An Infrared Spectrum Apodization Method and System for a Quasi-Trapezoidal Window

Abstract

The present invention provides an infrared spectral apodization method and system for a quasi-trapezoidal window. The method includes: analyzing no less than two classic window functions, and accordingly selecting the R-V window function as the mother function; performing time-domain self-convolution processing on the mother function, and constructing a self-convolution R-V window function suitable for sidelobe performance according to the mother function; introducing adjustable parameters and a rectangular window function, and accordingly improving the self-convolution R-V window function to obtain a quasi-trapezoidal window function; using the quasi-trapezoidal window function for sidelobe suppression, and adjusting the proportionality coefficient rT and the convolution order P according to the time-domain expression of the p-order self-convolution window R-V function to perform apodization operation. The present invention solves the technical problems of easy generation of false peak signals, easy reduction of the signal-to-noise ratio of the instrument, poor effect of suppressing spectral leakage, and low stability and flexibility.

Description

Technical Field

[0001] The present invention relates to the field of infrared spectral data processing, and in particular to an infrared spectral apodization method and system with a quasi-trapezoidal window. Background Art

[0002] In recent years, Fourier transform infrared spectroscopy technology has been widely applied in many research fields such as the petroleum industry, biomedicine, aerospace, and environmental science. In a Fourier transform infrared multi-component gas analyzer, the processing of target interference data is the core issue of spectral restoration technology, which affects the accuracy of gas concentration inversion. During the spectral restoration process, since the actual interferometer can only provide a limited optical path difference, directly using the Fourier transform will cause spectral energy leakage. In order to reduce spectral leakage, it is necessary to process the signal with an appropriate apodization function. Therefore, the apodization weighting link of the interferogram is an important part of the interference data processing. The Fourier transform is a commonly used method for interferometric data analysis and processing. Due to the truncation effect, spectral leakage will occur when directly performing the Fourier transform on the sample data. Generally, the method of weighting with an apodization function is used to reduce spectral leakage.

[0003] In recent years, numerous scholars have conducted in-depth and extensive research on using apodization functions to process spectral signals. Norton et al. proposed an apodization function applicable to Fourier spectroscopy and discussed three specific functions in detail. Based on this work, Naylor et al. proposed a method for determining the optimal coefficients of a cosine-combined window function. The coefficients determined by this method can achieve the optimal resolution when the sidelobe performance is certain. This function is simple to implement and calculate and can be used to study the trade-off between the signal-to-noise ratio and spectral resolution of the spectrum. Xianglibin et al. studied a small bilateral weighted and large bilateral triangular apodization method, which can ensure the accuracy of the restored spectrum and the apodization effect. Chen Jiejing et al. analyzed the optimized inversion results of different apodization functions with different line widths for interferograms with different signal-to-noise ratios using the Monte Carlo method. He Qian et al. utilized the characteristic that the spectral power is concentrated in the main lobe to obtain an optimized spatial resolution through a high-order self-convolution window. Currently, there are mainly two ways to construct new window functions: one is to construct window functions with different frequency-domain performances by adjusting the coefficients or parameters of classical window functions, such as cosine-combined windows and Kaiser windows with different numbers of terms or coefficients; the other is to construct convolution windows by performing time-domain convolution on classical window functions to improve the frequency-domain sidelobe performance. For example, the existing invention application document "A Pulse Compression Method with Ultra-Low Sidelobes" with publication number CN106908768A specifically includes the following process: Step 1, the transmitting end designs a weighted window function w(t) according to the transmitted linear frequency modulation signal s(t), and changes the transmitted signal to s(t)×w(t); Step 2, according to the transmitted signal, a corresponding pulse compression matching filter h(t) and a sidelobe suppression filter w(t) are designed at the receiving end, and the sidelobe suppression filter w(t) is designed according to the weighted window function w(t); Step 3, according to the matching filter h(t) and the sidelobe suppression filter w(t) at the receiving end, the pulse compression result y(t)=[s(t)×w(t)]*[h(t)×w(t)] of the echo signal is calculated; Step 4, the weighted window function at the transmitting end is cancelled, an equivalent filter hw(t) is designed at the receiving end, and the equivalent filter hw(n) is calculated according to the frequency-domain implementation method; Step 5, the linear frequency modulation signal s(t) is transmitted at the transmitting end, and the pulse compression equivalent filter hw(n) is designed at the receiving end to obtain ultra-low sidelobes. From the specific implementation content in this existing scheme, it can be seen that this existing technology cascades a sidelobe suppression filter with the frequency response of a tapering function behind the pulse compression filter, and the designed sidelobe suppression filter is the same as the weighted window function at the transmitting end, and this weighted window function is a Hamming window or a Kaiser window or a Blackman window. Another example is the existing invention patent document "Polarization-Sensitive Distributed Optical Frequency Domain Reflectometry Disturbance Sensing Device and Demodulation Method" with publication number CN102322880A, which includes an ultra-narrow linewidth tunable laser module, a polarization generation and polarization diversity detection module, an optical frequency and phase monitoring module, and a high-speed optical switch module, forming a large-scale long-distance optical sensing network.In the demodulation method, the suppression and compensation of optical frequency nonlinearity and light source phase noise, super-resolution analysis method, advanced denoising method, and polarization resolution method based on Jones and Mueller matrices of the fiber optic distributed waveplate model are used to extract the polarization information in the sensing optical cable. From the specific implementation content of suppressing the signal sidelobe after spectral analysis and processing of the signal in the foregoing existing solutions, it can be seen that the foregoing existing technical solutions use window functions: Kaiser window or Gaussian window or Blackman window to suppress the signal sidelobe. However, the adjustment of the classical window coefficients or parameters has limited improvement in the main lobe or sidelobe performance of the window. Although the time-domain convolution operation can greatly improve the sidelobe performance, it will widen the main lobe of the window function and has low flexibility.

[0004] In summary, the existing technology has technical problems such as being prone to generating false peak signals, easily causing the signal-to-noise ratio of the instrument to decrease, poor effect of suppressing spectral leakage, and low stability and flexibility. Summary of the Invention

[0005] The technical problem to be solved by the present invention is how to solve the technical problems in the existing technology, such as being prone to generating false peak signals, easily causing the signal-to-noise ratio of the instrument to decrease, poor effect of suppressing spectral leakage, and low stability and flexibility.

[0006] The present invention solves the above technical problems by adopting the following technical solutions: An infrared spectroscopy apodization method using a quasi-trapezoidal window includes:

[0007] S1. Analyze no less than 2 classical window functions, and select the R-V window function as the mother function accordingly. Step S1 also includes:

[0008] S11. Obtain the sidelobe peak level and sidelobe asymptotic attenuation rate of the classical window function;

[0009] S12. According to the sidelobe peak level and sidelobe asymptotic attenuation rate, and in combination with the spectral restoration signal-to-noise ratio requirement, select the R-V window function as the mother function;

[0010] S2. Perform time-domain self-convolution processing on the mother function, and construct a self-convolution R-V window function suitable for sidelobe performance according to the mother function;

[0011] S3. Introduce adjustable parameters and a rectangular window function, and improve the self-convolution R-V window function accordingly to obtain a quasi-trapezoidal window function. Step S3 also includes:

[0012] S31. Obtain the time-domain expression of the p-order self-convolution window R-V function processed by the self-convolution R-V window function;

[0013] S32. Introduce an adjustable parameter rT;

[0014] S33. Improve the self-convolution R-V window function through the rectangular window function to obtain a quasi-trapezoidal function;

[0015] S4. Use the quasi-trapezoidal window function to suppress the sidelobes. According to the time-domain expression of the p-order self-convolution window R-V function, adjust the proportionality coefficient rT and the convolution order P to perform the apodization operation.

[0016] Based on the analysis of various classical window functions, the present invention selects the R-V window as the mother window, constructs a self-convolution R-V window with significantly improved sidelobe performance by using time-domain self-convolution, then introduces a rectangular window with the best main-lobe performance to improve the self-convolution R-V window, establishes a quasi-trapezoidal window function with adjustable parameters, and conducts time-frequency characteristic analysis. On this basis, the quasi-trapezoidal window function is applied to the process of spectral restoration and gas concentration inversion. By adjusting the parameters, the spectral restoration effect is improved and the accuracy of gas concentration inversion is increased. At the same time, the present invention proposes and establishes a new apodization function, which allows for a very flexible trade-off between the width of the main lobe and the height of the sidelobe, and is applicable to different spectral restoration scenarios.

[0017] In a more specific technical solution, the time-domain representation of the R-V window function in step S12 is:

[0018]

[0019] where M is the number of terms of the window function; n = 1, 2,..., N - 1.

[0020] In a more specific technical solution, bm should satisfy the constraint condition:

[0021]

[0022] where bm is the coefficient parameter of the R-V window. In this application, it is a five-term R-V window function, and the specific values are:

[0023]

[0024] In a more specific technical solution, step S2 includes:

[0025] S21. Define the window function obtained by time-domain self-convolution;

[0026] S22. Perform p - 1 convolutions on p basic windows of the same length to obtain a p-order self-convolution R-V window function.

[0027] In a more specific technical solution, in step S21, the five-term Rife-Vincent (I) self-convolution window is defined as: a window function obtained by time-domain self-convolution of no less than 2 five-term Rife-Vincent (I) windows:

[0028]

[0029] Wherein, p is the number of basic windows participating in convolution, which is called the order of the window. w(t) represents the time-domain form of a single R-V window function.

[0030] In the present invention, the R-V window function is convolved in the time domain to construct a self-convolution R-V window with significantly improved sidelobe performance; subsequently, adjustable parameters m and a rectangular window function are introduced to improve the self-convolution R-V window function, thereby obtaining a quasi-trapezoidal window function with a narrower main lobe and optimal sidelobes. The present invention comprehensively considers the high signal-to-noise ratio requirement for spectral restoration, and truncates the signal with a five-term cosine window R-V(I) window, which can achieve better results.

[0031] In a more specific technical solution, the quasi-trapezoidal window function in step S33 is:

[0032]

[0033] Wherein:

[0034] N is the window function length

[0035] w RW (n) represents the rectangular window function.

[0036] L represents the length of the upper base of the quasi-trapezoidal window, and the calculation formula is: L = r T *N, r T is a coefficient (to ensure the basic quasi-trapezoidal shape, 0 < r T ≤ 0.9).

[0037] The present invention analyzes the principle of apodization of the interferogram, studies the influence of the main lobe width and sidelobe attenuation of the apodization function on spectral restoration, uses the R-V window as the mother window, further improves the sidelobe characteristics through self-convolution, and at the same time introduces a rectangular window with adjustable parameters and optimal main lobe performance to improve the self-convolution R-V window, thereby establishing a quasi-trapezoidal window function with a wide adjustment range of the main lobe width and sidelobe attenuation.

[0038] Based on the analysis of the principle of apodization of the interferogram, the present invention introduces adjustable parameters r T and p to construct a quasi-trapezoidal apodization function, and studies the time-frequency characteristics of the quasi-trapezoidal apodization function, which has the advantage of a wide adjustment range of the main lobe width and sidelobe attenuation.

[0039] In a more specific technical solution, the quasi-trapezoidal window function satisfies:

[0040] L = r T *N.

[0041] In a more specific technical solution, the value range of the adjustable parameter r T is set to include the interval of 0 < r T ≤ 0.9 to ensure the basic quasi-trapezoidal shape.

[0042] The present invention adopts a quasi-trapezoidal function. Compared with the prior art that adopts other classical window functions, the spectral resolution, the spectral signal-to-noise ratio are improved, and at the same time, the inversion stability is improved.

[0043] In a more specific technical solution, step S4 includes:

[0044] S41. Adjust the adjustable coefficient r T to achieve an applicable main lobe width;

[0045] S42. Adjust the convolution order p according to the actual demand data to optimize the sidelobe performance.

[0046] The parameter adjustment of the quasi-trapezoidal window function of the present invention is convenient. Through parameter adjustment of the quasi-trapezoidal window, the requirements for spectral restoration with high signal-to-noise ratio or high resolution can be met, and the inversion stability of gas concentration can be improved to a certain extent.

[0047] Through the adjustment of the proportionality coefficient r T and the convolution order p of the present invention, the quasi-trapezoidal apodization function has been greatly improved in terms of the main lobe width and the sidelobe peak adjustment. By adjusting r T the required main lobe width can be achieved, and by adjusting p, the required sidelobe performance can be achieved, enhancing the flexibility of the apodization function in engineering and being applicable to different occasions.

[0048] In a more specific technical solution, an infrared spectral apodization system with a quasi-trapezoidal window includes:

[0049] A mother function selection module for analyzing no less than two classical window functions and selecting the R-V window function as the mother function. The mother function selection module further includes:

[0050] A window function parameter acquisition module for acquiring the sidelobe peak level and the sidelobe asymptotic attenuation rate of the classical window function;

[0051] A window function selection module for selecting the R-V window function as the mother function according to the sidelobe peak level and the sidelobe asymptotic attenuation rate and in combination with the spectral restoration signal-to-noise ratio requirement. The window function selection module is connected to the window function parameter acquisition module;

[0052] A self-convolution R-V window function construction module for performing time-domain self-convolution processing on the mother function and constructing a self-convolution R-V window function suitable for the sidelobe performance according to the mother function. The self-convolution R-V window function construction module is connected to the mother function selection module;

[0053] A quasi-trapezoidal function acquisition module for introducing adjustable parameters and a rectangular window function to improve the self-convolution R-V window function to obtain a quasi-trapezoidal window function. The quasi-trapezoidal function acquisition module is connected to the self-convolution R-V window function construction module. The quasi-trapezoidal function acquisition module further includes:

[0054] A time-domain expression module for obtaining the time-domain expression of the p-order self-convolution window R-V function according to the processing of the self-convolution R-V window function;

[0055] An adjustable parameter introduction module for introducing an adjustable parameter r T ;

[0056] A rectangular window function improvement module for improving the self-convolution R-V window function through the rectangular window function to obtain a quasi-trapezoidal function. The rectangular window function improvement module is connected to the time-domain expression module and the adjustable parameter introduction module;

[0057] A parameter adjustment apodization module for suppressing sidelobes using the quasi-trapezoidal window function, and adjusting the proportionality coefficient r according to the time-domain expression of the p-order self-convolution window R-V function T and the convolution order p for apodization operation. The parameter adjustment apodization module is connected to the quasi-trapezoidal function acquisition module.

[0058] The present invention has the following advantages compared with the prior art: On the basis of analyzing various classical window functions, the R-V window is selected as the mother window, and the self-convolution R-V window with significantly improved sidelobe performance is constructed by using time-domain self-convolution. Then, the rectangular window with the best main lobe performance is introduced to improve the self-convolution R-V window, a quasi-trapezoidal window function with adjustable parameters is established, and time-frequency characteristics are analyzed. On this basis, the quasi-trapezoidal window function is applied to the process of spectral restoration and gas concentration inversion. By adjusting the parameters, the spectral restoration effect is improved and the accuracy of gas concentration inversion is increased. At the same time, the present invention proposes and establishes a new apodization function, which allows a very flexible trade-off between the width of the main lobe and the height of the sidelobe, and is applicable to different spectral restoration occasions.

[0059] The present invention performs time-domain convolution on the R-V window function to construct a self-convolution R-V window with significantly improved sidelobe performance; subsequently, adjustable parameters m and the rectangular window function are introduced to improve the self-convolution R-V window function, thereby obtaining a quasi-trapezoidal window function with a narrower main lobe and optimal sidelobes. The present invention comprehensively considers the high signal-to-noise ratio requirement of spectral restoration, and truncates the signal using the five-term cosine window R-V(I) window, which can obtain better results.

[0060] The present invention analyzes the principle of interferogram apodization, studies the influence of the main lobe width and sidelobe attenuation of the apodization function on spectral restoration, uses the R-V window as the mother window, further improves the sidelobe characteristics by self-convolution, and at the same time introduces a rectangular window with adjustable parameters and the best main lobe performance to improve the self-convolution R-V window, thereby establishing a quasi-trapezoidal window function with a wide adjustment range of the main lobe width and sidelobe attenuation.

[0061] Based on the analysis of the principle of interferogram apodization, the present invention introduces an adjustable parameter r T, p is used to construct a quasi-trapezoidal apodization function, and the time-frequency characteristics of the quasi-trapezoidal apodization function are studied, which has the advantages of a wide range of main lobe width and sidelobe attenuation adjustment.

[0062] The present invention adopts a quasi-trapezoidal function, compared with the prior art that adopts other classical window functions, it improves the spectral resolution, spectral signal-to-noise ratio, and at the same time improves the inversion stability.

[0063] The quasi-trapezoidal window function parameters of the present invention are convenient to adjust. Through parameter adjustment of the quasi-trapezoidal window, the requirements for spectral restoration with high signal-to-noise ratio or high resolution can be met, and the inversion stability of gas concentration can be improved to a certain extent.

[0064] The present invention adjusts the proportionality coefficient r T and the convolution order p. The quasi-trapezoidal apodization function has been greatly improved in terms of main lobe width and sidelobe peak adjustment. By adjusting r T the required main lobe width can be achieved, and by adjusting p, the required sidelobe performance can be achieved, enhancing the flexibility of the apodization function in engineering and being applicable to different occasions. The present invention solves the technical problems existing in the prior art, such as being prone to generating false peak signals, easily causing a decrease in the signal-to-noise ratio of the instrument, poor effect of suppressing spectral leakage, and low stability and flexibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 Schematic diagram of the basic steps of an infrared spectral apodization method using a quasi-trapezoidal window according to Embodiment 1 of the present invention;

[0066] Figure 2 Time domain diagram of a rectangular window according to Embodiment 1 of the present invention;

[0067] Figure 3 Frequency spectrum diagram of a rectangular window according to Embodiment 1 of the present invention;

[0068] Figure 4 Time domain waveform diagram of a quasi-trapezoidal window according to Embodiment 1 of the present invention;

[0069] Figure 5 Amplitude-frequency response diagram of a quasi-trapezoidal window according to Embodiment 1 of the present invention;

[0070] Figure 6 Corresponding relationship diagram between the normalized main lobe width and the proportionality coefficient of a quasi-trapezoidal window according to Embodiment 1 of the present invention;

[0071] Figure 7 Corresponding relationship diagram between the sidelobe peak level and the proportionality coefficient of a quasi-trapezoidal window according to Embodiment 1 of the present invention;

[0072] Figure 8 Schematic diagram of the working principle of a portable Fourier transform infrared spectrometer according to Embodiment 2 of the present invention;

[0073] Figure 9 It is the trend graph of the spectral resolution varying with rT in Embodiment 2 of the present invention;

[0074] Figure 10 It is the trend graph of the spectral signal-to-noise ratio varying with P in Embodiment 2 of the present invention;

[0075] Figure 11 It is the comparison graph of the standard absorption spectrum of C3H8 and different apodization spectra in Embodiment 3 of the present invention;

[0076] Figure 12 It is the comparison graph of the standard absorption spectrum of C2H4 and different apodization spectra in Embodiment 3 of the present invention;

[0077] Figure 13 It is the trend graph of the stability of C3H8 concentration inversion varying with the apodization degree in Embodiment 3 of the present invention;

[0078] Figure 14 It is the trend graph of the mean value of C3H8 concentration inversion varying with the apodization degree in Embodiment 3 of the present invention;

[0079] Figure 15 It is the trend graph of the inversion stability of C2H4 varying with the apodization degree in Embodiment 3 of the present invention;

[0080] Figure 16 It is the trend graph of the inversion mean value of C2H4 varying with the apodization degree in Embodiment 3 of the present invention. Specific embodiments

[0081] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0082] Embodiment 1

[0083] As Figure 1 shown, a method for apodizing infrared spectrum with a quasi-trapezoidal window provided by the present invention includes the following basic steps:

[0084] S1. Through the analysis of classical window functions, select the R-V window function as the mother function, perform time-domain convolution on the R-V window function, and construct a self-convolution R-V window with significantly improved sidelobe performance;

[0085] S2. Introduce adjustable parameters m and a rectangular window function to improve the self-convolution R-V window function, thereby obtaining a quasi-trapezoidal window function with a narrower main lobe and optimal sidelobes.

[0086] In this embodiment, the present invention proposes and establishes a new apodization function, which allows for a very flexible trade-off between the width of the main lobe and the height of the sidelobes, and is applicable to different spectral restoration scenarios. First, through the analysis of classical window functions, the R-V window function is selected as the mother function, and the R-V window function is convolved in the time domain to construct a self-convolved R-V window with significantly improved sidelobe performance; subsequently, adjustable parameters m and a rectangular window function are introduced to improve the self-convolved R-V window function, thereby obtaining a quasi-trapezoidal window function with a narrower main lobe and optimal sidelobes.

[0087] 1 Principle of Apodization of Interferogram

[0088] The basic formula for the principle of Fourier transform spectrometers is:

[0089]

[0090] In the formula: I(x) is the interferogram actually obtained by the spectrometer; R and T are the reflection coefficient and transmission coefficient of the beam splitter respectively; B0(ν) is the actual spectrum; B(ν) is the restored spectrum; ν is the spectral wave number; x is the optical path difference of the interferogram.

[0091] It can be seen from Equations (1) and (2) that after the spectrometer detects the interference data of the target, it must undergo a Fourier transform to obtain the final spectral data. In theory, to obtain a complete spectrum, the integration interval of the Fourier transform should be infinite. However, in actual instruments, due to the limitation of the scanning distance of the interferometer, the integration interval is finite. The actually collected interferogram is equivalent to multiplying the ideal interferogram by a rectangular truncation function D(x), which in the frequency domain is manifested as the convolution of the actual spectrum and the Sinc function:

[0092]

[0093] If M is the maximum scanning optical path difference of the interferometer, then:

[0094]

[0095] Its Fourier transform spectrum is in the form of a sinc function:

[0096]

[0097] Such as Figure 2 and Figure 3As shown, its Fourier transform D(ν) is the Sinc function. The Sinc function is an oscillating and convergent function. The intensity of its first sidelobe reaches 22% of the main peak value. While the strong positive and negative sidelobes mask the nearby real weak spectral information, they also bring false spectral signals. Therefore, these sidelobes must be suppressed, and this process is called apodization. Apodization processing is to multiply the actually measured interferogram by a tapering function to achieve the purpose of reducing sidelobes and alleviating the discontinuity of the interferogram. In addition, it can also be obtained by convolving the interferogram and the apodization function in the frequency domain after performing Fourier transforms on them separately.

[0098] In this embodiment, the apodization function affects the spectral performance. The main lobe width of the apodization function affects the spectral resolution. According to the full width at half maximum criterion of spectral resolution, the wider the main lobe, the lower the restored spectral resolution. The sidelobe performance of the apodization function affects the spectral signal-to-noise ratio. The positive sidelobes may generate false peak signals, while the negative sidelobes will weaken or submerge the adjacent weak signals, resulting in a decrease in the signal-to-noise ratio of the instrument. Therefore, the faster the sidelobe attenuation rate and the smaller the sidelobe value, the higher the signal-to-noise ratio of the restored spectrum. Therefore, choosing a suitable apodization function is of great significance for spectral restoration.

[0099] 2 Self-convolution R-V window function and analysis

[0100] 2.1 Selection of the mother window

[0101] In this embodiment, to reduce the influence of spectral leakage on the signal-to-noise ratio of the restored spectrum, a window function with a small sidelobe peak level and a large sidelobe asymptotic attenuation rate should be selected to process the signal. The R-V window function is a cosine combination window with excellent sidelobe peak level and sidelobe asymptotic attenuation performance. Its time-domain representation is

[0102]

[0103] where: M is the number of terms of the window function; n = 1, 2,..., N - 1; bm is the coefficient parameter of the R-V window, and it should satisfy the constraint condition: Table 1 gives the coefficients of the five-term R-V window function, and Table 2 gives the sidelobe characteristics of the R-V window and other commonly used combination windows.

[0104] Table 1 Coefficient table of the five-term R-V window function (I)

[0105]

[0106] Table 2 Sidelobe characteristic table of other commonly used combination windows

[0107]

[0108] In the calculations of this embodiment, time-domain truncation is equivalent to the operation of applying a rectangular window. The rectangular window belongs to the zero-order power window of the time variable. Its advantage is that the main lobe energy is relatively concentrated and the main lobe width is relatively small. However, its sidelobe peak is relatively high, and it cannot effectively suppress the influence brought by spectral leakage. The Triangle window is a simple improvement based on the rectangular window and is a first-order power window. Its main lobe width is twice that of the rectangular window, but its sidelobes are significantly reduced compared to the rectangular window. The Hanning window is a raised cosine window, equivalent to the algebraic sum of the spectra of 3 rectangular windows. Its main lobe width is comparable to that of the triangle window, and the sidelobe peak is significantly reduced, which can better suppress the influence of spectral leakage. Compared with the Hanning window, the Hamming window has smaller sidelobes, but its attenuation rate is relatively slow. The first sidelobe of the Blackman window decays to -57 dB, and its attenuation rate is comparable to that of the Hamming window. The Blackman-Harris window is a cosine combination window. Its main lobe is further broadened, but the sidelobe peak is as low as 92 dB, and the attenuation rate is slow, similar to the Hamming window. Although the sidelobe peak of the five-term Rife-Vincent (I) window is slightly higher than that of the Blackman-Harris window, its attenuation rate is very fast. Using this window function for calculation can obtain higher calculation accuracy. Considering the high signal-to-noise ratio requirement for spectral restoration, truncating the signal with the five-term cosine window R-V (I) window can achieve better results.

[0109] 2.2 Self-convolution window function

[0110] In this embodiment, the five-term Rife-Vincent (I) self-convolution window is defined as a window function obtained by performing time-domain self-convolution on several five-term Rife-Vincent (I) windows, that is

[0111]

[0112] In the formula, p is the number of basic windows participating in the convolution, called the order of the window. By performing p - 1 convolutions on p basic windows of the same length, a p-order self-convolution window can be obtained.

[0113] In this embodiment, according to the convolution property, when performing p - 1 convolution operations on two five-term Rife-Vincent (I) window sequences of length M, a sequence of length pM - p + 1 can be obtained. By padding p - 1 zeros at the beginning or end, a sequence of length pM can be obtained. Among them, the sidelobe peak level and the sidelobe attenuation rate are proportional to the convolution order p. As the convolution order p increases, the sidelobe performance of the five-term R-V self-convolution window is improved.

[0114] 3 Quasi-trapezoidal window function and analysis

[0115] 3.1 Quasi-trapezoidal window function

[0116] In this embodiment, based on the time-domain expression of the p-order self-convolution window R-V function, an adjustable parameter r is introduced. T , and the R-V window function is further improved by the rectangular window function to obtain the quasi-trapezoidal window function as:

[0117]

[0118] where L = r T *N, N is the window function length, rT is the coefficient. To ensure the basic quasi-trapezoidal shape, 0 < r T ≤0.9. According to equation (8), when the time-domain length N = 256, the convolution order P = 1, and the proportionality coefficient r T = 0.08, the quasi-trapezoidal window and its amplitude-frequency response are as Figure 4 、 Figure 5 shown.

[0119] 3.2 Frequency-domain characteristic analysis

[0120] In this embodiment, when the time-domain length N is fixed, the frequency-domain characteristics of the quasi-trapezoidal window are affected not only by the proportionality coefficient rT but also by the convolution order p. Set the time-domain length N of the quasi-trapezoidal window function to 256, and study the relationship between the frequency characteristics of the quasi-trapezoidal window function and the parameters r T 、p respectively.

[0121] 3.2.1 Influence of the proportionality coefficient r T on

[0122] Let P = 1 remain unchanged. When the proportionality coefficient r T changes, the variation rules of the sidelobe peak level and the normalized main lobe width of the quasi-trapezoidal window are shown in Table 3.

[0123] Table 3 Influence list of the change of the proportionality coefficient rT on the sidelobe peak level and the normalized main lobe width of the quasi-trapezoidal window

[0124]

[0125] As Figure 6 and Figure 7 shown, in this embodiment, the variation trend of the normalized main lobe width of the quasi-trapezoidal window with the proportionality coefficient rT is as Figure 4 shown. The normalized main lobe width of the quasi-trapezoidal window is positively correlated with the proportionality coefficient rT. As rT increases, the main lobe performance of the quasi-trapezoidal window is rapidly improved. While the main lobe performance is improved, the sidelobe performance will decrease to a certain extent. The variation trend of the sidelobe peak level of the quasi-trapezoidal window with the proportionality coefficient r T is as Figure 5 shown, and the sidelobe peak level is negatively correlated with the proportionality coefficient r T and as rT With the increase of

[0126] As shown in Table 3 and Figure 6 and 7 it can be seen that when the time-domain length N = 256, the convolution parameter p = 1, and the scaling factor r T ∈(0, 0.03), the quasi-trapezoidal window function can obtain a lower sidelobe peak level. Especially when r T is close to 0, the sidelobe peak level reaches the lowest value Asp = -72.10 dB. At this time, the sidelobe peak level of the quasi-trapezoidal window under this condition is close to that of the R-V window, and the sidelobe attenuation rate is the same as that of the R-V window. When r T = 0.07, the sidelobe peak level of the trapezoidal window is close to that of the Hamming window, the main lobe is narrower than that of the Hamming window, and the sidelobe attenuation rate is slightly lower than that of the Hanning window.

[0127] 4.2.1 Influence of Convolution Order P

[0128] In this embodiment, let r T = 0.008 remain unchanged. When the convolution order p changes, the variation laws of the sidelobe peak level and the normalized main lobe width of the quasi-trapezoidal window are shown in Table 4.

[0129] Table 4 Influence List of the Change of Convolution Order P on the Sidelobe Peak Level and the Normalized Main Lobe Width of the Quasi-Trapezoidal Window

[0130]

[0131] As can be seen from Table 4, the sidelobe peak level of the quasi-trapezoidal self-convolution window is positively correlated with the convolution order. Therefore, with the increase of the convolution order, the sidelobe performance of the quasi-trapezoidal window is rapidly improved.

[0132] From the above analysis, it can be obtained that: by adjusting the scaling factor r T and the convolution order p, the quasi-trapezoidal apodization function has been greatly improved in terms of the main lobe width and sidelobe peak adjustment. By adjusting r T the required main lobe width can be achieved, and by adjusting p, the required sidelobe performance can be achieved, enhancing the flexibility of the apodization function engineering and being applicable to different occasions.

[0133] Example 2

[0134] 4 Spectral Restoration

[0135] 4.1 Evaluation Index

[0136] 4.1.1 Spectral Resolution

[0137] Spectral resolution refers to the ability of a time-modulated Fourier transform spectrometer to resolve two adjacent spectral lines, expressed in wavenumbers (cm-1). Since the spectral resolution of the experimental instrument is lower than 0.5 cm-1, for instruments with a resolution lower than 0.5 cm-1, the water peak in the air can be measured. By collecting the background spectrum and obtaining the energy map of the background spectrum, using the definition of the full width at half maximum of the peak, calculate and select the full width at half maximum of the symmetric water spectral line in the range of 1900 cm-1 to 1700 cm-1, which is the resolution of the restored spectrum.

[0138] 4.1.2 Spectral signal-to-noise ratio

[0139] In this embodiment, there are two ways to represent the signal-to-noise ratio (SNR) of an infrared spectroscopic instrument: the transmittance method and the absorbance method. The transmittance representation method is to measure the background spectrum and the target absorption spectrum with the same number of scans respectively in the absence of the target gas, and then obtain the transmittance spectrum. Measure the peak-to-peak value of the transmittance spectrum in the range of 2600 - 2500 cm-1 or 2200 - 2100 cm-1, because these two ranges are less affected by water vapor and carbon dioxide in the air. Define the signal-to-noise ratio as 100 divided by the noise peak-to-peak value N measured by the transmittance representation method, that is: SNR = 100 / N.

[0140] 4.2 Restoration effect

[0141] In this embodiment, the main lobe performance and side lobe performance of the apodization function will directly affect the resolution and signal-to-noise ratio of the restored spectrum. The quasi-trapezoidal window function changes the main lobe performance and side lobe performance through parameter adjustment. Next, explore the relationship between the adjustment coefficient of the quasi-trapezoidal window function and the spectral resolution and signal-to-noise ratio.

[0142] In this embodiment, the interference data of this experiment is obtained by a self-developed Fourier transform infrared spectrometer. As Figure 8 shown, its core device, the interferometer, consists of a beam splitter, a moving mirror, and a fixed mirror.

[0143] As Figure 6 shown, in this embodiment, the infrared light emitted by the infrared light source passes through the beam splitter. In an ideal state, 50% of the light is reflected to the moving mirror and then reflected back to the beam splitter, and the other 50% of the light passes through the beam splitter to reach the fixed mirror and then is reflected back to the beam splitter, thus forming an optical path difference and generating interference. When the optical path difference is 0, the phases of the two beams of light reflected back to the beam splitter from the fixed mirror and the moving mirror are the same, and after superposition, no interference occurs, and the light intensity is the sum of the intensities of these two beams of light. When the moving mirror moves 1 / 4 wavelength, the optical path difference is half a wavelength. At this time, the phases of the two beams of light are opposite, and after superposition, they cancel each other out, and the light intensity is 0. When the moving mirror moves another 1 / 4 wavelength, the optical path difference is one wavelength, and the phase difference between the two beams of light is one wavelength, and the phases are the same, the same as the situation when the optical path difference is zero. When the moving mirror moves at a constant speed, the signal intensity detected by the detector changes cosine-like, forming an interference pattern.

[0144] In this embodiment, several classical window functions are used as apodization functions, and the collected interference data are windowed respectively. The signal-to-noise ratio and resolution of the restored spectrum are shown in Table 5.

[0145] Table 5 Spectral performance index table under the action of various conventional window functions

[0146]

[0147]

[0148] By adjusting the parameters of the quasi-trapezoidal window to form window functions with different degrees of apodization, the interference data are windowed, and the signal-to-noise ratio and resolution of the restored spectrum are shown in Table 6.

[0149] Table 6 Spectral performance index table under the action of quasi-trapezoidal window parameters with different parameters

[0150]

[0151]

[0152] In this embodiment, the degree of apodization represents the ratio of the full width at half maximum broadening of the water vapor spectral line in the spectrum after apodization to that without apodization. In the quasi-trapezoidal window function, the degree of apodization can be changed by adjusting the coefficients r T and p. When rT = 0.8 and p = 1, the degree of apodization of the quasi-trapezoidal window is 1.06. Compared with the Hanning window, the spectral resolution is increased by 17.46%. When rT = 0 and p = 4, the degree of apodization of the quasi-trapezoidal window is 2.71. Compared with the Blackman-Harris window, the signal-to-noise ratio of the spectrum is increased by 130.09%.

[0153] In this embodiment, the variation trend of the spectral resolution with rT is as Figure 9 shown. It can be seen that the spectral resolution is positively correlated with the proportionality coefficient rT. The larger rT is, the higher the spectral resolution is. The variation trend of the spectral signal-to-noise ratio with p is as Figure 10 shown. It can be seen that the spectral signal-to-noise ratio is positively correlated with the convolution order p. The larger p is, the higher the spectral signal-to-noise ratio is. By adjusting the proportionality coefficient rT and the convolution order p of the quasi-trapezoidal apodization function, the required spectral signal-to-noise ratio and resolution can be obtained.

[0154] Example 3

[0155] 5 Gas concentration inversion

[0156] 5.1 Samples and experiments

[0157] 5.1.1 Samples

[0158] In this embodiment, in order to study the influence of the quasi-trapezoidal window function on the inversion of different types of gas concentrations, propane and ethylene are selected, which have absorption characteristics of wide peaks and narrow peaks respectively, and propane and ethylene are the main components of petroleum catalytic cracking. Studying these two gases is beneficial to the environmental monitoring of petrochemical industrial parks. The multi-component gas samples with different concentrations used in the experiment are obtained by a standard gas through a dynamic multi-component gas distribution device. Each group of samples is a mixed gas of propane and ethylene, with the propane component concentration of 209 μmol·mol-1 and the ethylene component concentration of 199 μmol·mol-1.

[0159] 5.1.2 Experiment

[0160] In this embodiment, interference data is obtained by a self-developed open-path Fourier transform infrared spectrometer. The spectral range is 500 - 5000 cm-1, the moving mirror speed is 0.2875 cm / s, the detector is MCT, and the maximum optical path difference is 0.01 m. The inhalation method is adopted to introduce the gas to be measured into the gas cell. In the experimental process, first, the sample gas is introduced to exhaust the air in the gas cell, then the sample gas is measured, and the interference data is saved. 400 groups of interference data are measured, the middle 240 groups of interference data are taken, and the average value is taken for every 8 consecutive groups to obtain 30 groups of interference data.

[0161] In this embodiment, the 30 groups of interference data are apodized respectively with five groups of quasi-trapezoidal windows with different parameters (as shown in Table 7, where AD represents the apodization degree), and the processed interference data is imported into the FTIR spectral automatic quantitative analysis software, which is independently developed by the laboratory and adopts the nonlinear least squares quantitative analysis method based on the synthetic background spectrum. The gas inversion concentration is obtained through the FTIR spectral automatic quantitative analysis software.

[0162] Table 7 Five groups of different parameter tables of the quasi-trapezoidal window

[0163]

[0164] For the inversion results of the gas concentration, two indicators, relative accuracy RE and standard deviation STD, are selected to evaluate the accuracy and stability of the gas concentration inversion. The calculation formulas of RE and STD are shown in Equations (9) and (10) respectively

[0165]

[0166] 5.2 Spectral characteristics

[0167] As Figure 11 shown, in this embodiment, the C3H8 gas concentration inversion band is set to 2900 - 3040 cm-1, and C3H8 is at 1 cm -1The full width at half maximum of the standard absorbance spectrum at a resolution of 100 ppm concentration is approximately 16 cm-1. The comparison diagrams of the sample spectra with different apodization degrees and the C3H8 standard absorbance spectrum are as shown in Figure 11 shown. As can be seen from Figure 11 , the spectral characteristics of C3H8 are relatively wide, without sharp absorption peaks. The higher the apodization degree, the smoother the spectral curve. The detailed changes of the spectra in groups 1-4 are basically the same. For those with a higher apodization degree, the absorption is slightly weaker. When the apodization degree is 2.58 (i.e., the spectrum of group 5), the details of the C3H8 absorption spectrum are significantly different, but the change trend is the same.

[0168] As shown in Figure 12 , in this embodiment, the C2H4 gas concentration inversion band is set to 940-960 cm-1. The full width at half maximum of the standard absorbance spectrum of C2H4 at a resolution of 1 cm -1 and a concentration of 100 ppm is approximately 0.8 cm-1. The comparison diagrams of the sample spectra with different apodization degrees and the C2H4 standard absorbance spectrum are as shown in Figure 12 shown. As can be seen from Figure 12 , the spectral characteristics of C2H4 are relatively narrow, but the absorption peaks are single and concentrated. The resolution reduction caused by apodization changes results in an increase in the signal-to-noise ratio, and the spectral curve with lower resolution is smoother. When the apodization degree is 2.58, certain information of the secondary peak of the C2H4 absorption spectrum is lost, and the absorption intensity of the main peak decreases significantly.

[0169] 5.3 Result Analysis

[0170] Since the gas cell length of the mixed gas introduced into the infrared spectrometer is 0.02 m, the concentrations of propane and ethylene under a reduced absorption optical path of 1 m are 4.18 ppm and 3.98 ppm respectively. When no apodization (rectangular window) is performed, the full width at half maximum of the symmetric water spectral line at 1900 cm-1 to 1700 cm-1 is 0.91 cm-1, and the signal-to-noise ratio is 3795.98.

[0171] Statistical analysis is performed on the gas inversion concentration data obtained by the FTIR spectral automatic quantitative analysis software to calculate the mean value, standard deviation, and stability of the gas concentration, so as to characterize the accuracy and stability of gas inversion. The results are shown in Table 8. As can be seen from Table 8: For propane and ethylene, when the apodization degree of the interference data changes, the stability and accuracy of the inversion concentration change inconsistently when using the nonlinear least squares method with the synthetic background spectrum for quantitative analysis. It is speculated from the above results that this should be due to the different specific absorption characteristics of propane and ethylene. Therefore, the inversion concentration analysis of the two gases needs to be discussed separately.

[0172] Table 8 Gas Concentration Inversion Data Table

[0173]

[0174] 5.3.1 Wide-peak gas analysis with propane as an example

[0175] The variation trend of the stability of propane inversion concentration with the apodization degree is as follows Figure 13 shown. It can be seen that with the increase of the apodization degree and the improvement of the signal-to-noise ratio, the stability of propane concentration inversion is improved. When the apodization degree is 2.58, the standard deviation is the smallest, only 0.804, and the stability is the highest. The variation trend of the mean value of propane inversion concentration with the apodization degree is as follows Figure 14 shown. It can be seen that when the apodization degree increases, the relative error of propane inversion concentration is relatively stable, and the variation range of the relative error is within 3%, basically remaining stable, but the amplitude has an obvious downward trend. When inverting the concentration of C3H8 gas, when the apodization degree is increased from 1.24 to 2.58, the stability is increased by 6.62%, and the accuracy remains basically unchanged.

[0176] 5.3.2 Narrow-peak gas analysis with ethylene as an example

[0177] In this embodiment, the variation trend of the stability of ethylene inversion concentration with the apodization degree is as follows Figure 15 shown. It can be seen that with the increase of the apodization degree and the improvement of the signal-to-noise ratio, the stability of propane concentration inversion is improved. When the apodization degree is 2.58, the standard deviation is the smallest, only 0.429, and the stability is the highest. The variation trend of the mean value of ethylene inversion concentration with the apodization degree is as follows Figure 16 shown. It can be seen that when the apodization degree is 1.24 - 2.09, the relative error of ethylene concentration inversion is relatively stable, and the variation range of the relative error is within 3%, basically remaining stable; when the apodization degree is 2.58, the mean value of ethylene concentration inversion decreases significantly, and the relative error is 9.28%. When inverting the concentration of C2H4 gas, when the apodization degree is increased from 1.24 to 2.58, the stability is increased by 22.98%, and the accuracy decreases significantly. At this time, if you want to ensure the accuracy, you can correct the actual inversion concentration.

[0178] In summary, for wide-peak gases or narrow-peak gases with a single and concentrated absorption peak, when performing concentration inversion, there is no need to pursue too high spectral resolution. Using the quasi-trapezoidal window function to reduce the resolution and improve the signal-to-noise ratio can improve the inversion stability to a certain extent.

[0179] Conclusion

[0180] The present invention studies the apodization function of the interferogram of an infrared multi-component gas analyzer and proposes a quasi-trapezoidal window function. On the basis of analyzing the principle of interferogram apodization, adjustable parameters rT and p are introduced to construct the quasi-trapezoidal apodization function, and the time-frequency characteristics of the quasi-trapezoidal apodization function are studied, which has the advantage of a wide adjustment range of the main lobe width and sidelobe attenuation. Applying the quasi-trapezoidal window to the spectral restoration process, through parameter adjustment, restored spectra with different signal-to-noise ratios and resolutions can be obtained. When the apodization degree of the quasi-trapezoidal window is 1.06, compared with the Hanning window, the spectral resolution is increased by 17.46%; when the apodization degree is 2.71, compared with the Blackman-Harris window, the spectral signal-to-noise ratio is increased by 130.09%. The gas concentration inversion experiments of C3H8 and C2H4 show that: for C3H8 gas, when the apodization degree is increased from 1.24 to 2.58, the inversion stability is increased by 6.62%; for C2H4 gas, when the apodization degree is increased from 1.24 to 2.58, the inversion stability is increased by 22.98%, but the accuracy decreases significantly.

[0181] In summary, on the basis of analyzing a variety of classical window functions, the present invention selects the R-V window as the mother window, uses time-domain self-convolution to construct a self-convolution R-V window with significantly improved sidelobe performance, and then introduces a rectangular window with the best main lobe performance to improve the self-convolution R-V window, establishes a quasi-trapezoidal window function with adjustable parameters, and conducts time-frequency characteristic analysis. On this basis, the quasi-trapezoidal window function is applied to the process of spectral restoration and gas concentration inversion. By adjusting the parameters, the spectral restoration effect is improved and the accuracy of gas concentration inversion is increased. At the same time, the present invention proposes and establishes a new apodization function, which allows for a very flexible trade-off between the width of the main lobe and the height of the sidelobe, and is applicable to different spectral restoration occasions.

[0182] The present invention performs time-domain convolution on the R-V window function to construct a self-convolution R-V window with significantly improved sidelobe performance; subsequently, adjustable parameters m and a rectangular window function are introduced to improve the self-convolution R-V window function, thereby obtaining a quasi-trapezoidal window function with a narrower main lobe and optimal sidelobes. The present invention comprehensively considers the high signal-to-noise ratio requirement of spectral restoration, and using a five-term cosine window R-V(I) window to truncate the signal can obtain better results.

[0183] The present invention analyzes the principle of interferogram apodization, studies the influence of the main lobe width and sidelobe attenuation of the apodization function on spectral restoration, uses the R-V window as the mother window, further improves the sidelobe characteristics through self-convolution, and at the same time introduces a rectangular window with adjustable parameters and the best main lobe performance to improve the self-convolution R-V window, thereby establishing a quasi-trapezoidal window function with a wide adjustment range of the main lobe width and sidelobe attenuation.

[0184] Based on the analysis of the apodization principle of the interference pattern, the present invention introduces adjustable parameters rT and p to construct a quasi-trapezoidal apodization function, and studies the time-frequency characteristics of the quasi-trapezoidal apodization function, which has the advantage of a wide adjustment range of the main lobe width and sidelobe attenuation.

[0185] The present invention adopts a quasi-trapezoidal function, which improves the spectral resolution, spectral signal-to-noise ratio, and at the same time improves the inversion stability compared with the prior art that uses other classical window functions.

[0186] The parameters of the quasi-trapezoidal window function of the present invention are easy to adjust. Through parameter adjustment of the quasi-trapezoidal window, the requirements for spectral restoration with high signal-to-noise ratio or high resolution can be met, and the inversion stability of gas concentration can be improved to a certain extent.

[0187] Through the adjustment of the proportionality coefficient rT and the convolution order p, the quasi-trapezoidal apodization function has been greatly improved in terms of the main lobe width and sidelobe peak adjustment. By adjusting rT, the required main lobe width can be achieved, and by adjusting p, the required sidelobe performance can be achieved, enhancing the flexibility of the apodization function in engineering and being applicable to different occasions. The present invention solves the technical problems existing in the prior art, such as being prone to generating false peak signals, easily causing a decrease in the signal-to-noise ratio of the instrument, poor effect of suppressing spectral leakage, and low stability and flexibility.

[0188] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An infrared spectral apodization method for a quasi-trapezoidal window, characterized in that, The method includes: S1. Analyze no less than two classic window functions, and select the R-V window function as the mother function accordingly. Step S1 also includes: S11. Obtain the sidelobe peak level and sidelobe asymptotic attenuation rate of the classic window function; S12. Select the R-V window function as the mother function according to the sidelobe peak level and sidelobe asymptotic attenuation rate, and in combination with the spectral restoration signal-to-noise ratio requirement; The time domain representation of the R-V window function in step S12 is: where M is the number of terms of the window function; n = 1, 2, …, N - 1, and b m is the coefficient parameter of the R-V window; S2. Perform time domain self-convolution on the mother function, and construct a self-convolution R-V window function suitable for sidelobe performance according to the mother function; Step S2 includes: S21. Define the window function obtained by time domain self-convolution; S22. Perform p - 1 convolutions on p basic windows of the same length to obtain a p-order self-convolution R-V window function; S3. Introduce adjustable parameters and a rectangular window function to improve the self-convolution R-V window function to obtain a quasi-trapezoidal window function. Step S3 also includes: S31. Obtain the time domain expression of the p-order self-convolution window R-V function according to the self-convolution R-V window function; S32. Introduce an adjustable parameter r T ; S33. Improve the self-convolution R-V window function through the rectangular window function to obtain a quasi-trapezoidal window function; The quasi-trapezoidal window function in step S33 is: where \(L = r\) T *N, N is the length of the window function, and r T is a coefficient. To ensure the basic quasi-trapezoidal shape, \(0 \lt r\) T \(\leq 0.9\) is the length of the upper base of the quasi-trapezoidal window, and \(w\) RW (n) represents the rectangular window function; S4. Use the quasi-trapezoidal window function to suppress sidelobes, and adjust the proportionality coefficient r according to the time-domain expression of the p-th order self-convolution window R-V function T and the convolution order p to perform apodization operation.

2. The infrared spectral apodization method for a quasi-trapezoidal window according to claim 1, wherein The said b m shall satisfy the constraint condition:

3. The infrared spectral apodization method for a quasi-trapezoidal window according to claim 1, characterized in that, In step S21, the five-term Rife-Vincent (I) self-convolution window is defined as: the window function obtained by time domain self-convolution of no less than two five-term Rife-Vincent (I) windows; In the formula, p is the number of basic windows participating in the convolution, called the order of the window, and w(t) represents the time domain form of a single R-V window function.

4. The infrared spectral apodization method for a quasi-trapezoidal window according to claim 1, characterized in that Step S4 includes: S41. Adjust the adjustable coefficient r T to achieve the applicable main lobe width; S42. Adjust the convolution order p according to the actual demand data to optimize the sidelobe performance.

5. An infrared spectral apodization system for a quasi-trapezoidal window, which is used to perform the infrared spectral apodization method for a quasi-trapezoidal window according to any one of the preceding claims 1 to 4, characterized in that, The system includes: A mother function selection module for analyzing no less than two classic window functions and selecting the R-V window function as the mother function. The mother function selection module also includes: A window function parameter acquisition module for obtaining the sidelobe peak level and sidelobe asymptotic attenuation rate of the classic window function; A window function selection module for selecting the R-V window function as the mother function according to the sidelobe peak level and the sidelobe asymptotic attenuation rate, and in combination with the spectral restoration signal-to-noise ratio requirement. The window function selection module is connected to the window function parameter acquisition module; A self-convolution R-V window function construction module for performing time domain self-convolution on the mother function and constructing a self-convolution R-V window function suitable for sidelobe performance according to the mother function. The self-convolution R-V window function construction module is connected to the mother function selection module; A quasi-trapezoidal function acquisition module for introducing adjustable parameters and a rectangular window function to improve the self-convolution R-V window function to obtain a quasi-trapezoidal window function. The quasi-trapezoidal function acquisition module is connected to the self-convolution R-V window function construction module. The quasi-trapezoidal function acquisition module also includes: A time domain expression module for obtaining the time domain expression of the p-order self-convolution window R-V function according to the self-convolution R-V window function; An adjustable parameter introduction module for introducing an adjustable parameter r T ; A rectangular window function improvement module is used to improve the self-convolution R-V window function through the rectangular window function to obtain the quasi-trapezoidal window function. The rectangular window function improvement module is connected to the time-domain expression module and the adjustable parameter introduction module; The parameter adjustment apodization module is used to suppress sidelobes by using the quasi-trapezoidal window function, and adjust the proportionality coefficient r according to the time-domain expression of the p-order self-convolution window R-V function T and the convolution order p to perform apodization operations. The parameter adjustment apodization module is connected to the quasi-trapezoidal function acquisition module.

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