High-resolution adaptive filtering ultrasonic imaging method based on range standard deviation product coefficient

Abstract

The invention relates to a high-resolution adaptive filtering ultrasonic imaging method based on a range standard deviation product coefficient, and belongs to the technical field of ultrasonic imaging. The method comprises the following steps: carrying out delay processing on a sampling signal to obtain ultrasonic echo data, and solving the range and the standard deviation of the echo data; multiplying the range and the standard deviation of the echo data point of each imaging point, and taking the reciprocal to obtain a range and standard deviation product coefficient; solving a symbol coherence coefficient of echo data of each imaging point, and performing parameter correction on the range standard deviation product coefficient by using the solved symbol coherence coefficient as a weighting coefficient; summing the echo data of the N channels to obtain a delay superposition result, and weighting the delay summation result of the echo data of the N channels by using the corrected RSF coefficient; and weighting the output of the improved adaptive filter by the coefficient after the 32-order FIR filtering to obtain a scanning line signal formed by an adaptive beam, and carrying out final imaging by adopting the optimized scanning line signal.

Description

Technical Field

[0001] The invention belongs to the technical field of ultrasonic imaging, and relates to a high-resolution adaptive filtering ultrasonic imaging method based on a range standard deviation product coefficient. Background Art

[0002] Ultrasonic imaging technology is widely used in industrial nondestructive testing due to its advantages such as good directionality, strong penetration, concentrated energy, wide application range and real-time imaging. The widely used B-type digital ultrasonic imaging currently uses ultrasonic pulse echo technology, that is, after the excitation probe emits an ultrasonic pulse wave, the system receives and processes the reflected ultrasonic signal, and finally obtains a real-time image reflecting the internal acoustic impedance characteristics of the object being measured. In the process of ultrasonic imaging, generally, steps such as ultrasonic pulse emission, time gain compensation, receiving focusing, beamforming, envelope detection, logarithmic compression, and imaging post-processing are involved. The delay superposition algorithm (DAS) is the simplest and most widely used beamforming algorithm. When transmitting, DAS achieves transmission focusing by applying different delay parameters to a series of array elements. When receiving, DAS dynamically delays and sums the signals received from all channels to form an image. However, the beam focused by this method has problems such as wide main lobe, high side lobe, poor lateral resolution, and clutter interference.

[0003] The minimum variance distortionless beamformer (MV) can effectively improve the resolution of the image and filter out the interference and noise signals through the directional difference between the interference signal and the desired signal. However, its robustness is poor, which is not conducive to practical applications. The generalized sidelobe canceller (GSC), as an equivalent structure of the minimum variance distortionless beamformer, has a similar improvement effect on imaging and can significantly improve the lateral resolution, but the sidelobe suppression capability is still weak, and the contrast has not been improved accordingly. In addition, since the adaptive beamforming method contains a large number of matrix operations, the robustness of the adaptive beamforming is not as good as the traditional DAS algorithm.

[0004] In summary, there is an urgent need for a beamforming algorithm that can maintain high resolution and improve imaging contrast. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a high-resolution adaptive filtering ultrasound imaging method based on the range standard deviation product coefficient, which can effectively improve the algorithm imaging contrast while maintaining the good resolution performance of the traditional high-resolution adaptive filtering beamforming algorithm, thereby improving the overall imaging quality of the algorithm.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A high-resolution adaptive filtering ultrasonic imaging method based on range standard deviation product coefficient, the method comprising the following steps:

[0008] S1: Amplify, AD convert, delay focus and digitally filter the echo signal received by the ultrasonic array element to obtain ultrasonic echo data x(k);

[0009] S2: Solve the range and standard deviation of the echo data of each imaging point, multiply the range and standard deviation of the echo data of each imaging point and take the inverse to obtain the range standard deviation product coefficient;

[0010] S3: solving the symbol coherence coefficient of the echo data of each imaging point and performing threshold parameter correction on the product coefficient of the range standard deviation of the echo data of the same imaging point;

[0011] S4: summing up the echo data of N channels to obtain a delay superposition result, and weighting the summation result with the modified RSF coefficient;

[0012] S5: The coefficients after the 32-order FIR filter are weighted to the output of the improved adaptive filter structure to obtain a scan line signal for adaptive beamforming, and the optimized scan line signal is used for final imaging.

[0013] Further, in S2, the range and standard deviation of the echo data of each imaging point are solved respectively, and then the range and standard deviation of the echo data of each imaging point are multiplied and the inverse is taken to obtain the range standard deviation product coefficient, which specifically includes the following steps:

[0014] S21: For a sensor array with N equally spaced elements, the range R(k) and standard deviation σ(k) of the echo data at each imaging point are solved as follows:

[0015] R(k)=max(x(k))-min(x(k))

[0016]

[0017] Where x(k) is the N-channel echo data after amplification, AD conversion, time-delay focusing and filtering, max() is the maximum value operation of the one-dimensional array, min() is the minimum value operation of the one-dimensional array; u(k) is the average value of the N-channel echo data x(k), that is,

[0018] S22: Multiply the obtained range by the standard deviation and take the inverse to obtain the range standard deviation product coefficient RSF(k):

[0019]

[0020] Furthermore, in S3, the symbol coherence coefficient of the echo data of each imaging point is solved and the threshold parameter correction is performed on the range standard deviation product coefficient of the echo data of the same imaging point, which specifically includes the following steps:

[0021] S31: Divide the N-channel echo data into (-π / 2,π / 2] and [-π,-π / 2]∪(π / 2,π]; when all phases of the echo signal are (-π / 2,π / 2], the signal is positively correlated; when all phases are [-π,-π / 2]∪(π / 2,π], the signal is negatively correlated:

[0022]

[0023] In the formula, i is the array element number, k is the sampling point number;

[0024] S32: Solve for b i The variance of (k) is:

[0025]

[0026] because The above formula is simplified to:

[0027]

[0028] S33: By b i (k) Solve for the symbolic coherence coefficient SCF(k):

[0029]

[0030] When the polarity of all echo data is the same, the value of SCF(k) is the largest and is 1; when the polarity of the echo data is half positive and half negative, SCF(k) is 0;

[0031] S34: The SCF coefficient is used to determine whether the echo data point is a defect detection point or a background point; when the normalized SCF coefficient of the imaging point is greater than 0.9, it is considered to be a defect detection point, and the RSF coefficient is corrected at this time; when the SCF coefficient is less than 0.9, the imaging point is a background point, and the RSF coefficient remains unchanged; the correction expression is:

[0032]

[0033] Where RSF is the coefficient matrix composed of the RSF(k) coefficients of each imaging point, and max(RSF) is the maximum value of the RSF coefficients of all imaging points.

[0034] Further, in S4, the echo data of N channels are summed to obtain a delayed superposition result, and the summation result is weighted by the modified RSF coefficient, which specifically includes the following steps:

[0035] S41: summing the echo data of N ultrasonic arrays to obtain a delay superposition result:

[0036]

[0037] Where k is the number of sampling points of the imaging point, that is, k = N, x i (k-Δ i )(i=1,...,N) represents the ultrasonic signal after focusing and delaying the N channel echoes, Δ i Indicates the delay time applied to each array element signal;

[0038] S42: Weight the summation result using the modified RSF coefficient:

[0039]

[0040] Further, in S5, the 32nd order FIR bandpass filter coefficient with a center frequency of 5.26 MHz and a bandwidth of 1.4 MHz is used as a weighting factor to multiply the output of the improved adaptive filtering structure to obtain a scan line signal of adaptive beamforming, and the optimized scan line signal is used for final imaging:

[0041]

[0042] c k represents the filter coefficient, which is obtained by multiplying the impulse response of the ideal filter by a window function; c k In the frequency domain, it is expressed as a window function added to a specific frequency interval. The value outside this interval is 0 or a minimum value. It is multiplied with the original signal in the frequency domain, that is, convolution calculation is performed in the time domain. The value of the original signal outside the specific frequency interval is removed in the frequency domain, and the clutter outside the passband frequency is filtered out in the time domain.

[0043] The beneficial effect of the present invention is that compared with the existing high-resolution adaptive filtering algorithm, the present invention can improve the imaging contrast performance while ensuring its high-resolution performance. The present invention can significantly suppress the noise clutter existing in non-destructive testing ultrasonic imaging, and can overcome the trade-off between high-resolution image and high-contrast.

[0044] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0046] Figure 1 is a flow chart of the ultrasonic imaging method of the present invention;

[0047] Figure 2 The overall structural framework diagram of the high-resolution adaptive filter based on the product coefficient of the range standard deviation;

[0048] Figure 3 This is a schematic diagram of the imaging area of ​​the 20# steel test block;

[0049] Figure 4 This is the 10mm depth imaging comparison picture of the 20# steel test block;

[0050] Figure 5 This is the lateral resolution curve of 20# steel test block at 10mm depth;

[0051] Figure 6 This is a partial enlarged view of the resolution curve of imaging points 7 and 8;

[0052] Figure 7 It is a schematic diagram of the imaging area of ​​the aluminum test block;

[0053] Figure 8 This is a comparison image of the aluminum test block at 65mm depth;

[0054] Fig. 9 This is the lateral resolution curve of the aluminum test block at 65 mm depth;

[0055] Fig.10 This is a local enlarged image of imaging point No. 1. DETAILED DESCRIPTION

[0056] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0057] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0058] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0059] See also Figures 1 to 10 , Figure 1 It is a flow chart of the method of the present invention, such as Figure 1 As shown, the present invention provides a high-resolution adaptive filtering ultrasonic imaging method based on the range standard deviation product coefficient, comprising the following steps:

[0060] S1: Amplify, AD convert, delay focus and digitally filter the 32-channel echo signals received by the ultrasonic array element to obtain ultrasonic echo data x(k);

[0061] S2: Solve the range and standard deviation of the echo data of each imaging point respectively, multiply the range and standard deviation of the echo data of each imaging point and take the inverse to obtain the range standard deviation product coefficient of the imaging point, which specifically includes the following steps:

[0062] S21: For a sensor array with 32 equally spaced elements, the range R(k) and standard deviation σ(k) of the echo data at each imaging point are solved as follows:

[0063] R(k)=max(x)-min(x)

[0064]

[0065] Where x(k) is the 32-channel echo data after amplification, AD conversion, time-delay focusing and filtering. max() is the maximum value operation of the one-dimensional array, and min() is the minimum value operation of the one-dimensional array. u(k) is the average value of the 32-channel echo data x(k), that is,

[0066] S22: Multiply the obtained range by the standard deviation and take the inverse to obtain the range standard deviation product coefficient RSF(k) of the imaging point:

[0067]

[0068] S3: Solving the symbol coherence coefficient of the echo data of each imaging point and performing threshold parameter correction on the range standard deviation product coefficient of the echo data of the same imaging point, specifically including the following steps:

[0069] S31: Divide the 32-channel echo data into (-π / 2,π / 2] and [-π,-π / 2]∪(π / 2,π]. When all phases of the echo signal are (-π / 2,π / 2], the signal is positively correlated; when all phases are [-π,-π / 2]∪(π / 2,π], the signal is negatively correlated:

[0070]

[0071] In the formula, i is the array element number, k is the sampling point number;

[0072] S32: Solve for b i The variance of (k) is:

[0073]

[0074] because The above formula can be simplified to:

[0075]

[0076] S33: By b i (k) Solve for the symbolic coherence coefficient SCF(k):

[0077]

[0078] When the polarities of all echo data are the same, the value of SCF(k) is the maximum and is 1; when the polarities of the echo data are half positive and half negative, SCF(k) is 0.

[0079] S34: Use the SCF coefficient to determine whether the imaging point is a defect detection point or a background point. When the normalized SCF coefficient of the imaging point is greater than 0.9, it is considered to be a defect detection point, and the RSF coefficient is corrected; when the SCF coefficient is less than 0.9, the imaging point is a background point, and the RSF coefficient remains unchanged. The correction expression is:

[0080]

[0081] Where RSF is the coefficient matrix composed of the RSF(k) coefficients of each imaging point, and max(RSF) is the maximum value of the RSF coefficients of all imaging points.

[0082] S4: summing up the echo data of 32 channels to obtain a delay superposition result, and weighting the summation result with the modified RSF coefficient, which specifically includes the following steps:

[0083] S41: summing up the echo data of 32 ultrasonic arrays to obtain the delay superposition result:

[0084]

[0085] Where k is the number of sampling points of the imaging point, that is, k = 32, x i (k-Δ i )(i=1,...,32) represents the ultrasonic signal after focusing and delaying the echoes of 32 channels, Δ i Indicates the delay time applied to each array element signal;

[0086] S42: Weight the summation result using the modified RSF coefficient:

[0087]

[0088] S5: The 32nd-order FIR bandpass filter coefficient with a center frequency of 5.26MHz and a bandwidth of 1.4MHz (the frequency parameter of the imaging system of this patent, different imaging systems need to be adjusted accordingly) is used as a weighting factor and multiplied by the output of the improved adaptive filtering structure to obtain the scan line signal of adaptive beamforming, and the optimized scan line signal is used for final imaging:

[0089]

[0090] c k Represents the filter coefficient, which is the impulse response of the ideal filter multiplied by a window function. k In the frequency domain, it is expressed as a window function added to a specific frequency interval. The value outside this interval is 0 or a minimum value. Multiplying it with the original signal in the frequency domain, that is, performing convolution calculation in the time domain, can remove the value of the original signal outside the specific frequency interval in the frequency domain and filter out the clutter outside the passband frequency in the time domain.

[0091] Experimental verification:

[0092] The experiment uses a portable ultrasonic phased array detector to detect 20# steel test blocks with side holes and aluminum test blocks, and collects ultrasonic signals to verify the imaging algorithm. The ultrasonic probe uses a phased array transducer model 5L128-0.75x10-C58-P-110-2.0-D1 produced by Shantou Ultrasonic Electronics Co., Ltd. to transmit and receive ultrasonic waves. The center frequency of the transducer is 5.26MHz, the sampling frequency is 50MHz, the array element spacing is 0.75mm, and the total number of array elements is 128. The longitudinal wave velocity of the 20# steel experimental test block is 5900m / s. Figure 3 As shown in the figure, the depth of the imaging area focused in this experiment is 10mm, the simulated defect point is a circular hole with a diameter of 1mm, and the circular hole spacing is 3mm, with a total of 13 points to be tested. The longitudinal wave speed of the aluminum test block is 5900m / s. The test block is as follows Figure 7 As shown in the figure, the depth of the imaging area is 65mm, the simulated defect point is a circular hole with a diameter of 2mm, and the circular hole spacing is 5mm, 10mm and 15mm. In the experiment, the B-type sliding line scan is used to collect the original imaging data, and the delay superposition algorithm (DAS), the phase-apodized cross-correlation clutter suppression beamforming algorithm (MPAX), the adaptive beamforming algorithm based on window function selection (LCA), the coherence coefficient algorithm (CF), the symbol coherence weighting algorithm (SCF) and the adaptive filtering algorithm based on the product coefficient of the range standard deviation (RSF) are used for comparative imaging experiments on the above two experimental targets.

[0093] Figure 4 The imaging results of 20# steel test block using 6 algorithms are given. Figure 5 The full width at half maximum (FWHM) curve is given. Figure 6 The following is a partial enlarged view. Table 1 and Table 2 give the half-maximum full width and contrast of each algorithm for the 20# steel test block. Figure 4It can be seen that there are a lot of background noise and artifacts in the DAS image. The MPAX and LCA algorithms suppress the background noise to a certain extent, improve the resolution of defects, and improve the overall image quality. Compared with MPAX, LCA has a greater improvement in artifact suppression effect but no improvement in contrast. As can be seen from Tables 1 and 2, compared with DAS, the MPAX algorithm's half-maximum width and contrast are improved by 4.14% and 41.46%, respectively, while the LCA algorithm's half-maximum width and contrast are improved by 33.23% and 19.75%, respectively. Compared with DAS, CF and SCF have a greater improvement in clutter suppression ability and resolution. The CF algorithm's half-maximum width and contrast are improved by 42.28% and 121.03%, respectively, and the SCF algorithm's half-maximum width and contrast are improved by 50.06% and 161.81%, respectively. Compared with the first five algorithms, the RSF algorithm completely eliminates artifacts and improves resolution and clutter suppression to the best effect. The full width at half maximum and contrast of the RSF algorithm are increased by 62.50% and 223.85% respectively.

[0094] Table 120# steel test block full width at half maximum (FWHM) of each algorithm

[0095]

[0096] Table 220# steel test block algorithm contrast (CR)

[0097]

[0098] Figure 8 The imaging results of aluminum test blocks of 6 algorithms are given. Fig. 9 The full width at half maximum (FWHM) curve is given. Fig.10 The following is a partial enlarged image. Tables 3 and 4 give the full width at half maximum and contrast of each algorithm for the aluminum test block. The imaging results are shown in Figure 8As shown in the figure, it can be seen that the imaging using the DAS algorithm will introduce a lot of clutter and the resolution is low. From Tables 3 and 4, it can be seen that the full width at half maximum (FWHM) and contrast (CR) of the DAS algorithm are 4.2113 and 12.6416 respectively. The MPAX and LCA algorithms do not improve the overall imaging quality much. The MPAX algorithm improves the full width at half maximum and contrast by 0.46% and 26.52% respectively, and the LCA algorithm improves the full width at half maximum and contrast by 6.84% and 16.57% respectively. The CF algorithm and the SCF algorithm use coherence to suppress background noise, which greatly improves the imaging quality. The CF algorithm improves the full width at half maximum and contrast by 25.42% and 84.95% respectively, and the SCF improves the full width at half maximum and contrast by 37.48% and 117.16% respectively. The RSF algorithm uses the range standard deviation product coefficient combined with the SCF coefficient to suppress background noise and achieve the best imaging effect. The RSF algorithm improves the half-maximum full width and contrast by 50.87% and 201.15% respectively.

[0099] Table 3 Full Width at Half Maximum (FWHM) of Aluminum Test Block

[0100]

[0101]

[0102] Table 4 Contrast Ratio (CR) of Aluminum Test Block

[0103]

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A high-resolution adaptive filtering ultrasonic imaging method based on range-standard deviation product coefficient, characterized in that: The method comprises the following steps: S1: Amplify, AD convert, delay focus and digitally filter the echo signal received by the ultrasonic array element to obtain ultrasonic echo data x(k); S2: Solve the range and standard deviation of the echo data of each imaging point, multiply the range and standard deviation of the echo data of each imaging point and take the inverse to obtain the range standard deviation product coefficient; S3: solving the symbol coherence coefficient of the echo data of each imaging point and performing threshold parameter correction on the product coefficient of the range standard deviation of the echo data of the same imaging point; S4: summing up the echo data of N channels to obtain a delay superposition result, and weighting the summation result with the modified RSF coefficient; S5: The coefficients after the 32-order FIR filter are weighted to the output of the improved adaptive filter structure to obtain a scan line signal for adaptive beamforming, and the optimized scan line signal is used for final imaging.

2. The high-resolution adaptive filtering ultrasonic imaging method based on range-standard deviation product coefficient according to claim 1, characterized in that: In S2, the range and standard deviation of the echo data of each imaging point are solved respectively, and then the range and standard deviation of the echo data of each imaging point are multiplied and the inverse is taken to obtain the range standard deviation product coefficient, which specifically includes the following steps: S21: For a sensor array with N equally spaced elements, the range R(k) and standard deviation σ(k) of the echo data at each imaging point are solved as follows: R(k)=max(x(k))-min(x(k)) Where x(k) is the N-channel echo data after amplification, AD conversion, time-delay focusing and filtering, max() is the maximum value operation of the one-dimensional array, min() is the minimum value operation of the one-dimensional array; u(k) is the average value of the N-channel echo data x(k), that is, S22: Multiply the obtained range by the standard deviation and take the inverse to obtain the range standard deviation product coefficient RSF(k):

3. The high-resolution adaptive filtering ultrasonic imaging method based on range-standard deviation product coefficient according to claim 1, characterized in that: In the above S3, the symbol coherence coefficient of the echo data of each imaging point is solved and the threshold parameter correction is performed on the product coefficient of the range standard deviation of the echo data of the same imaging point, which specifically includes the following steps: S31: Divide the N-channel echo data into (-π / 2,π / 2] and [-π,-π / 2]∪(π / 2,π]; when all phases of the echo signal are (-π / 2,π / 2], the signal is positively correlated; when all phases are [-π,-π / 2]∪(π / 2,π], the signal is negatively correlated: In the formula, i is the array element number, k is the sampling point number; S32: Solve b i The variance of (k) is: because The above formula is simplified to: S33: By b i (k) Solve for the symbolic coherence coefficient SCF(k): When the polarity of all echo data is the same, the value of SCF(k) is the largest and is 1; when the polarity of the echo data is half positive and half negative, SCF(k) is 0; S34: The SCF coefficient is used to determine whether the echo data point is a defect detection point or a background point; when the normalized SCF coefficient of the imaging point is greater than 0.9, it is considered to be a defect detection point, and the RSF coefficient is corrected at this time; when the SCF coefficient is less than 0.9, the imaging point is a background point, and the RSF coefficient remains unchanged; the correction expression is: Where RSF is the coefficient matrix composed of the RSF(k) coefficients of each imaging point, and max(RSF) is the maximum value of the RSF coefficients of all imaging points.

4. The high-resolution adaptive filtering ultrasonic imaging method based on range-standard deviation product coefficient according to claim 1, characterized in that: In S4, the echo data of N channels are summed to obtain a delayed superposition result, and the summation result is weighted by the modified RSF coefficient, which specifically includes the following steps: S41: summing the echo data of N ultrasonic arrays to obtain a delay superposition result: Where k is the number of sampling points of the imaging point, that is, k = N, x i (k-Δ i ), i = 1, ..., N represents the ultrasonic signal after focusing and delaying the N channel echoes, Δ i Indicates the delay time applied to each array element signal; S42: Weight the summation result using the modified RSF coefficient:

5. The high-resolution adaptive filtering ultrasonic imaging method based on range-standard deviation product coefficient according to claim 1, characterized in that: In S5, the 32nd-order FIR bandpass filter coefficient with a center frequency of 5.26 MHz and a bandwidth of 1.4 MHz is used as a weighting factor to multiply the output of the improved adaptive filtering structure to obtain a scan line signal of adaptive beamforming, and the optimized scan line signal is used for final imaging: c k represents the filter coefficient, which is obtained by multiplying the impulse response of the ideal filter by a window function; c k In the frequency domain, it is expressed as a window function added to a specific frequency interval. The value outside this specific frequency interval is 0 or a minimum value. It is multiplied with the original signal in the frequency domain, that is, convolution calculation is performed in the time domain. The value of the original signal outside the specific frequency interval is removed in the frequency domain, and the clutter outside the passband frequency is filtered out in the time domain.

Images