A spectral resolution enhancement filtering method

Abstract

A spectral resolution enhancement filter combines a frequency cutoff response function and a frequency adjustment response function into a single filter. This filter shrinks the peak width while cutting off newly generated, undesirable high-frequency components. This effectively avoids noise interference and ensures the robustness of the spectral resolution enhancement operation. This stable, accurate, easy-to-use, and widely used resolution enhancement algorithm is suitable for solving resolution enhancement problems in various instruments and situations. During the spectral resolution enhancement process, the appropriate frequency cutoff response function and frequency adjustment response function are determined through parameter adjustment. The number of convolutions between the convolution kernel and the original spectrum can be gradually adjusted to output the desired result.

Description

Technical Field

[0001] The present invention relates to the field of filters, and in particular to a spectral resolution enhancement filtering method. Background Art

[0002] Resolution is a key performance metric for a spectrometer, directly impacting its applicability and price. Traditionally, hardware improvements have been employed. Factors influencing spectral resolution include the selection and design of the spectrometer's optical components, optical path, and detectors. With technological advancements, signal processing techniques are playing a more important role. Currently, two main types of techniques have been reported: frequency-domain inverse Fourier transform (IFT) and time-domain deconvolution. A common limitation of these techniques is their susceptibility to noise, which hinders robustness.

[0003] The essence of improving spectral resolution is to reduce the width of the underlying independent peaks. This reduction in peak width correspondingly increases peak height. The narrower the original peak, the more pronounced the change in peak height after reduction. Uniform high- and low-frequency components in the noise become more prominent as the peaks shrink. Consequently, even tiny amounts of original noise can mask signals of interest after processing, even leading to unusable output. Summary of the Invention

[0004] In order to solve the problems existing in the above-mentioned prior art, the object of the present invention is to provide a spectral resolution enhancement filtering method;

[0005] To achieve the above object, the technical solution of the present invention is:

[0006] A spectral resolution enhancement filtering method, the implementation steps of which are as follows:

[0007] Step 1: transform the input spectrum SR into the frequency domain and determine the frequency fraction b to be retained;

[0008] Step 2: Define the frequency cutoff response function FRS: FRS = Sech((ω / b) ps ), where ps is the peak cutoff parameter. It is recommended that ps be any number in the range of 1-3. The larger the bottom broadening of the spectrum, that is, the more it tends to the Lorentz peak type, the smaller the value of ps should be.

[0009] Step 3: Define the frequency adjustment response function FRT; FRT = exp((ω / (2b)) pt ), where pt and ps have similar functions as peak shape adjustment parameters. The recommended range for pt is 1-2. Similarly, the more the spectrum tends to be in a Lorentzian peak shape, the smaller the value of pt. pt and ps can take the same value, or different values ​​depending on the complexity of the actual peak shape distribution.

[0010] Step 4: Combine FRS and FRT into a unified frequency response function FR, FR = FRS·FRT;

[0011] Step 5: FR is transformed by FFT (Fast Fourier Transform), and the real part after transformation is taken as the convolution kernel KC in the time domain;

[0012] Step 6: Calculate the convolution of KC and SR successively, and gradually shrink the peak width of SR to the required level.

[0013] Compared with the prior art, the present invention has the following beneficial effects:

[0014] The present invention provides a spectral resolution enhancement filtering method that combines a frequency cutoff response function and a frequency adjustment response function into a single filter. This filter reduces the peak width while cutting off newly generated, undesirable high-frequency components, effectively avoiding noise interference and ensuring the robustness of the spectral resolution enhancement operation. This stable, accurate, easy-to-use, and widely used resolution enhancement algorithm is suitable for addressing resolution enhancement issues in various instruments and situations. During the spectral resolution enhancement process, the appropriate frequency cutoff response function and frequency adjustment response function are determined through parameter adjustment. The number of convolutions between the convolution kernel and the original spectrum can be gradually adjusted to output the desired result. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 The original spectrum contains three independent broad peaks;

[0016] Figure 2 It is the normalized frequency diagram of the original spectrum transformed into the frequency domain;

[0017] Figure 3 is the frequency cutoff response function diagram;

[0018] Figure 4 It is the frequency adjustment response function graph;

[0019] Figure 5 is the frequency response function diagram after compounding;

[0020] Figure 6 is the convolution kernel image in the time domain;

[0021] Figure 7 This is the processing effect diagram of overlapping peaks under different convolution times;

[0022] Figure 8 This is the result of enhancing the Raman spectral resolution of ibuprofen using this method. DETAILED DESCRIPTION

[0023] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0024] Example 1:

[0025] like Figure 1-8 As shown, a spectral resolution enhancement filtering method is implemented as follows:

[0026] Step 1: Figure 1 It is an overlapping peak SR containing three independent broad peaks. Due to the large peak width, the three peaks overlap and each independent peak cannot be clearly identified.

[0027] Transform SR to the frequency domain, normalize the standardized frequency ω, and determine the frequency fraction b that needs to be retained in the entire frequency range, such as Figure 2 As shown in Figure 2, ω is the frequency fraction b when the amplitude approaches 0.

[0028] Step 2: Define the frequency cutoff response function FRS, FRS = Sech((ω / b) ps ), select ps = 2, b = 0.04, and get the frequency cutoff response function as Figure 3 shown.

[0029] Step 3: Define the frequency adjustment response function FRT, FRT = exp((ω / (2b)) pt ), select pt = 1.6, b = 0.04, and get the frequency adjustment response function as follows Figure 4 shown.

[0030] Step 4: Combine FRS and FRT into a unified frequency response function FR, FR = FRS·FRT. Figure 5 To obtain the frequency response function FR.

[0031] Step 5: After performing fast Fourier transform on FR, take its real part to obtain the convolution kernel KC in the time domain, as shown in Figure 6 shown.

[0032] Step 6: Calculate the convolution of KC and SR successively, and gradually shrink the peak width of SR to the required level. Figure 7 The curves from bottom to top are the original spectrum and the results after 2, 10, 20, 30, and 40 convolutions, respectively.

[0033] from Figure 7 As can be seen, after processing the overlapping peaks of three independent broad peaks using the method of the present invention, only two convolutions are required to clearly identify the individual peaks. As the number of convolutions increases, spectral resolution gradually improves. The filter proposed in this invention can effectively reduce peak widths while effectively avoiding noise interference, ensuring the robustness of the spectral resolution enhancement operation.

[0034] Example 2

[0035] The Raman spectrum of ibuprofen (AR) was collected. According to the implementation steps of the present invention, b=0.4, ps=1.1, and pt=1.2 were set to process the Raman spectrum of ibuprofen in the group region. Figure 8 The original spectrum, the processing results after 10 and 20 repeated convolutions, can be seen that the present invention can effectively achieve spectral resolution enhancement. After 20 repeated convolutions, the original overlap at 2878 cm -1 and 2966cm -1 The weak peaks within the main peak are clearly identified.

[0036] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that are not conceived through creative work should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection defined in the claims.

Claims

1. A spectral resolution enhancement filtering method, the implementation steps of which are as follows: Step 1: transform the input spectrum SR into the frequency domain and determine the frequency fraction b to be retained; Step 2: Define the frequency cutoff response function FRS: , where ps is the peak cutoff parameter; Step 3: Define the frequency adjustment response function FRT; , where pt is the peak shape adjustment parameter; Step 4: Combine FRS and FRT into a unified frequency response function FR. ; Step 5: FR is transformed by FFT (Fast Fourier Transform), and the real part after transformation is taken as the convolution kernel KC in the time domain; Step 6: Calculate the convolution of KC and SR successively, and gradually shrink the peak width of SR to the required level.

2. The method according to claim 1, characterized in that In step 2, ps is any number ranging from 1 to 3. The greater the bottom broadening of the spectrum, that is, the more it tends to be a Lorentz peak type, the smaller the value of ps is.

3. The method according to claim 1, characterized in that In step 3, pt is any number between 1 and 2. The more the spectrum tends to be in the Lorentzian peak shape, the smaller the value of pt is.

4. The method according to any one of claims 2 or 3, characterized in that pt and ps take the same value or different values ​​according to the complexity of the actual peak distribution.

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