalman filtering on the quadrature component signal and the cosine component signal respectively, filter out the high-frequency components and noise, and obtain a quadrature filtered component signal and a cosine filtered component signal;

[0102] S106: Perform fast Fourier transform on the quadrature filtered component signal and the cosine filtered component signal respectively, filter out the high-frequency noise, and then perform inverse Fourier transform to obtain a quadrature time-domain signal and a cosine time-domain signal;

[0103] S107: Perform adaptive filtering on 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: Average the orthogonal adaptive signal and the cosine adaptive signal respectively, and extract the corresponding orthogonal DC component and cosine DC component from them;

[0105] S109: Calculate and obtain the amplitude and phase of the target signal to be extracted based on the orthogonal DC component and the cosine DC component.

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

[0107] S103-1: The preset signal representation of the target signal to be extracted is: U 0 sin(ω 0 t + φ 0 );

[0108] S103-2: Based on phase-sensitive detection, obtain the phase difference δ between the input signal and the orthogonal reference signal;

[0109] S103-3: Construct the input signal expression as: x(t) = U 0 sin(ω 0 t + φ 0 ) + μ(t);

[0110] S103-4: Construct the orthogonal reference signal expression as: x rl (t) = U r *sin(ω 0 t + δ);

[0111] S103-5: Construct the cosine reference signal expression as: x r2 (t) = U r *cos(ω 0 t + δ);

[0112] Among them, U 0 , ω 0 and φ 0 respectively represent the amplitude, angular frequency, and phase of the target signal to be extracted, μ(t) represents noise, and U r represents the amplitude of the orthogonal reference signal and the cosine reference signal.

[0113] Specifically, in step S104, the obtained orthogonal component signal and cosine component signal include:

[0114] S104-1: The orthogonal component signal is expressed as:

[0115]

[0116]

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

[0118]

[0119] where and represent the orthogonal DC component and the cosine DC component respectively; and represent the orthogonal high-frequency component and the cosine high-frequency component with a frequency of 2ω respectively; U r μ(t)sin(ω 0 t + δ) and U r μ(t)cos(ω 0 t + δ) represent the orthogonal mixing component and the cosine mixing component introduced by noise respectively.

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

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

[0122]

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

[0124]

[0125] where represents the target orthogonal state estimate obtained based on Kalman filtering, represents the target cosine state estimate obtained based on Kalman filtering.

[0126] Specifically, the obtaining of the target orthogonal state estimate and the target cosine state estimate both include:

[0127] Predicted state estimate, expressed as:

[0128] Prediction error covariance, expressed as:

[0129] For each time instant k, updating the predicted state estimate, expressed as:

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

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

[0132] where τ ∈ {I, Q}. When τ = I, calculate and obtain the target quadrature state estimate. When τ = Q, calculate and obtain the target cosine state estimate; A represents the state transition matrix, represents the process noise covariance matrix; H represents the observation matrix, represents the identity matrix, represents the iteration covariance matrix; represents the Kalman gain, and the expression is: R represents the measurement noise covariance matrix.

[0133] Specifically, in step S106, obtaining the quadrature time-domain signal and the cosine time-domain signal includes:

[0134] S106-1: Perform fast Fourier transforms on the quadrature filtered component signal and the cosine filtered component signal respectively to obtain the quadrature FFT component and the cosine FFT component, including:

[0135] The quadrature FFT component is expressed as:

[0136] The cosine FFT component is expressed as:

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

[0138] The frequency-domain representation of the quadrature FFT component is expressed as:

[0139]

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

[0141]

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

[0143] Quadrature frequency-domain filtering is expressed as:

[0144] Cosine frequency-domain filtering is expressed as:

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

[0146] Orthogonal IFFT signal, expressed as:

[0147] Cosine IFFT signal, expressed as:

[0148] S106-5: Obtain the orthogonal time-domain signal and the cosine time-domain signal, including:

[0149] Orthogonal time-domain signal:

[0150] Cosine time-domain signal:

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

[0152] In the embodiment of the present invention, by setting an appropriate cut-off frequency f cutoff , high-frequency noise and high-frequency signal components with frequencies higher than f cutoff can be effectively filtered out. The filtered I time_filtered (n) and Q time_filtered (n) signals mainly retain the DC component and low-frequency component of the target signal, reducing the influence of noise. After the orthogonal component and cosine component after Kalman filtering pass through the fast Fourier transform FFT, the high-frequency and low-frequency components can be effectively separated. 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, enabling the digital lock-in amplifier to reliably extract the target signal even in a low signal-to-noise ratio environment.

[0153] Specifically, in step S107, obtain the orthogonal adaptive signal and the cosine adaptive signal, including:

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

[0155] S107-2: For each moment n, calculate the orthogonal adaptive signal I adaptive (n) and the cosine adaptive signal and Q adaptive (n), expressed as:

[0156]

[0157] S107-3: Calculate the quadrature error e I (n) and the 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 the filter weights and expressed as:

[0161]

[0162] S107-5: Express the quadrature adaptive signal and the cosine adaptive signal after adaptive filtering as:

[0163] Quadrature adaptive signal:

[0164] Cosine adaptive signal:

[0165] where x(n - i) is the historical sample of the input signal, w i (n) is the i-th filter weight; d(n) is the preset desired signal, and the desired signals d I (n) and d Q (n) are set to zero signals.

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

[0167] S108-1: Average the quadrature adaptive signal to eliminate the residual low-frequency noise and extract the DC component, expressed as:

[0168] S108-2: Substitute and simplify the expression of the quadrature adaptive signal I adaptive (t) to obtain the quadrature DC component, expressed as:

[0169] S108-3: Average the cosine adaptive signal to eliminate the residual low-frequency noise and extract the DC component, expressed as:

[0170] S108-4: Substitute the cosine adaptive signal Qadaptive Substitute the expression of (t) and simplify to obtain the DC component of cosine, expressed as:

[0171] where T represents the preset average time.

[0172] Specifically, in step S109, calculating and obtaining the amplitude and phase of the target signal to be extracted includes:

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

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

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

[0176] Specifically, after obtaining the input signal containing noise and the target signal to be extracted, it further includes preprocessing the input signal, including: after amplifying and filtering the input signal, obtaining the input signal that meets the preset A / D resolution, and obtaining the discrete sequence of the input signal through A / D sampling. The signal input channel of the digital lock-in amplifier is built with analog devices to complete signal preprocessing such as amplifying and filtering the input signal to be measured, and after obtaining the signal to be measured that meets the A / D resolution requirement, it is input into the microprocessor through A / D sampling to obtain a discrete sequence; while the reference input channel and the correlator both adopt internal implementation methods, that is, internal programming in the microprocessor is used. 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 dependence on low-pass filters, not only reducing the complexity of system design but also improving the speed and accuracy of signal processing. Moreover, through multi-stage processing in the frequency domain and time domain, the present invention can extract the amplitude and phase of signals more precisely, especially in low signal-to-noise ratio environments, where the advantages are more obvious. Compared with traditional fixed low-pass filters, the adaptive filter in the present invention can dynamically adjust filtering parameters according to real-time signals to optimize the filtering effect. FFT provides accurate spectrum analysis capabilities, can identify and remove noise at specific frequencies, ensure that the frequency components of the signal are purer, and thus optimize the calculation of amplitude and phase; through the combination of Kalman filtering and adaptive filtering, stable noise suppression effects can be maintained in different noise environments to ensure the stability and accuracy of signal estimation. Through multi-stage filtering and optimization algorithms, the present invention can improve the calculation efficiency while maintaining high-precision signal estimation, and is applicable to real-time signal processing scenarios. In summary, the present invention has significant advantages in terms of signal processing accuracy, real-time performance, and adaptability, solves some key technical problems faced by traditional digital lock-in amplifiers, and has good application prospects.

[0178] Referring to Figure 2 As shown, it is the main algorithm architecture diagram of a traditional lock-in amplifier, including an input signal channel, two reference signal channels with a 90-degree phase difference (sine and cosine), 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 signals at specific frequencies, which is crucial in the signal preparation stage. The present invention optimizes the extraction of the amplitude and phase of the subsequent target to be extracted based on this algorithm structure.

[0179] Based on the above embodiments, in the embodiments of the present invention, referring to Figure 3 As shown, it is the schematic diagram of the working process of the optimized digital lock-in amplifier. After Kalman filtering, fast Fourier transform (FFT), and adaptive filter processing, both 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 working process of the optimized digital lock-in amplifier used in the present invention includes:

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

[0181] The input signal x(t) contains the signal to be measured and noise. The goal is to distinguish between the two through processing. A sine wave is selected 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 to extract the amplitude and phase information from the input signal. This method is based on the basic principle of Fourier transform, in which a signal can be decomposed into sine and cosine components.

[0182] Refer to Figure 4 As shown, it is a schematic diagram of the signal input channel; the signal input channel of the digital lock-in amplifier is built with analog devices to complete signal preprocessing such as amplifying the input signal to be measured as attached Figure 4 As shown, after obtaining the signal to be measured that meets the A / D resolution requirement, it is sampled by A / D to obtain a discrete sequence and input into the microprocessor; while the reference input channel and the correlator are both implemented internally, that is, programmed inside the microprocessor. After the internal correlation operation is completed, the amplitude and initial phase are calculated, and the useful signal to be measured can be obtained.

[0183] The input signal selects or generates a composite signal x(t) that contains the signal to be measured and background noise. The target signal is usually a simple sine wave in the form of U 0 sin(ω 0 t + φ 0 ), where U 0 , ω 0 , φ 0 represent the amplitude, angular frequency, and phase of the signal respectively. The background noise μ(t) can be Gaussian white noise to simulate the interference in the actual environment.

[0184] x(t) = U 0 sin(ω 0 t + φ 0 ) + μ(t) = U 0 sin(2πf 0 t + θ) + μ(t);

[0185] After being phase-shifted by 90° through a phase shifter, two orthogonal reference signals xr1(t) = Ursin(ω 0 t) and the cosine reference signal xr2(t) = Urcos(ω 0 t) are formed. These two signals are used 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 the mixed information of the target signal and noise, and in this way, the useful signal components can be separated in subsequent steps. This is the key to eliminating noise using the orthogonality property. These two signals contain the amplitude and phase information of the original signal;

[0188]

[0189] The first term: and represent the DC component, reflecting the amplitude and phase of the signal.

[0190] The second term: and represent the high-frequency component with a frequency of 2ω, which needs to be filtered out.

[0191] The third term: U r μ(t)sin(ω 0 t + δ) and U r μ(t)cos(ω 0 t + δ) represent the mixing components introduced by noise, which are the product of the noise and the reference signal. Since the sine signal is periodic and not correlated with the noise signal, the integral of this term is 0.

[0192] Through the multiplication operation, the input signal is mixed with the reference signal, and the two generated signals I(t) and Q(t) contain the mixed information of the target signal and noise. This process is equivalent to shifting the input signal to the DC component, thus facilitating subsequent low-frequency filtering and processing. In this way, the 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] The Kalman filter calculates the optimal estimated value at the current moment through the prediction of the previous moment state prediction value, the current moment observation value, and the prediction error, and then predicts the next state. The signals I(t) and Q(t) obtained through PSD are:

[0195]

[0196] The Kalman filter gradually suppresses the high-frequency component with a frequency of 2ω through the 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 true signal.

[0197] The specific steps of the Kalman filter include:

[0198] ① Initialization:

[0199] ② Iteration steps (for each time instant k):

[0200] For I mixed : State prediction:

[0201] represents the predicted state estimate at time instant k, A represents the state transition matrix, which describes the state transition relationship of the system from time instant 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] State update:

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

[0206] Error covariance update:

[0207] P k|k is the iteration 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 passing through the Kalman filter becomes:

[0211]

[0212] The above calculation process is similarly applied to the channel output of the reference signal Q mixed (cosine wave) after a 90 - degree phase shift. The Q filtered signal after passing through the Kalman filter is:

[0213]

[0214] By processing I mixcd and Q mixcdThe signal filters out high-frequency components and some noise, making the filtered signal closer to the DC component of the target signal. 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 signals and noise environments, being 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 the accuracy and stability of the signal, enabling the digital lock-in amplifier to reliably extract the target signal even in a low signal-to-noise ratio environment.

[0216] S204: Perform FFT on the I and Q components after Kalman filtering. The purpose of FFT is to transform the time-domain signal to the frequency domain for 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 the fast Fourier transform FFT for frequency-domain analysis can effectively transform the signal from the time domain to the frequency domain, making component separation and analysis easier. By transforming the time-domain signal to the frequency domain through FFT, specific frequency components can be precisely selected and filtered out. Frequency-domain filtering provides high-resolution spectral 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 components of the 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 be manifested as high-frequency spectral components, while the DC component of the target signal will be concentrated at low frequencies.

[0230] By frequency-domain filtering, 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 cut-off frequency f cutoff , the high-frequency noise can be removed and only the low-frequency part of the signal can be 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 locking situation. The digital low-pass filter is essential 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 phase-locked amplifier and improve the anti-noise performance.

[0236] Then perform the 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] By performing the inverse Fourier transform IFFT to convert the filtered signal back to the time domain, the filtered time-domain signal is obtained. This processing method can effectively improve the signal-to-noise ratio of the signal, enabling the digital phase-locked amplifier to reliably extract the target signal even in a low signal-to-noise ratio environment.

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

[0243] The expressions of the signals I and Q after being processed through these steps are:

[0244]

[0245] After these signals are subjected to frequency-domain filtering and inverse Fourier transform, the main components of the target signal are retained, high-frequency noise is filtered out, and the accuracy and stability of the signal are improved.

[0246] S205: Perform adaptive filtering on the I and Q components after frequency-domain filtering to further suppress noise;

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

[0248]

[0249] The adaptive filter can better adapt to different signal and noise environments by dynamically adjusting the filter parameters, further suppress low-frequency noise, and improve the signal-to-noise ratio of the signal. The adaptive filter 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] Applied to I time_filtered and Q time_filtered For the I component I time_filtered (t) and the Q component Q time_filtered (t), an adaptive filter is applied for processing. Set the filter length M and the learning rate μ, and initialize the filter weight w i (0) = 0. For each time instant n, calculate the filter outputs I adaptive (n) and Q adaptive (n).

[0251] Calculate the filter output:

[0252]

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

[0254] Calculate the filter errors 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 the filter weights and

[0259]

[0260] where μ is the learning rate.

[0261] The signals I adaptive (t) and Q adaptive (t) after adaptive filtering are:

[0262]

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

[0264] Average the filtered signal to eliminate the residual low-frequency noise and extract the DC component. By calculating the mean values of the filtered I adaptive (t) and Q adaptive (t) to extract the DC component:

[0265]

[0266] Substitute the expression of I adaptive (t) to get:

[0267]

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

[0269]

[0270] Since is a constant, it can be taken 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 method for extracting the target signal based on the improved digital lock-in amplifier according to the present invention designs a new digital lock-in amplifier through a Kalman filter, a fast Fourier transform, and an adaptive filter; the adaptive filter can dynamically adjust the filtering parameters according to the real-time signal to optimize the filtering effect; the FFT provides accurate spectrum analysis capabilities, can identify and remove the noise of specific frequencies, ensures that the frequency components of the signal are purer, and further optimizes the calculation of the amplitude and phase; through the combination of the Kalman filter and the adaptive filter, it can maintain a stable noise suppression effect in different noise environments, ensuring the stability and accuracy of signal estimation; the present invention can more accurately extract the amplitude and phase of the signal through multi-stage processing in the frequency domain and the time domain, especially in the low signal-to-noise ratio environment, the advantage is more obvious. The present invention directly processes the product of the input signal and the reference signal by adopting a method based on time analysis, uses mathematical statistical methods and fast Fourier transforms to stabilize and extract the DC component of the signal, reduces the dependence on the low-pass filter, does not rely on the low-pass filter to obtain the DC component, can improve the performance of signal detection in the low signal-to-noise ratio environment, and avoids the bandwidth limitation problem brought by the traditional low-pass filter, not only reducing the complexity of system design, but also improving the speed and accuracy of signal processing, providing higher real-time performance and noise suppression capabilities.

[0277] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

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

[0279] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including an instruction means that implements the functions in the process Figure 1 one process or multiple processes and / or blocks Figure 1 specified in one block or multiple blocks.

[0280] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in the process Figure 1 one process or multiple processes and / or blocks Figure 1 specified in one block or multiple blocks.

[0281] Obviously, the above embodiments are merely examples given for clear illustration and are not limitations on the implementation manners. For those of ordinary skill 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 enumerate all the implementation manners here. And the obvious changes or modifications derived therefrom are still within the protection scope 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 filtering component signal and the cosine filtering 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 output by the filter is calculated adaptive (n) and the cosine adaptive signal 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.

Images