A wavelength modulation spectroscopy harmonic extraction method based on single-step empirical mode decomposition

Abstract

The application provides a wavelength modulation spectrum harmonic extraction method based on single-step empirical mode decomposition, which is used for high-order harmonic component extraction of wavelength modulation method in laser absorption spectrum technology. The method mainly comprises the following steps: firstly, according to the wavelength modulation method, a wavelength modulation spectrum signal sequence after passing through a measured object is acquired; then, single-step empirical mode decomposition is used to extract a resolvable expression component in the original wavelength modulation spectrum signal; finally, the resolvable expression of the wavelength modulation spectrum signal is acquired, all harmonic components of the wavelength modulation spectrum signal are obtained according to a Fourier series formula, and temperature concentration and other parameters are further obtained. The application proposes a new harmonic extraction idea, all harmonic components can be directly extracted once by using absorption spectrum data, the original absorption spectrum data does not need to be repeatedly used for calculation, the operation is simple, and the application has a wide application prospect in the field of dynamic absorption spectrum testing such as combustion diagnosis.

Description

Technical Field

[0001] This invention relates to a method for extracting signal harmonics, and more particularly to a method for extracting harmonics from wavelength modulation spectra based on single-step empirical mode decomposition, belonging to the field of laser absorption spectroscopy and gas parameter measurement technology. Background Technology

[0002] Tunable Diode Laser Absorption Spectroscopy (TDLAS) utilizes a narrowband laser to scan the absorption spectrum of a gas. Based on the principle of stimulated absorption caused by the interaction between photons and gas molecules, it obtains the absorption rate of the gas molecules to the laser, and then calculates parameters such as the temperature of the gas absorbing along the laser path. Since the 1970s, this technology has been applied to the measurement of parameters in combustion fields. It has advantages such as being non-invasive, highly selective, capable of detecting multiple parameters, having strong environmental adaptability, and being suitable for industrial applications. It has significant application value and development prospects in the field of gas parameter monitoring.

[0003] The main methods for implementing TDLAS include Direct Absorption Spectroscopy (DAS) and Wavelength Modulation Spectroscopy (WMS). Both methods aim to accurately obtain the gas absorption line function, thereby enabling the inversion of parameters such as temperature and concentration of the analyte gas. DAS directly fits the ratio of transmitted light intensity to incident light intensity to obtain the gas's absorptivity line function. The fitted absorptivity line function includes information such as the temperature, concentration, and pressure of the analyte gas. However, this method is susceptible to factors such as particulate matter concentration, laser intensity fluctuations, and spectral line overlap under high pressure, leading to increased measurement errors. Direct absorption is more suitable for conditions with strong absorption. In 2016, Zhanrong Zhang et al. published a paper titled "Detection of gas temperature using a distributed feed-back laser at O2 absorption wavelength 760 nm" in the *Journal of Optical Technology*, Volume 83, page 673. This paper used the direct absorption method to measure the gas temperature in a tube furnace within the temperature range of 300-900 K. The accuracy of the temperature measurement at low temperatures was superior to that at high temperatures. The direct absorption method is intuitive and simple, and can extract the complete absorption spectrum; however, it has weak noise immunity and is not suitable for harsh industrial environments. The Wavelength Modulation and Measurement (WMS) method typically involves using a current-controlled laser with a sinusoidal signal superimposed on a sawtooth wave to emit a high-frequency modulated scanning laser. The acquired wavelength-modulated spectral signal is then demodulated to obtain the corresponding harmonics, thereby measuring absorption parameters such as gas temperature and concentration. In WMS, the measured information is high-frequency modulated and shifted to the high-frequency region, which suppresses background interference to some extent.In their 2019 paper, "Demonstration of non-absorbing interference rejection using wavelength modulation spectroscopy in high-pressure shock tubes," published in *Applied Physics B*, Volume 125, No. 9, Wei Wei et al. conducted experiments on the non-absorbing interference suppression capability of wavelength modulation spectroscopy. They directly compared the measurements obtained using the wavelength modulation method with those obtained using the direct absorption method, evaluating the WMS detection system under reflected shock pressures of 3.5 atm, 8.5 atm, and 18 atm. The results showed that compared to parallel DAS measurements, the signal-to-noise ratio of the WMS detection system was improved, increasing from 37.5 dB, 18.4 dB, and 11.5 dB to 44 dB, 33 dB, and 17.5 dB, respectively. Therefore, the WMS method has stronger noise immunity and a lower detection limit than DAS, making it more suitable for detecting gas parameters under conditions of low absorption.

[0004] Currently, wavelength modulation methods for calculating gas parameters based on higher harmonics mainly include single-harmonic and multi-harmonic methods. The single-harmonic method primarily utilizes a single higher harmonic, such as the first or second harmonic, of the wavelength-modulated spectral signal to obtain gas parameters. Adam J. Reid et al., in their 1981 paper "Second-harmonic detection with tunable diode lasers—comparison of experiment and theory" published in the *Journal of Applied Physics*, Vol. 26, p. 203, used wavelength modulation to perform high-frequency modulation on the narrowband laser scanning process. They used the second harmonic of the high-frequency signal to calculate the gas absorbance and extract gas parameters. This method effectively reduced background interference in the measurement system, improved the measurement accuracy of TDLAS, and can be used for absorption coefficients in the range of 10⁻⁶. -5 ~10 -6 m -1The paper "VCSEL-Based atmospherictrace gas sensor using first harmonic detection," published by Lijuan Lan et al. in IEEE Sensors Journal, Volume 19, page 4923, 2019, utilizes the first harmonic of wavelength-modulated spectral signals and employs a vertical-cavity surface-emitting laser to measure the concentrations of carbon dioxide and water in the atmosphere. The developed system separates and eliminates residual amplitude modulation signals from the harmonic signals. Based on Allen's variance analysis, wide-wavelength scanning improves measurement accuracy, ultimately achieving a first harmonic detection accuracy approximately twice that of traditional second harmonic detection. The paper "Wavelength modulation spectroscopy by employing the first harmonic phase angle method," published by Chenguang Yang et al. in *Optics Express*, Volume 27, page 12137, 2019, employs a first harmonic phase angle method that is unaffected by laser intensity and phase. It fully utilizes the first harmonic for analysis, and the results show that this method achieves higher detection sensitivity than the traditional 2f / 1f method under conditions of high modulation frequency or limited modulation amplitude, such as strong turbulence or high pressure environments. Generally, single-harmonic methods use only one higher harmonic, are easily affected by background noise, and require calibration of known gases when calculating gas parameters, increasing system complexity. Therefore, research is needed on obtaining gas absorption parameter information through multi-harmonic analysis in waveguide microscopy (WMS). Among these methods, the calibration-free first harmonic normalized second harmonic method, i.e., the 2f / 1f method, is the most widely used in WMS, offering advantages such as strong noise immunity and no need for on-site calibration. In recent years, many scholars have also used combinations of other higher harmonics to measure gas parameters.The paper "A new RAM normalized 1f-WMS technique for the measurement of gas parameters in harsh environments and a comparison With 2f / 1f" published by Abhishek Upadhyay et al. in IEEE Photonics Journal, Volume 1, page 99, 2018, introduces a calibration-free first harmonic (1f) wavelength modulation spectroscopy technique for measuring gas component parameters. In this technique, the total amplitude of the 1f-WMS signal is normalized by one component of the 1f residual amplitude modulated signal. This method retains the advantages of the traditional nf / 1f method, can accurately recover gas parameters without being affected by background signals, and does not require background normalization under high pressure or high modulation coefficients. In their 2020 paper "A Method for Recovering Absorption Rate Functions Based on Even Harmonics," published in *Laser & Infrared*, Vol. 50, p. 293, Zhou Peili et al. proposed a method for recovering absorption spectral patterns using even harmonic components of wavelength-modulated signals. This method constructs the relationship between the absorption spectral pattern and the higher harmonics of the modulation signal based on the Taylor expansion of the absorption spectral pattern. However, it is limited by the conditions of the Taylor expansion, namely, an approximation under small modulation. As can be seen, WMS (Wavelength Modulation Measurement System) measures gas parameters based on multiple harmonics extracted from wavelength-modulated spectral signals. The accuracy and convenience of harmonic extraction significantly impact the measurement process and results.

[0005] To address the harmonic extraction problem, most current research employs lock-in amplification (LIA) technology for extracting multiple harmonics. Whether it's offline signal harmonic extraction based on software algorithms or online demodulation based on hardware LIA amplifiers, LIA technology is widely used in WMS (Wireless Management System). The paper "An FPGA-based lock-in detection system to enable chemical species tomography using TDLAS," published by Andrea Chighine et al. at the 2015 IEEE International Conference on Imaging Systems and Techniques, introduces the design, implementation, and testing of a small, low-cost, all-digital signal recovery system for TDLAS. Based on a field-programmable gate array (FPGA) digital lock-in amplifier (DLIA) combined with wavelength modulation spectroscopy, it demodulates and extracts the first harmonic (1f) and second harmonic (2f) signals of carbon dioxide characteristics in the 1997.2 nm spectral range. A comparative experiment was conducted between the DLIA and a traditional rack-mount commercial lock-in amplifier. The comparison between the two systems showed good consistency, verifying the feasibility of the method and demonstrating its potential for expansion to large-scale multi-channel systems for chemical species tomography. The paper "Self-calibrated multiharmonic CO2 sensor using VCSEL for urban in situ measurement," published by Lijuan Lan et al. in 2019 in IEEE Transactions on Instrumentation and Measurement, Volume 68, page 1140, describes a self-calibrated multiharmonic measurement system. Using LabVIEW software, they developed a lock-in amplification program to simultaneously extract multiple harmonics from the wavelength modulation spectral signal for CO2 and H2O concentration measurements. They found that compared to traditional second-harmonic detection, using multiple higher-order harmonic components can improve system accuracy by two to three times, and first to third harmonics are sufficient to minimize Allan bias. However, the lock-in amplification technology requires a reference signal and a low-pass filtering algorithm, and its hardware implementation is resource-intensive.

[0006] Therefore, in addition to the mature and widely used lock-in amplification technology, harmonic extraction methods based on Fourier analysis and Hilbert-Huang transform have also been studied for harmonic extraction in WMS. Chinese patent CN109696415A, "An Online Measurement Method for Gas Absorbency Based on Fast Fourier Transform" (patent number: 201910036652.3), proposes an online measurement method for gas absorbability based on fast Fourier transform. This method uses a data acquisition card to digitize the light intensity signal detected by the photodetector and then performs a fast Fourier transform to obtain the high-order harmonic signals of the relevant wavelength modulation signal. The paper "TDLAS-WMS second harmonic detection based on spectral analysis," published by Chunlei Jiang et al. in *Review of Scientific Instruments*, Volume 89, page 08316, 2018, uses spectral analysis to obtain the second harmonic component in the frequency domain through a rectangular window. Experiments show that the relative detection error of this method is 3%. Compared with the lock-in amplification method, this method does not require a reference signal and low-pass filtering algorithm, simplifying the data processing for harmonic extraction. Although Fourier transform-based harmonic extraction methods simplify the data processing to some extent, the resulting spectral leakage effect can also affect the harmonic extraction results. Furthermore, for the extraction of multiple harmonics, it is necessary to repeatedly select different frequency domain windows. The paper "TDLAS second harmonic demodulation based on Hilbert transform," published by Junfeng Wu et al. in PLOS One, Volume 17, page 0278724 in 2022, proposes a TDLAS second harmonic demodulation method based on the Hilbert transform. This method does not require a reference signal and can easily obtain the second harmonic of the TDLAS signal. It is convenient to operate and highly efficient. Simulation analysis of the measurement error under different absorbance values ​​shows that when the absorbance is below 3%, the absolute error of the second harmonic remains within 1%. However, the harmonic extraction method based on the Hilbert transform uses the approximate condition that the second harmonic is much smaller than the first harmonic under low absorption conditions, which is not applicable to other absorption conditions. Furthermore, this method has limitations in extracting other higher harmonics and fails to achieve the extraction of multiple harmonics.

[0007] In summary, accurate and rapid extraction of multiple harmonics is crucial for subsequent gas parameter measurements in WMS. This invention proposes a wavelength modulation spectrum harmonic extraction method based on single-step empirical mode decomposition (EMD) to accurately extract multiple harmonics from a wavelength modulation spectral signal in a single operation. The method mainly consists of three steps: First, using the wavelength modulation method, the wavelength modulation spectral signal sequence after passing through the measured object is obtained; then, single-step EMD is used to extract the analyzable components from the original wavelength modulation spectral signal; finally, the precise analytical expression of the wavelength modulation spectral signal is calculated, and all harmonics of the wavelength modulation spectral signal are obtained using the Fourier series formula. This method fully utilizes the good noise resistance and analyzable signal expression characteristics of EMD, combined with the Fourier series expansion formula, to simultaneously obtain multiple harmonic components of the wavelength modulation spectral signal without reusing the original absorption spectral signal. This provides a novel harmonic extraction method with broad application prospects in the field of laser absorption spectroscopy gas parameter measurement. Summary of the Invention

[0008] (a) Technical problems to be solved

[0009] The purpose of this invention is to provide a harmonic extraction method for wavelength modulation spectra based on single-step empirical mode decomposition, which solves the problem of multiple harmonic extraction in wavelength modulation methods in laser absorption spectroscopy. Based on single-step empirical mode decomposition, an accurate analytical expression of the wavelength modulation spectrum signal is given, and all its harmonics are obtained by combining the Fourier series formula. When calculating multiple harmonics, it is not necessary to reuse the original data, which provides a new approach to harmonic extraction and has broad application prospects.

[0010] (II) Technical Solution

[0011] This invention, namely a wavelength modulation spectrum harmonic extraction method based on single-step empirical mode decomposition, mainly includes the following steps:

[0012] Step 1: Obtain the wavelength modulation spectral signal sequence. Based on the wavelength modulation method in laser absorption spectroscopy, a current signal modulated by a sawtooth wave superimposed with a high-frequency sine wave is injected into the laser control module to drive the distributed feedback laser to emit scanning laser light. By changing the injected current, the laser wavelength and intensity can be tuned near the center wavelength. The incident laser wavenumber ν(t) and intensity I... i (t) are respectively represented as:

[0013]

[0014]

[0015] in, It is the scanning wavenumber of the incident laser that changes relatively slowly before sinusoidal modulation, where a is the sinusoidal modulation amplitude, and f is the wavenumber of the incident laser. m It is the sinusoidal modulation frequency; ρ is the incident laser intensity before sinusoidal modulation, and b is the intensity modulation amplitude coefficient. This is the phase difference between wavelength modulation and light intensity modulation. When the wavelength-modulated incident laser passes through the flame being measured, specific gas molecules absorb it, and the transmittance τ(ν) varies periodically due to the high-frequency sinusoidal modulation of the incident laser wavenumber. Therefore, its Fourier series expansion can be obtained as follows:

[0016]

[0017] in, These are the coefficients of the k-th order Fourier component after performing a Fourier series expansion on τ(ν). The transmitted light intensity I can be obtained from the transmittance. t (t) is:

[0018]

[0019] Among them, H k (t) and These represent the amplitude and phase of the k-th harmonic of the transmitted light intensity, respectively. In the case of weak absorption, i.e., the gas absorptivity α... v When (t) < 0.05, the solution H k (t) (usually the first or second harmonic) can be obtained The mapping relationship with the temperature T of the measured gas is crucial, therefore, the extraction of harmonics from the transmitted light intensity signal is essential in the wavelength modulation method. The transmitted light intensity is converted into an electrical signal E(t) by the photodetector as follows:

[0020]

[0021] Where G is the photoelectric conversion coefficient of the detector, D(t) is the interference noise of the entire process, and the signal E(t) is converted into a digital signal sequence X(n) by the data acquisition module (n is the time series coordinate of the sampling point). N is the total number of sampling points, f s (Sampling rate).

[0022] Step 2: Utilize single-step empirical mode decomposition to extract the analyzable components from the original wavelength-modulated spectral signal. The specific process is as follows:

[0023] First, initialize k=1, let the input signal x(n) be a wavelength modulation spectral signal sequence X(n), and detect and obtain its set of maxima P. max and the set of minimum points P min ;

[0024] Then, cubic spline interpolation is used to apply the upper envelope set L. max and the lower envelope set L min Interpolation fitting is performed to obtain the upper and lower envelope sequences e of the input signal sequence. max (n), e min (n), where:

[0025]

[0026]

[0027] According to the principle of cubic spline interpolation, the two adjacent maxima or minima (t) in the upper and lower envelopes are considered to be... m t n The signal between them can be expressed as a cubic polynomial as follows:

[0028] L mn =a·(tt) m ) 3 +b·(tt m ) 2 +c·(tt m )+d,t m ≤t≤t n (8)

[0029] Record the interval points t of the upper and lower envelope signal expressions during cubic spline interpolation. m t n And the coefficients a, b, c, d of the cubic polynomial, and respectively obtain the set of interval points A of the upper envelope. k and the set of polynomial coefficients Λ k and the set of interval points B of the lower envelope k and the set of polynomial coefficients Ω k The set of segmented intervals A of the signal envelope k and the set of polynomial coefficients and Λ k For example, its specific expression is as follows:

[0030] A k ={t1, t2, ..., t m} (9)

[0031] Λ k ={(a1, b1, c1, d1), (a2, b2, c2, d2), ..., (a m b m c m d m )} (10)

[0032] Among them, (a l b l cl d l ) for t l and t l+1 The coefficients of the cubic polynomial between (l: 1, 2, ..., m, when l = m, t) l+1 =N / f s );

[0033] Finally, calculate the average m of the upper and lower envelope sequences of the signal. k (n), that is:

[0034]

[0035] Subtract m from the input signal sequence x(n) k (n) obtain h k (n):

[0036] h k (n)=x(n)-m k (n) (12)

[0037] And determine h k Whether (n) satisfies the intrinsic modulus function condition is usually calculated using the following formula (13):

[0038]

[0039] Where h0(n) = x(n), ε is the error factor, usually chosen between 0.2 and 0.3. If the condition in equation (13) above is satisfied, then h k Let (n) be the first intrinsic mode function of the wavelength modulation spectral signal sequence, denoted as c1(n), and stop iterating; otherwise, let x(n) = h. k If X(n) is n and k = k + 1, repeat step two iteratively until the first eigenmode function of X(n) is determined.

[0040] After step two, the original wavelength modulation spectral signal sequence X(n) can be expressed as:

[0041]

[0042] Where, m i (n) is the average envelope sequence in the i-th iteration process, which is obtained by averaging the upper and lower envelopes obtained by cubic spline interpolation. Therefore, it belongs to the analytically expressible component. c1(n) is the first intrinsic mode function. For the characteristics of wavelength modulation spectral signal, it can be approximated as the interference noise component D(t) in equation (5). Therefore, the non-analytical high-frequency noise component in the wavelength modulation spectral signal can be removed by single-step empirical mode decomposition, and the analytically expressible component can be extracted.

[0043] Step 3: Calculate the precise analytical expression of the wavelength-modulated spectral signal, and obtain all harmonics of the wavelength-modulated spectral signal using the Fourier series formula. The specific process is as follows:

[0044] First, according to equation (14), the accurate wavelength modulation spectrum signal X after high-frequency noise removal can be obtained from the analytically expressible average envelope signal. WMS (t):

[0045]

[0046] Among them, the upper and lower envelopes e generated during the i-th screening process after single-step empirical mode decomposition are... max_i (t) and e min_i If (t) has a specific analytical expression, then X WMS (t) can also be expressed parsably, based on the set A of interval points on the envelope of each group of records. i (i = 1, 2, ..., k) and the set of interval points B of the lower envelope. i For sampling interval Perform segmentation, in each sub-interval [t] i , t i+1 The set of polynomial coefficients Λ of each recorded upper envelope is used as the basis for further information. i (i = 1, 2, ..., k) and the set of polynomial coefficients Ω of the lower envelope. i By performing polynomial merging, we finally obtain X. WMS The specific analytical expression of (t) is a piecewise polynomial in the form of:

[0047]

[0048] in, In each subinterval [t] m , t n The coefficients of the polynomials after combining within the polynomial.

[0049] Then, because the wavelength-modulated spectral signal is modulated by a high-frequency sine wave, it exhibits a certain periodicity, and the signal expression X WMS (t) Given that, the amplitude change H of the corresponding kth harmonic can be obtained directly using the Fourier series formula. k (t), combining the characteristics of the wavelength modulation spectral signal, the kth harmonic value at sampling time t0 is defined as:

[0050]

[0051] in,

[0052]

[0053] Calculate sequentially from arrive The kth harmonic value of the sampling point sequence is obtained as H. k (n), because the wavelength-modulated spectral signal is affected by the sawtooth wave scanning, it is not an absolutely periodic signal. The integration process of the Fourier series expansion will make the calculated H... k (n) contains the corresponding high-frequency kω m The sine and cosine signal components, therefore for sequence H k (n) Perform digital filtering to remove the influence of the corresponding high-frequency components, and obtain the final kth harmonic of the wavelength-modulated spectral signal.

[0054] (III) Beneficial Effects

[0055] The beneficial effects of this invention lie in combining the periodic characteristics of the wavelength modulation spectral signal, processing it based on single-step empirical mode decomposition, separating high-frequency noise components and obtaining an accurate analytical expression for the wavelength modulation spectral signal, and extracting all harmonics according to the Fourier series formula. This method has good noise resistance and does not require repeated use of the original wavelength modulation spectral data for calculation, providing a new approach for the extraction of multiple harmonics in the absorption spectrum of the wavelength modulation method in laser absorption spectroscopy. Attached Figure Description

[0056] Appendix Figure 1 Flowchart of a Wavelength Modulation Spectral Harmonic Extraction Method Based on Single-Step Empirical Mode Decomposition

[0057] Appendix Figure 2 : Complete and partial wavelength-modulated spectral signal X(n)

[0058] Appendix Figure 3 Precise wavelength-modulated spectral signals and high-frequency noise components

[0059] Appendix Figure 4 Extracted first and second harmonics Detailed Implementation

[0060] Reference Appendix Figure 1 This is a flowchart of a wavelength modulation spectrum harmonic extraction method based on single-step empirical mode decomposition. The specific steps are illustrated with an example:

[0061] Step 1: A 200Hz sawtooth wave superimposed with a 200kHz high-frequency sinusoidal wave modulated current signal is simultaneously injected into the laser control module to drive the distributed feedback laser to emit a scanning laser. The wavelength-modulated incident laser passes through the flame being measured, and specific gas molecules absorb it, resulting in transmitted laser light. This transmitted laser light is converted into an electrical signal by a photodetector and then acquired by a data acquisition module with a sampling rate of 20MSPS, and converted into a digital signal sequence as shown in the attached figure. Figure 2 As shown.

[0062] Step 2: Perform single-step empirical mode decomposition to extract the analyzable components from the original wavelength modulation spectral signal. The specific process is as follows:

[0063] First, initialize k = 1, and let the input signal x(n) (n is the time series coordinate of the sampling points, ...) be 1. N is the total number of sampling points, 8400, f s 20×10 6 Given a wavelength-modulated spectral signal sequence X(n), detect all maxima and minima of the input signal.

[0064] Then, cubic spline interpolation is performed on all maxima and minima to generate the upper and lower envelope sequences e of x(n). max (n), e min (n), according to the principle of cubic spline interpolation, two adjacent maxima or minima (t) m t n The signal between them can be expressed as a cubic polynomial as follows:

[0065] Env mn =a·(tt) m ) 3 +b·(tt m ) 2 +c·(tt m )+d,t m ≤t≤t n (1)

[0066] Record the interval points t of the signal expression for each segment during cubic spline interpolation. m t n And the coefficients a, b, c, d of the cubic polynomial, and respectively obtain the set of interval points A of the upper envelope. k and the set of polynomial coefficients Λ k and the set of interval points B of the lower envelope k and the set of polynomial coefficients Ω k ;

[0067] Finally, calculate the average m of the upper and lower envelope sequences of the signal. k (n), subtract m from the input signal sequence x(n). k (n) obtain h k (n):

[0068] h k (n)=x(n)-m k (n) (2)

[0069] And determine h kWhether (n) satisfies the intrinsic modulus function condition is calculated using the following formula (3):

[0070]

[0071] Where h0(n) = x(n), ε is the error factor, which is chosen to be 0.3 here. If the condition in equation (3) above is satisfied, then h k Let (n) be the first intrinsic mode function of the wavelength modulation spectral signal sequence, denoted as c1(n), and stop iterating; otherwise, let x(n) = h. k (n) and k = k + 1, repeat the above process in step two iteratively until the first eigenmode function is selected. For this wavelength modulation spectral signal data, after 3 iterations, its first eigenmode function is extracted, that is, the original wavelength modulation spectral signal X(n) can be expressed as:

[0072]

[0073] Where, m i c1(n) is the average envelope sequence during the i-th iteration, and c1(n) is the first intrinsic mode function. Considering the characteristics of the wavelength-modulated spectral signal, c1(n) approximates as a high-frequency noise component, the magnitude of which is shown in the attached figure. Figure 3 As shown in (a), after removing the non-analytical high-frequency noise components, the analytical components in the original absorption spectrum signal can be extracted.

[0074] Step 3: Calculate the analytical expression of the accurate wavelength modulation spectral signal; according to equation (4), the accurate wavelength modulation spectral signal X after high-frequency noise removal can be obtained from the analytically expressible average envelope signal. WMS (t):

[0075]

[0076] Among them, e max_i (t) and e min_i (t) represents the upper and lower envelopes generated during the i-th filtering process, based on the set A of interval points of each recorded upper envelope. i (i = 1, 2, 3) and the set of interval points B of the lower envelope i For the sampling time interval [5×10 -8 4.2×10 -4 Divide the interval [t] into sub-intervals. i , t i+1 The set of polynomial coefficients Λ of each recorded upper envelope is used as the basis for further information. i (i = 1, 2, 3) and the set of polynomial coefficients Ω of the lower envelope. i By performing polynomial merging, we finally obtain X. WMSThe specific analytical expression of (t) is a piecewise polynomial in the form of:

[0077]

[0078] in, In each subinterval [t] m ,t n The coefficients of the polynomials after merging are t1 = 5 × 10 -8 t n =4.2×10 -4 The precise wavelength-modulated spectral signal within the sampling interval recovered by this expression is shown in the attached figure. Figure 3 As shown in (a), the signal differs from the original signal only by a high-frequency noise component. Figure 3 (b) and appendix Figure 2 (b) By comparing the local absorption spectrum signals, we can more clearly see that the absorption spectrum signal after single-step empirical mode decomposition is smoother.

[0079] Based on the kth harmonic value at the defined sampling time t0:

[0080]

[0081] in,

[0082]

[0083] Calculate sequentially from 5×10 -8 Up to 4.2×10 -4 The first and second harmonic values ​​of the sampling point sequence within s are obtained as H1(n) and H2(n). Then, the calculated H1(n) and H2(n) are digitally filtered. An IIR filter is selected as the digital filter, and the cutoff frequency is set to 40kHz to filter out the corresponding high-frequency noise, thus obtaining the final first and second harmonic values. As attached Figure 4 .

[0084] The above description of the present invention and its embodiments is not limited thereto, and the accompanying drawings are merely one embodiment of the present invention. Any structure or embodiment similar to this technical solution designed without departing from the spirit of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for extracting harmonics from wavelength-modulated spectra based on single-step empirical mode decomposition, characterized in that, The method includes the following steps: Step 1: Obtain the wavelength modulation spectral signal sequence. Based on the wavelength modulation method in laser absorption spectroscopy, inject the sawtooth wave superimposed with a high-frequency sine wave modulated current signal into the laser control module to drive the distributed feedback laser to emit scanning laser light. The transmitted light, after being absorbed by specific gas molecules, illuminates the photodetector. Assume the electrical signal output by the photodetector... for: in, The photoelectric conversion coefficient of the detector. The incident light intensity signal Transmittance as a function of wavenumber Changes, and These represent the transmitted light intensity, respectively. Subharmonic amplitude variation and phase This signal is the interference noise throughout the process. The data acquisition module converts the data into a digital signal sequence. ( The time series coordinates of the sampling points , The total number of sampling points. (sampling rate); Step 2: Using single-step empirical mode decomposition, extract the resolvable components from the original wavelength modulation spectral signal. The specific process is as follows: First, initialization. Let the input signal Wavelength-modulated spectral signal sequence Detect all maximum and minimum points of the input signal; Then, cubic spline interpolation is performed on all maximum and minimum points respectively to generate... upper and lower envelope sequences , According to the principle of cubic spline interpolation, two adjacent maxima or minima ( , The signal between them can be expressed as a cubic polynomial: Record the interval points of the upper and lower envelope signal expressions during cubic spline interpolation. , and cubic polynomial coefficients , , , And obtain the set of interval points of the upper envelope respectively. and the set of polynomial coefficients and the set of interval points of the lower envelope. and the set of polynomial coefficients ; Finally, calculate the average of the upper and lower envelope sequences of the signal. From the input signal sequence Subtract get : And judge Whether an eigenfunction meets the intrinsic modulus condition is usually determined using the following formula. calculate: in, , The error factor is typically chosen to be between 0.2 and 0.3, provided the above formula is satisfied. Under the given conditions, Let be the first eigenmode function of the wavelength-modulated spectral signal sequence, denoted as . And stop iterating; otherwise, let and Return to step one and repeat all the above steps iteratively until the desired selection is found. The first intrinsic modulus function; Through all the above processes, the original wavelength modulation spectral signal sequence This can be expressed as: in, It is the first The average envelope sequence in the iteration process is obtained by averaging the upper and lower envelopes obtained from cubic spline interpolation, and therefore belongs to the analyzable representation components. It is the first eigenmode function, which, for the characteristics of wavelength-modulated spectral signals, can be approximated by the formula: Interference noise components By using single-step empirical mode decomposition, non-analytical high-frequency noise components in wavelength-modulated spectral signals can be removed, and analyzable expressible components can be extracted. Step 3: Calculate the precise analytical expression of the wavelength-modulated spectral signal. Using the Fourier series formula, obtain all harmonics of the wavelength-modulated spectral signal. The specific process is as follows: First, calculate the analytical expression for the precise wavelength-modulated spectral signal, based on the formula... The accurate wavelength modulation spectrum signal after high-frequency noise removal can be obtained from the analytically expressible average envelope signal. : Among them, after single-step empirical mode decomposition, the first The upper and lower envelopes generated during the secondary screening process and It has its specific analytical expression, then It can also be parsed, based on the set of interval points of each group's upper envelope recorded. ( and the set of interval points of the lower envelope. For sampling interval Divide into sub-intervals. Internally based on the set of polynomial coefficients of each set of upper envelopes recorded. ( and the set of polynomial coefficients of the lower envelope. By performing polynomial merging, we finally obtain The specific analytical expression is represented as a piecewise polynomial: in, , , , In each sub-interval The coefficients of the inner polynomials after merging. , ; Then, according to the Fourier series formula, all harmonics of the wavelength-modulated spectral signal are obtained; since the wavelength-modulated spectral signal is modulated by a high-frequency sine wave, it exhibits a certain periodicity, and the signal expression... Given that, the corresponding value can be obtained directly using the Fourier series formula. Subharmonic amplitude variation Based on the characteristics of wavelength-modulated spectral signals, the sampling time is defined. place The value of the second harmonic is: in, Calculate sequentially from arrive The sampling point sequence The value of the subharmonic is obtained. Because the wavelength-modulated spectral signal is affected by sawtooth wave scanning and is not an absolutely periodic signal, the integration process of the Fourier series expansion will affect the calculated result. Contains corresponding high frequency The sine and cosine signal components, therefore for the sequence Digital filtering is performed to remove the influence of corresponding high-frequency components, resulting in the final wavelength-modulated spectral signal. Subharmonic .

Images