CN111490752A - A Method for Obtaining Spectral Derivatives of Digital Filters - Google Patents

Abstract

The present invention provides a method for obtaining a spectral derivative for a digital filter, comprising: step 1, selecting a spectrum Sp to be derived; step 2, constructing a convolution transfer function H; step 3, obtaining the derivative of the spectrum Sp; convolution The transfer function H is obtained through the following steps: designing the transfer function PF of the smoothing filter, performing inverse Fourier transform on the PF to obtain an array H0, and obtaining the convolution transfer function H from the array H0; Calculate the convolution of H and the spectral data Sp, and obtain the 0th-order result after selective excision; and use the H difference to replace the derivation to obtain the results of each order difference, calculate its convolution with Sp, and obtain the Sp after selective excision. The nth derivative result. The invention can calculate the derivative spectrum of each order which is easy to be clearly identified; the derivative spectrum obtained by the method of the invention can obtain clearer and definite information, which is of great significance for the identification, identification and in-depth analysis of the spectrum.

Description

A Method for Obtaining Spectral Derivatives of Digital Filters

technical field

The present invention relates to the field, in particular to a method for obtaining spectral derivatives of a digital filter.

Background technique

Derivative spectroscopy has been a mature and effective method in UV-Vis spectral analysis, because it can effectively improve the spectral resolution and selectivity, and play an important role in solving the direct measurement problem of complex multi-component systems. At the same time, for near-infrared spectroscopy, it is also a conventional data preprocessing method to eliminate the scattering drift by obtaining the first derivative. However, for other spectra, especially Raman and infrared spectra with sharp and narrow peaks, there are not many applications. The reason is not that the method is not suitable, but the lack of effective means of obtaining derivative spectra; Due to the limitation of the derivation ability, the spectrum and derivative spectroscopy basically adopts the first-order processing, and stops at the second-order, and it is difficult to realize the derivative spectrum of the second-order and above.

The difficulty of spectral derivation lies in noise interference. For signals of different frequencies, its amplitude decays exponentially with frequency. Direct derivation, unless the signal-to-noise ratio is very high, the high-frequency part of the noise in the signal will completely cover the real signal after derivative processing. Therefore, an effective derivative noise reduction method must be adopted to filter out the high-frequency part of the signal and retain the relatively low-frequency real signal. The reason why derivative spectroscopy can be implemented on the broad peaks of the ultraviolet or near-infrared spectrum is that the lower the frequency of the real signal being denoised, the greater the difference from the high frequency of the noise, and the less difficult it is to calculate the derivative. On the narrow peaks such as Raman and mid-infrared, the frequency is close to the high frequency of the noise, and the difficulty of the problem is significantly improved.

The spectral derivation method has two solutions: software and hardware. Through the hardware method of electronic differential components, in addition to the increase in equipment and design costs, the effect is also limited, and more often it relies on software implementation of signal processing algorithms. In terms of the algorithm approach, the S-G digital differential filter is relatively feasible at present, but to achieve better results, it is still limited by the signal-to-noise ratio of the signal. The accuracy of the S-G algorithm is limited, and the parameter setting jump degree is large, which cannot be fine-tuned. Therefore, the calculation error of the second derivative increases significantly, and with the increase of the filtering strength, the peak shape has obvious errors.

The existing S-G filter has a good direct smoothing performance for spectral data, but as the derivative order increases, its precision setting is limited, resulting in the inability to fine-tune the error, and the calculation error of the derivative above the second order is obvious. Since the filtering noise reduction-derivation method has a reliable mathematical principle, the key to reducing the calculation error is to improve the adjustable accuracy of the method.

The polynomial fitting represented by the S-G filter - the least squares optimization filter, in principle boils down to a simplified FIR filter. The direct problem encountered by the polynomial fitting approach is the Runge phenomenon caused by the use of high-order polynomial fitting; the higher the accuracy, the higher the polynomial order required, and the greater the possibility of Runge phenomenon. Therefore, the optional order is limited, the adjustable range is usually 2-8 order integers, and the range of optional parameters is very small; in addition, the frame width of the S-G filter is limited, and it can only be an odd number, and the minimum step width is 2, which cannot be Further fine-tuning the segmentation.

High-precision high-order derivative measurement or calculation is a key technology in the design and manufacture of international high-end instruments. Without effective algorithms, it has to rely on instrument hardware with a very high signal-to-noise ratio, pushing up product costs. The high-precision digital filter derivation algorithm has very high technical and industrial value in instrument R&D and product performance.

The inventor found that the calculation principle of the digital filter is the convolution calculation of the original signal and the transfer function. To improve the adjustable ability of the filter, the accuracy of the transfer function can be improved. Further, according to the property of convolution, the calculation of the derivative of the original signal can be realized by convolution of the original signal and the derivative of the transfer function.

SUMMARY OF THE INVENTION

In order to solve the above deficiencies in the related art, the present invention provides a method for obtaining a spectral derivative of a digital filter.

A method for obtaining the spectral derivative of a digital filter invented by the invention is realized by the following technical solutions:

A method for obtaining a spectral derivative for a digital filter, comprising:

Step 1, select the spectrum Sp to be differentiated;

Step 2, constructing the convolution transfer function H for derivation calculation;

Step 3, through the convolution transfer function H, the derivative of the spectrum Sp is obtained.

Further, the convolution transfer function H described in step 2 is obtained through the following steps:

Step a, design the transfer function PF of the smoothing filter;

Step b, inverse Fourier transform is performed on the transfer function PF, and the real part array of the output transform array is obtained to obtain the array H0;

In step c, the convolution transfer function H is obtained according to the array H0 obtained in step b.

Further, obtaining the derivative of the spectrum Sp described in step 3 includes obtaining the 0-order result of Sp and obtaining the n-order result of Sp; wherein, n is a positive integer.

Further, the 0th-order result of obtaining Sp is obtained by the following method:

directly compute the convolution of H with the filtered spectral data Sp;

If there are m elements in H, m/2 elements are removed from the front and rear of the convolution result, and the remaining array elements correspond to the result of Sp smoothing, that is, the 0-order result;

where m is a non-negative integer.

Further, the nth-order result of obtaining Sp is obtained by the following method:

Using H difference instead of derivation, you can obtain H(1), H(2), ..., H(n) and other order difference results in sequence, and calculate the convolution of H(n) and Sp of each order difference of H;

If the number of elements m of H(n) is an even number, m/2 elements are removed from the front and rear of the convolution result, and the remaining elements are the result of the n-order derivative of Sp;

If the number of elements m of H(n) is an odd number, (m+1)/2 elements are removed from the front and rear of the convolution result, and (m-1)/2 elements are removed from the back end, and the remaining element is Sp The result of the nth derivative of .

Further, the transfer function PF described in step a is represented as an array, and the transfer function PF includes a band-stop segment Wr and a band-pass segment Wp;

The band-stop section Wr is selected to describe the right half of the distribution function of the band-pass behavior of the signal, and is used to set the percentage of frequencies that can be passed, and the passed frequency range includes low-frequency signals;

The bandpass section Wp is used to allow 100% of the frequency to pass;

Among them, Wr and Wp are non-negative integers, and the smaller the number, the greater the filtering strength.

Further, the array H0 described in step b refers to the array from the head of the output real part array to the half position of the whole array.

Further, the convolution transfer function H described in step c is obtained by merging H1 obtained by flipping H0 and H0 before and after, and dividing by the sum value of all elements;

The formula of the convolution transfer function H is:

H=[H1, H0]/sum([H1, H0]).

Further, the formula of the transfer function PF is as follows:

Compared with the prior art, the derivation method of the present invention has the following advantages:

1) Obtain the derivative (difference) of each order of the transfer function in turn, and then obtain the convolution of the original signal and the derivative (difference) of each order of the transfer function, and realize the acquisition of the multi-order derivative spectrum;

2) The present invention can calculate the derivative spectrum of each order that is easy and clearly identified;

3) Using the derivative spectrum obtained by the method of the present invention, clearer and definite information can be obtained;

4) The method of the present invention is of great significance for the identification, identification and in-depth analysis of the spectrum.

Description of drawings

The accompanying drawings are used to provide a further understanding of the present invention, and constitute a part of the specification, and are used to explain the present invention together with the embodiments of the present invention, and do not constitute a limitation to the present invention.

Fig. 1 is the analog frequency blocking amplitude function PF in the embodiment 1 of the present invention;

2 is a schematic diagram of the output of the real part after the inverse Fourier transform of the frequency blocking-pass amplitude function PF in Embodiment 1 of the present invention;

3 is a schematic diagram of the constitution of the transfer function H in Embodiment 1 of the present invention;

4 is a schematic diagram of each order derivative (difference) transfer function in Embodiment 1 of the present invention;

Fig. 5 is the convolution result of simulated spectrum Sp and 0th-order to 4th-order transfer function in the embodiment of the present invention 1;

Fig. 6 is the derivative result of each order output in the embodiment 1 of the present invention;

Fig. 7 is the direct difference result of spectral data Sp1 in the embodiment 2 of the present invention;

Fig. 8 is the derivative result of adopting the derivative filter of the present invention to spectral data Sp1 in the embodiment 2 of the present invention;

Fig. 9 is the result comparison of different processing methods in the embodiment of the present invention 2;

FIG. 10 is the result of spectral processing of aspirin using the method of the present invention in Example 3 of the present invention.

Detailed ways

The embodiments of the present invention are described below by specific embodiments, and those skilled in the art can easily understand other advantages of the present invention from the contents disclosed in this specification.

A method for obtaining a spectral derivative for a digital filter, comprising: step 1, selecting a spectrum Sp to be differentiated; step 2, constructing a convolution transfer function H for derivation calculation; step 3, passing the Convolve the transfer function H to find the derivative of the spectrum Sp.

Further, the convolution transfer function H described in step 2 is obtained through the following steps: step a, design the transfer function PF of the smoothing filter; step b, perform inverse Fourier transform on the transfer function PF, and output a transform array In step c, the convolution transfer function H is obtained according to the array H0 obtained in step b.

Further, obtaining the derivative of the spectrum Sp described in step 3 includes obtaining the 0-order result of Sp and obtaining the n-order result of Sp; wherein, n is a positive integer.

Further, the 0th-order result of the described seeking Sp is obtained by the following method: directly calculate the convolution of H and the filtered spectral data Sp; if H contains m elements, remove each m/ 2 elements, and the remaining array elements correspond to the result of Sp smoothing, that is, the 0-order result; where m is a non-negative integer.

Further, the n-order result of obtaining Sp is obtained by the following method: using H difference instead of derivation, H(1), H(2), ..., H(n) and other order differences can be obtained sequentially As a result, calculate the convolution of H(n) and Sp of each order difference of H; if the number of elements m of H(n) is an even number, m/2 elements are removed from the front and rear of the convolution result, and the remaining elements are The result of the n-order derivative of Sp; if the number of elements m of H(n) is an odd number, (m+1)/2 elements are removed from the front and rear of the convolution result, and (m-1)/2 elements are removed from the back end, The remaining element is the result of the n-order derivative of Sp;

Among them, the H difference is the common sense of numerical calculation, and the discrete calculation needs to calculate the differential, which is replaced by the difference calculation.

Further, the transfer function PF in step a is represented as an array, and the transfer function PF includes a band-stop segment Wr and a band-pass segment Wp; the band-stop segment Wr selects the right side of the distribution function used to describe the band-pass behavior of the signal. The half part is used to set the percentage of frequencies that can be passed, and the passed frequency range includes low-frequency signals; the band pass section Wp is used to allow 100% of the frequency to pass; wherein, Wr and Wp are non-negative integers, the smaller the number , the greater the filter strength.

Further, the array H0 described in step b refers to the array from the head of the output real part array to the half position of the whole array.

Further, the convolution transfer function H described in step c is obtained by merging H1 obtained by flipping H0 and H0 before and after, and dividing by the sum value of all elements; the formula of the convolution transfer function H is:

H=[H1, H0]/sum([H1, H0]).

Further, the formula of the transfer function PF is as follows:

Example 1

The present embodiment provides a method for obtaining a spectral derivative by a digital filter, including:

First, select the spectrum Sp to be differentiated; then, with Wr and Wp both being 500, construct the transfer function H, and its 1st, 2nd, 3rd, and 4th order transfer functions H(1), H(2), H( 3), H(4).

The distribution function used to describe the bandpass behavior of the signal in this embodiment adopts Gaussian distribution.

As shown in Figure 1. Set an array with Wp elements of 1 to form the bandpass part; then, take Wr as the peak width, construct the right half of the Gaussian peak, normalize it, and get the bandstop part; combine the two parts to get the complete frequency The blocking amplitude function PF.

Perform the inverse Fourier transform on the frequency block-pass amplitude function PF, and take the output of the real part of the inverse Fourier transform result, as shown in Figure 2.

Take the output of the first half of the real part of the inverse Fourier transform of the frequency block-pass amplitude function PF as H0, turn H0 into H1, and combine H1 and H0 to form the transfer function H, as shown in Figure 3.

H( 1 ) to H( 4 ) shown in FIG. 4 are the derivative (difference) transfer functions of each order obtained by taking the difference with respect to H .

Figure 5 is a convolution result of a simulated Gaussian peak Sp with a transfer function of order 0 to 4. The m/2 data points are cut off before and after the convolution result, and the derivative results of each order can be obtained, as shown in Figure 6.

Example 2

This embodiment provides a method for a digital filter to obtain a spectral derivative:

The distribution function used to describe the bandpass behavior of the signal in this embodiment adopts Gaussian distribution.

First, by constructing five Gaussian peaks with different widths and superimposing white noise with a maximum peak height of 1% intensity, the fitted spectral data Sp1 is obtained, as shown in Figure 7(a). Figure 7(b)-(e) are the direct 1-4th order difference results. It can be seen that after the order is greater than 1, the signal is covered by noise and is almost unrecognizable.

Using the derivation method proposed above in the present invention, the smoothing and the 1-4 order derivative calculation are completed in sequence. The results are shown in Fig. 8. When the filtering parameters Wp=500 and Wr=800, the signal in the fourth-order derivative can still be effectively identified.

Figure 9 is a comparison of the results of the noise-free direct second-order difference, the second-order derivative of the S-G filter, and the second-order derivative of the signal under three conditions of the method of the present invention. The figure shows the narrowest peak width of the signal, and here is the derivative The most significant part of the error when processing. It can be seen that the present invention has better performance and adjustability than S-G filtering, which is currently considered to be the best filtering derivation method.

As can be seen from Fig. 9, the two parameters selected by the present invention have a large room for adjustment, so a smoother curve can be finely adjusted, and at the peak, the consistency with the real signal is maintained, and the S-G filter There is a trade-off between curve smoothness and realism.

Example 3

Raman spectra of pure aspirin were collected and analyzed under 785nm laser excitation and 1ms integration time. Using the above-mentioned method for obtaining the derivative of the present invention, the measured Raman spectrum of aspirin is subjected to 4th order derivation to obtain the 4th order derivative spectrum, as shown in FIG. 10 .

By applying the present invention, the fourth-order derivative spectrum that is easy to be clearly identified can be calculated. By comparing the original spectrum and the derivative spectrum, it can be found that on the derivative spectrum, the originally overlapping Raman peaks have been completely separated. Clear and definite information is of great significance for the identification, identification and in-depth analysis of spectra.

Claims (9)

1. a method for obtaining spectral derivative for digital filter, is characterized in that, comprises: Step 1, select the spectrum Sp to be differentiated; Step 2, constructing the convolution transfer function H for derivation calculation; Step 3, through the convolution transfer function H, the derivative of the spectrum Sp is obtained. 2. a kind of method that is used for digital filter to obtain spectral derivative as claimed in claim 1, is characterized in that, the described convolution transfer function H of step 2 is obtained by following steps: Step a, design the transfer function PF of the smoothing filter; Step b, inverse Fourier transform is performed on the transfer function PF, and the real part array of the output transform array is obtained to obtain the array H0; In step c, the convolution transfer function H is obtained according to the array H0 obtained in step b. 3. a kind of method that is used for digital filter to obtain spectral derivative as claimed in claim 1 and 2, is characterized in that, the described derivative of seeking spectrum Sp of step 3 comprises the 0th order result of seeking Sp and seeking The nth order result of Sp; where n is a positive integer. 4. a kind of method that is used for digital filter to obtain spectral derivative as claimed in claim 3, it is characterized in that, described to obtain the 0th order result of Sp is obtained by following method: directly compute the convolution of H with the filtered spectral data Sp; If there are m elements in H, m/2 elements are removed from the front and rear of the convolution result, and the remaining array elements correspond to the result of Sp smoothing, that is, the 0-order result; where m is a non-negative integer. 5. a kind of method that is used for digital filter to obtain spectral derivative as claimed in claim 3 or 4, it is characterized in that, the n-order result of described seeking Sp is obtained by the following method: Using H difference instead of derivation, you can obtain H(1), H(2), ..., H(n) and other order difference results in sequence, and calculate the convolution of H(n) and Sp of each order difference of H; If the number of elements m of H(n) is an even number, m/2 elements are removed from the front and rear of the convolution result, and the remaining elements are the result of the n-order derivative of Sp; If the number of elements m of H(n) is an odd number, (m+1)/2 elements are removed from the front and rear of the convolution result, and (m-1)/2 elements are removed from the back end, and the remaining element is Sp The result of the nth derivative of . 6. A method for obtaining spectral derivatives for a digital filter as claimed in claim 3, wherein the transfer function PF in step a is represented as an array, and the transfer function PF comprises a band stop section Wr and Bandpass segment Wp; The band-stop section Wr is selected to describe the right half of the distribution function of the band-pass behavior of the signal, and is used to set the passable frequency percentage; The bandpass section Wp is used to allow 100% of the frequency to pass; where Wr and Wp are non-negative integers. 7. a kind of method that is used for digital filter to obtain spectral derivative as claimed in claim 3, it is characterised in that the array H0 described in step b refers to the half position from the head of the output real part array to the whole array array. 8. a kind of method that is used for digital filter to obtain spectral derivative as claimed in claim 2 or 7, it is characterized in that, the described convolution transfer function H of step c is by H0 and H0 by turning the H0 and H0 back and forth to obtain the merger , and divided by the sum of all elements; The formula of the convolution transfer function H is: H=[H1, H0]/sum([H1, H0]). 9. a kind of method that is used for digital filter to obtain spectral derivative as claimed in claim 3, is characterized in that, the formula of described transfer function PF is as follows:

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