Quadratic Harmonic Signal Demodulation Method and System Based on Hilbert Transform and Differential Transform

Abstract

The present invention provides a method and system for demodulating second harmonic signals based on Hilbert transform and differential transform. The second harmonic signals of a TDLAS system are demodulated through two Hilbert transforms and one first-order derivative. This demodulation method does not require a reference signal, and the obtained second harmonic signals are the same as those obtained by the phase-locked demodulation method.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and particularly to a method and system for demodulating second harmonic signals based on Hilbert transform and differential transform. Background Art

[0002] In recent years, with the progress of technology and the development of the global economy, people's living standards have been significantly improved. While seeking development and enjoying a better life, people's utilization of natural resources has been increasing, resulting in corresponding environmental problems. Gas pollution is one of the many environmental problems, which brings particularly serious harm to people's living environment. For example, the frequent occurrence of coal mine accidents due to the excessive concentration of combustible gases such as methane, and the haze weather, air pollution, greenhouse effect, etc. caused by industrial manufacturing and vehicle exhaust emissions. Therefore, the detection of harmful gases has become an increasingly concerned topic for people.

[0003] Among many gas detection methods, the infrared absorption spectroscopy method is widely used to measure gas concentration due to its advantages such as high accuracy, fast response speed, and dynamic non-contact measurement. Lasers and detectors are the core components for measuring gas concentration by the infrared absorption spectroscopy method. Most gas molecules have characteristic absorption spectra in the infrared band. When the infrared light emitted by a laser irradiates the gas, infrared absorption occurs, and the light intensity will attenuate accordingly. The gas concentration is determined by measuring the change in light intensity through a detector. Tunable Diode Laser Absorption Spectroscopy (TDLAS) technology is an optical and spectroscopic measurement method that applies lasers to absorption spectroscopy measurement technology. Due to its characteristics such as high spectral resolution, high sensitivity, and good selectivity, it has become one of the effective methods for rapid and on-line analysis of trace gases. In particular, the second harmonic signal detection technology among them has been practically applied in the fields of atmospheric chemistry research and harmful gas monitoring. In a TDLAS system, the laser output light frequency is jointly excited by a triangular wave and a sine wave. The intensity of the second harmonic signal of the light intensity signal after passing through gas absorption is proportional to the gas concentration, and the detected gas concentration is calculated accordingly.

[0004] To obtain the second - harmonic signal related to the gas concentration, in the prior art, we use a lock - in amplifier to process the signal output by the detector. A lock - in amplifier is an amplifier that performs phase - sensitive demodulation on alternating signals using the correlation of signals. It is widely used in many scientific fields for weak - signal detection, such as optics, communication, electrochemistry, electronics, biomedicine, machinery, and fundamental physics, and is also widely used in gas detection. The core technology of the lock - in amplifier is correlation detection, which extracts useful signals by using the frequency and phase relationship between the measured signal and the reference signal. It can greatly suppress background noise, improve the signal - to - noise ratio, has high detection sensitivity, and has high flexibility and stability. In gas detection, the signal output by the detector is subjected to Fourier transform, and the lock - in amplifier is used to extract the required second - harmonic signal for gas - concentration detection.

[0005] In the prior art, in the gas detection of TDLAS technology, a lock - in amplifier is usually used to extract the second - harmonic signal related to the gas. That is, the demodulation of the TDLAS second - harmonic signal is mostly the lock - in amplification demodulation method in practical applications. However, the lock - in amplification demodulation requires a reference signal as input. Without accurately knowing the frequency and phase of the output optical intensity simultaneously, the second - harmonic signal cannot be correctly demodulated, which brings inconvenience to the demodulation of the second - harmonic signal.

[0006] Therefore, how to demodulate and obtain the TDLAS second - harmonic signal without knowing the frequency and phase of the output optical intensity is a technical problem that needs to be solved in the TDLAS detection technology. Summary of the Invention

[0007] To solve the above - mentioned technical problems, the present invention provides a method and system for demodulating the second - harmonic signal based on Hilbert transform and differential transform. For the TDLAS system that collects the laser modulated by a traditional triangular wave combined with a sine wave, a demodulation method combining double - low - pass Hilbert transform and the first - order derivative is used to demodulate the second - harmonic signal of the TDLAS system, and the TDLAS second - harmonic signal with the same waveform as the waveform demodulated by the lock - in amplification can be demodulated without a reference signal.

[0008] The first aspect of the embodiment of the present invention provides a method for demodulating a second harmonic signal based on Hilbert transform and differential transform, including the following steps: Step S1: Perform high-pass filtering on the transmitted light signal collected by the TDLAS system to obtain the AC component of the signal; Step S2: Perform Hilbert transform on the AC component of the signal, and jointly form the first analytic signal in the complex domain with the signal before and after the transform, take the modulus length of the first analytic signal, and perform low-pass filtering to obtain the envelope signal of the AC component of the signal; and Step S3: Perform differential transform on the envelope signal to obtain the first derivative of the envelope signal, perform Hilbert transform on the first derivative of the envelope signal, and jointly form the second analytic signal in the complex domain with the signal before and after the transform, take the modulus length of the second analytic signal, and perform low-pass filtering to obtain the second harmonic signal.

[0009] Optionally, the expression of the modulated laser signal v(t) in the TDLAS system in step S1 is: Where, is a triangular wave, scanning back and forth near the gas absorption peak; ω is the sine excitation frequency, whose value is much larger than the triangular wave scanning frequency; Δv is the sine excitation modulation amplitude; η is the initial phase of the sine excitation signal.

[0010] Optionally, the expression of the transmitted light signal I t (t) collected in the TDLAS system in step S1 is: Where, θ = (ωt + η); is the DC component of the transmitted light signal; A k (t) is the amplitude of the k-th harmonic, whose value changes with time t due to the triangular wave modulation of the laser output wavenumber scanning back and forth near the gas absorption peak, but the change frequency is much smaller than ω; is the phase shift introduced by the laser during the entire process from excitation to being collected.

[0011] Optionally, the expression of the AC component I S1 (t) obtained by high-pass filtering in step S1 is:

[0012]

[0013] Optionally, the expressions of the first analytic signal f1(t) obtained by Hilbert transform and the modulus length Abs[f1(t)] of the first analytic signal f1(t) in step S2 are respectively: f1(t) = I S1 (t) + jH[I S1 (t)], Abs[f1(t)] = ||f1(t)||, where, H[I S1 (t)] is I S1The Hilbert transform of (t), where "*" represents convolution and j is the imaginary unit; in step S2, the magnitude Abs[f1(t)] of the first analytic signal f1(t) is low-pass filtered to obtain the envelope signal E of the AC component of the signal. s2 (t).

[0014] Optionally, in step S3, the envelope signal is subjected to a differential transform to obtain the first derivative E S2 The expression for '(t) is: In step S3, the first derivative E S2 '(t) is subjected to a Hilbert transform to obtain the second analytic signal f2(t), and the expressions for the magnitude Abs[f2(t)] of the second analytic signal f2(t) are: f2(t) = E s2 '(t) + jH[E s2 '(t)], Abs[f2(t)] = ||f2(t)|| where H[E s2 '(t)] is the Hilbert transform of E' s2 (t), "*" represents convolution, and j is the imaginary unit; in step S3, the magnitude Abs[f2(t)] of the second analytic signal f2(t) is low-pass filtered to obtain the second harmonic signal A2(t).

[0015] Another aspect of the embodiments of the present invention provides a second harmonic signal demodulation system based on Hilbert transform and differential transform, including: a high-pass filter for high-pass filtering the transmitted light signal collected by the TDLAS system to obtain the AC component of the signal; a first Hilbert transformer for performing a Hilbert transform on the AC component of the signal and jointly forming the first analytic signal in the complex domain before and after the transform, and taking the magnitude of the first analytic signal; a first low-pass filter for low-pass filtering the magnitude of the first analytic signal to obtain the envelope signal of the AC component of the signal; a differential transformer for performing a differential transform on the envelope signal to obtain the first derivative of the envelope signal; a second Hilbert transformer for performing a Hilbert transform on the first derivative of the envelope signal and jointly forming the second analytic signal in the complex domain before and after the transform, and taking the magnitude of the second analytic signal; and a second low-pass filter for low-pass filtering the magnitude of the second analytic signal to obtain the second harmonic signal.

[0016] Optionally, the expression for the modulated laser signal v(t) in the TDLAS system is: The expression for the collected transmitted light signal I t (t) is: The expression for the AC component I S1 (t) of the signal after being processed by the first high-pass filter is: Among them, is a triangular wave, Δv is the modulation amplitude of the sine excitation, ω is the sine excitation frequency, t is time, η is the initial phase of the sine excitation signal, θ = (ωt + η), is the DC component of the transmitted optical signal, A k (t) is the amplitude of the k-th harmonic, is the phase shift introduced by the laser during the entire process from excitation to acquisition.

[0017] Optionally, the expressions of the first analytic signal f1(t) and its modulus Abs[f1(t)] after being processed by the first Hilbert transformer are respectively: f1(t) = I S1 (t) + jH[I S1 (t)], Abs[f1(t)] = ||f1(t ) ||, where H[I S1 (t)] is the Hilbert transform of I S1 (t), "*" represents convolution, and j is an imaginary number; the modulus Abs[f1(t)] of the first analytic signal f1(t) obtains the envelope signal E s2 (t) of the AC component of the signal after being processed by the first low-pass filter.

[0018] Optionally, the expression of the first derivative E S2 ′(t) after being processed by the differential transformer is: The expressions of the second analytic signal f2(t) and its modulus Abs[f2(t)] after being processed by the second Hilbert transformer are respectively: f2(t) = E s2 ′(t) + jH[E s2 ′(t)], Abs[f2(t)] = ||f2(t)||, where H[E s2 ′(t)] is the Hilbert transform of E′ s2 (t), "*" represents convolution, and j is an imaginary number; the modulus Abs[f2(t)] of the second analytic signal f2(t) obtains the second harmonic signal A2(t) after being processed by the second low-pass filter.

[0019] Compared with the prior art, the second harmonic signal demodulation method and system based on Hilbert transform and differential transform proposed by the present invention demodulate the second harmonic signal of the TDLAS system through two Hilbert transforms and one first derivative. This demodulation method does not require a reference signal, and the obtained second harmonic signal is the same as the demodulation result obtained by the phase-locked demodulation method. Description of the Drawings

[0020] Figure 1Schematic diagram of the process of a second-harmonic signal demodulation method based on Hilbert transform and differential transform according to an embodiment of the present invention;

[0021] Figure 2 Schematic diagram of the structure of a second-harmonic signal demodulation system based on Hilbert transform and differential transform according to an embodiment of the present invention. Specific embodiments

[0022] In order to make the objectives and advantages of the present invention more clearly understood, the present invention will be further described below in conjunction with embodiments; it should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0023] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are only used to explain the technical principle of the present invention and do not limit the protection scope of the present invention.

[0024] On the one hand, an embodiment of the present invention proposes a second-harmonic signal demodulation method based on Hilbert transform and differential transform, referring to Figure 1 , Figure 1 Schematic diagram of the process of a second-harmonic signal demodulation method based on Hilbert transform and differential transform according to an embodiment of the present invention. The method includes the following steps:

[0025] Step S1: Perform high-pass filtering on the transmitted light signal collected by the TDLAS system to eliminate the part modulated by the triangular wave in the signal and obtain the AC component of the signal;

[0026] Step S2: Perform Hilbert transform on the AC component of the signal in step S1, and jointly form the first analytic signal in the complex domain with the signal before and after the transform. Take the modulus of the first analytic signal and perform low-pass filtering to obtain the envelope signal of the AC component of the signal; and

[0027] Step S3: Perform differential transform on the envelope signal in step S2 to obtain the first derivative of the envelope signal. Perform Hilbert transform on the first derivative of the envelope signal, and jointly form the second analytic signal in the complex domain with the signal before and after the transform. Take the modulus of the second analytic signal and perform low-pass filtering to obtain the second-harmonic signal of the TDLAS system.

[0028] The specific demodulation process of the second-harmonic signal of the TDLAS system will be described below.

[0029] TDLAS stands for Tunable Diode Laser Absorption Spectroscopy. Because of the good monochromaticity of the laser and its very high optical power spectral density, the light source used in TDLAS technology is a tunable diode laser source, which has very good tunable characteristics. The tunable semiconductor laser using this technology emits a single narrow-band laser frequency to scan a certain gas absorption line. The frequency of the light wave emitted by the laser is proportional to the injected driving current. After stabilizing the laser frequency (or wavelength) emitted by the laser at the absorption peak of the gas to be measured, the current is tuned to change the frequency by changing the injected current so that it gradually scans across the absorption peak of the gas. After the gas performs "frequency selection" absorption on it, the light intensity will decay accordingly. Analyze the attenuation amount at the detector receiving end to obtain the gas concentration.

[0030] When measuring the gas concentration by the method based on TDLAS technology, the light intensity signal received by the detector is very small compared to the large background signal, which is not conducive to directly measuring the concentration. To improve its sensitivity and accuracy, a sine wave modulation technology is often added to modulate the injected current of the light source.

[0031] In the embodiment of the present invention, the laser is excited by a triangular wave combined with a sine wave, and the output optical wave number is expressed as:

[0032]

[0033] Among them, is a triangular wave, which scans back and forth near the gas absorption peak; ω is the sine excitation frequency, and its value is much larger than the triangular wave scanning frequency; Δv is the sine excitation modulation amplitude; η is the initial phase of the sine excitation signal. For the sake of simplified expression, (ωt + η) will be uniformly represented as "θ" in the following text.

[0034] The transmitted laser light passing through the gas absorption is then obtained through an optoelectronic acquisition system to obtain a transmitted light signal, which is expressed as the superposition of many harmonic components:

[0035]

[0036] Among them, is the DC component of the transmitted light signal; A k (t) is the amplitude of the k-th harmonic, and its value changes with time t because the laser output wave number is modulated by a triangular wave and scans back and forth near the gas absorption peak, but the change frequency is much smaller than ω; is the phase shift introduced by the laser during the entire process from excitation to optoelectronic acquisition.

[0037] Step S1: Perform high-pass filtering on the transmitted light signal collected by the TDLAS system to obtain the signal AC component I S1 (t):

[0038]

[0039] Step S2: Perform Hilbert transform on the AC component of the optical signal. The analytical signal f1(t) of the Hilbert transform is expressed as:

[0040] f1(t) = I S1 (t) + jH[I S1 (t)] (4)

[0041] H[I S1 (t)] is the Hilbert transform of I S1 (t), expressed as "*" represents convolution, and j is an imaginary number;

[0042] Obtain the modulus Abs[f1(t)] of the analytical signal f1(t) according to Abs[f1(t)] = ||f1(t)||, and perform low-pass filtering on Abs[f1(t)] to obtain the envelope signal E s2 (t);

[0043] Step S3: Perform differential transformation on E S2 (t) to obtain its first derivative E S2 ′(t)

[0044]

[0045] Perform Hilbert transform on E s2 ′(t). The analytical signal f2(t) of the Hilbert transform is expressed as:

[0046] f2(t) = E s2 ′(t) + jH[E s2 ′(t)] (6)

[0047] H[E s2 ′(t)] is the Hilbert transform of E′ s2 (t), expressed as "*" represents convolution, and j is an imaginary number;

[0048] Obtain the modulus Abs[f2(t)] of the analytical signal f2(t) according to Abs[f2(t)] = ||f2(t)||, and perform low-pass filtering on Abs[f2(t)] to obtain A2(t), finally completing the demodulation of the second harmonic signal of the TDLAS system.

[0049] On the other hand, an embodiment of the present invention proposes a second harmonic signal demodulation system based on Hilbert transform and differential transform. Refer to Figure 2 , Figure 2Schematic diagram of the structure of a quadratic harmonic signal demodulation system based on Hilbert transform and differential transform according to an embodiment of the present invention. The system includes: a high-pass filter, a first Hilbert transformer, a first low-pass filter, a differential transformer, a second Hilbert transformer, and a second low-pass filter. Among them, the high-pass filter is used to perform high-pass filtering on the transmitted light signal collected by the TDLAS system to obtain the AC component of the signal; the first Hilbert transformer is used to perform Hilbert transform on the AC component of the signal, and jointly form the first analytic signal in the complex domain before and after the transform, and take the modulus length of the first analytic signal; the first low-pass filter is used to perform low-pass filtering on the modulus length of the first analytic signal to obtain the envelope signal of the AC component of the signal; the differential transformer is used to perform differential transform on the envelope signal to obtain the first derivative of the envelope signal; the second Hilbert transformer is used to perform Hilbert transform on the first derivative of the envelope signal, and jointly form the second analytic signal in the complex domain before and after the transform, and take the modulus length of the second analytic signal; the second low-pass filter is used to perform low-pass filtering on the modulus length of the second analytic signal to obtain the quadratic harmonic signal.

[0050] The expression of the modulated laser signal v(t) in the TDLAS system is:

[0051]

[0052] The transmitted light signal I t (t) after acquisition has the following expression:

[0053]

[0054] The AC component I S1 (t) of the signal after being processed by the first high-pass filter has the following expression:

[0055]

[0056] Among them, is a triangular wave, Δv is the sine excitation modulation amplitude, ω is the sine excitation frequency, t is time, η is the initial phase of the sine excitation signal, θ = (ωt + η), is the DC component of the transmitted light signal, A k (t) is the amplitude of the k-th harmonic, is the phase shift introduced by the laser during the entire process from excitation to acquisition.

[0057] The expressions of the first analytic signal f1(t) and its modulus length Abs[f1(t)] after being processed by the first Hilbert transformer are respectively:

[0058] f1(t) = I S1 (t) + jH[I S1 (t)] (10)

[0059]

[0060] Abs[f1(t)] = ||f1(t)|| (12)

[0061] where H[I S1 (t)] is the Hilbert transform of I S1 (t), "*" represents convolution, and j is the imaginary unit;

[0062] The envelope signal E s2 (t) of the AC component of the signal is obtained after processing the magnitude Abs[f1(t)] of the first analytic signal f1(t) through the first low-pass filter. The expression for the first derivative E S2 ′(t) after processing by the differential transducer is:

[0063]

[0064] The expressions for the second analytic signal f2(t) and its magnitude Abs[f2(t)] after processing by the second Hilbert transducer are respectively:

[0065] f2(t) = E s2 ′(t) + jH[E s2 ′(t)] (14)

[0066]

[0067] Abs[f2(t)] = ||f2(t)|| (16)

[0068] where H[E s2 ′(t)] is the Hilbert transform of E′ s2 (t), "*" represents convolution, and j is the imaginary unit;

[0069] The second harmonic signal A2(t) is obtained after processing the magnitude Abs[f2(t)] of the second analytic signal f2(t) through the second low-pass filter.

[0070] In summary, for the second harmonic signal demodulation method and apparatus proposed by the present invention, first, the TDLAS optoelectronic signal is high-pass filtered to obtain a sine wave modulation signal, then, the Hilbert transform is performed on the sine wave modulation signal and low-pass filtered to obtain the envelope of the signal, and finally, the first derivative of the signal envelope is calculated, the Hilbert transform is performed on the first derivative of the envelope, and the second harmonic signal of the TDLAS system is output through low-pass filtering. Compared with the traditional demodulation algorithm, the TDLAS second harmonic demodulation method of the present invention does not require a reference signal.

[0071] The present invention has been described by the above related embodiments. However, the above embodiments are only examples for implementing the present invention. In addition, the technical features involved in different embodiments of the present invention described above can be combined with each other as long as they do not conflict with each other. It must be pointed out that the disclosed embodiments do not limit the scope of the present invention. On the contrary, modifications and refinements made without departing from the spirit and scope of the present invention fall within the scope of patent protection of the present invention.

Claims

1. A demodulation method for second harmonic signals based on Hilbert transform and differential transform, characterized in that, It includes the following steps: Step S1: Perform high-pass filtering on the transmitted light signal collected by the TDLAS system to obtain the signal AC component; Step S2: Perform Hilbert transform on the signal AC component, and jointly form the first analytic signal in the complex domain with the signals before and after the transform. Take the modulus length of the first analytic signal and perform low-pass filtering to obtain the envelope signal of the signal AC component; And Step S3: Perform differential transform on the envelope signal to obtain the first derivative of the envelope signal. Perform Hilbert transform on the first derivative of the envelope signal, and jointly form the second analytic signal in the complex domain with the signals before and after the transform. Take the modulus length of the second analytic signal and perform low-pass filtering to obtain the second harmonic signal; The expressions of the first analytic signal f1(t) obtained by Hilbert transform in Step S2 and the modulus length Abs[f1(t)] of the first analytic signal f1(t) are respectively: f1(t) = I S1 (t) + jH[I S1 (t)], Abs[f1(t)] = ||f1(t)||, where H[I S1 (t)] is the Hilbert transform of I S1 (t), "*" represents convolution, and j is the imaginary unit; In step S2, the magnitude Abs[f1(t)] of the first parsed signal f1(t) is low-pass filtered to obtain the envelope signal E of the AC component of the signal; s2 (t); In step S3, the envelope signal is subjected to a differential transformation to obtain the first derivative E S2 The expression of ′(t) is as follows: In step S3, the first derivative E S2 ′(t) is subjected to Hilbert transform to obtain the second analytic signal f2(t), and the expressions for taking the modulus length Abs[f2(t)] of the second analytic signal f2(t) are respectively: f2(t) = E s2 ′(t) + jH[E s2 ′(t)], Abs[f2(t)] = ||f2(t)||, where, H[E s2 ′(t)] is the Hilbert transform of E′ s2 (t), "*" represents convolution, and j is the imaginary unit; In Step S3, perform low-pass filtering on the modulus length Abs[f2(t)] of the second analytic signal f2(t) to obtain the second harmonic signal A2(t).

2. The quadratic harmonic signal demodulation method based on Hilbert transform and differential transform according to claim 1, characterized in that, The expression of the modulated laser signal v(t) in the TDLAS system in Step S1 is: Among them, is a triangular wave that scans back and forth near the gas absorption peak; ω is the sine excitation frequency, whose value is much greater than the triangular wave scanning frequency; Δν is the sine excitation modulation amplitude; η is the initial phase of the sine excitation signal.

3. The quadratic harmonic signal demodulation method based on Hilbert transform and differential transform according to claim 2, wherein The collected transmitted light signal I in the TDLAS system in step S1 t (t) is expressed as: where θ = (ωt + η); is the DC component of the transmitted optical signal; A k (t) is the amplitude of the k-th harmonic, whose value changes with time t because the laser output wavenumber is reciprocally scanned near the gas absorption peak through triangular wave modulation, but the change frequency is much smaller than ω; is the phase shift introduced by the laser during the entire process from excitation to acquisition.

4. The method for demodulating a second harmonic signal based on Hilbert transform and differential transform according to claim 3, wherein The AC component I of the signal obtained by high-pass filtering in step S1 S1 (t) is expressed as:

5. A quadratic harmonic signal demodulation system based on Hilbert transform and differential transform, characterized in that, It includes: The first high-pass filter is used to perform high-pass filtering on the transmitted light signal collected by the TDLAS system to obtain the signal AC component; The first Hilbert transformer is used to perform Hilbert transform on the signal AC component, and jointly form the first analytic signal in the complex domain with the signals before and after the transform, and take the modulus length of the first analytic signal; The first low-pass filter is used to perform low-pass filtering on the modulus length of the first analytic signal to obtain the envelope signal of the signal AC component; The differential transformer is used to perform differential transform on the envelope signal to obtain the first derivative of the envelope signal; The second Hilbert transformer is used to perform Hilbert transform on the first derivative of the envelope signal, and jointly form the second analytic signal in the complex domain with the signals before and after the transform, and take the modulus length of the second analytic signal; And The second low-pass filter is used to perform low-pass filtering on the modulus length of the second analytic signal to obtain the second harmonic signal.

6. The quadratic harmonic signal demodulation system based on Hilbert transform and differential transform according to claim 5, characterized in that, The expression of the modulated laser signal ν(t) in the TDLAS system is: The transmitted light signal I after collection t (t) is expressed as: The AC component I of the signal after being processed by the first high-pass filter S1 (t) is expressed as: Among them, is a triangular wave, Δν is the modulation amplitude of the sine excitation, ω is the sine excitation frequency, t is time, η is the initial phase of the sine excitation signal, θ = (ωt + η), is the DC component of the transmitted optical signal, A k (t) is the amplitude of the k-th harmonic, is the phase shift introduced by the laser during the entire process from excitation to acquisition.

7. The quadratic harmonic signal demodulation system based on Hilbert transform and differential transform according to claim 6, wherein The expressions of the first analytic signal f1(t) processed by the first Hilbert transformer and its modulus length Abs[f1(t)] are respectively: f1(t) = I S1 (t) + jH[I S1 (t)], Abs[f1(t)] = ||f1(t)||, where, H[I S1 (t)] is the Hilbert transform of I S1 (t), "*" represents convolution, and j is the imaginary unit; The envelope signal E(t) of the AC component of the signal is obtained after the magnitude Abs[f1(t)] of the first analysis signal f1(t) is processed by the first low-pass filter. s2 (t).

8. The quadratic harmonic signal demodulation system based on Hilbert transform and differential transform according to claim 7, wherein The first derivative E S2 ′(t) after being processed by the differential transducer has the following expression: The expressions of the second analytic signal f2(t) processed by the second Hilbert transformer and its modulus length Abs[f2(t)] are respectively: f2(t) = E s2 ′(t) + jH[E s2 ′(t)], Abs[f2(t)] = ||f2(t)||, where, H[E s2 ′(t)] is the Hilbert transform of E′ s2 (t), "*" represents convolution, and j is the imaginary unit; The modulus length Abs[f2(t)] of the second analytic signal f2(t) is processed by the second low-pass filter to obtain the second harmonic signal A2(t).

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