A non-contact real-time heart rate detection method based on RGB-NIR camera

Abstract

The present application discloses a non-contact real-time heart rate detection method based on an RGB-NIR camera, comprising: an RGB-NIR camera; face detection and recognition; selection of a facial skin region of interest and a background reference region; extraction of an original heart rate signal; extraction of a background signal; extraction of a BVP signal; and estimation of heart rate information. The key technical points are: a method for estimating heart rate information using a facial skin region and a background reference region to improve the accuracy of heart rate detection results under conditions of ambient light changes; accurate heart rate measurement is achieved using remote photoplethysmography; compared with the prior art, the method has the following advantages: the extraction results are calculated based on RGB and NIR images, and the influence of light is eliminated to a certain extent by comparing the facial image with the ambient background, so that the accuracy is improved compared with the prior art; a camera suitable for medical health and home environments is selected, and the use scenarios are expanded to health monitoring.

Description

Technical Field

[0001] The invention belongs to the field of image and video processing, and in particular is a non-contact real-time heart rate detection method based on an RGB-NIR camera. Background Art

[0002] The "China Cardiovascular Health and Disease Report 2020" released in 2020 shows that cardiovascular disease deaths in China account for the largest number of deaths among urban and rural residents, with 46.66% in rural areas and 43.81% in cities. It has become the number one killer threatening people's lives and health; therefore, the prevention, monitoring, and treatment of cardiovascular disease are particularly important.

[0003] In recent years, the research on video-based non-contact heart rate detection has attracted a lot of attention in the field of computer vision. This method mainly uses remote photoplethysmography, and its basic principle is: when light passes through skin tissue and then reflects to the photosensor at the receiving end, the intensity of the obtained light signal will change to a certain extent; except for the areas where the absorption of light by human muscles, bones, veins and other tissues is basically constant, the absorption or attenuation of light by arteries flowing through the skin is constantly changing. This periodic change causes slight changes in skin color, thereby obtaining corresponding vital signs estimates by separating the blood volume pulse (BVP) signal; compared with traditional heart rate measurement methods, the biggest advantage of this method is its non-contact, low-cost and convenience, which is very suitable for use in daily scenarios.

[0004] At present, the main challenges faced by the heart rate detection method based on rPPG are the changes in ambient lighting and the influence of human head movement. In actual scenarios, the ambient lighting often changes, and this change may bring periodically changing noise signals, which will have a greater impact on the final heart rate information detection. Especially when the light is dim, the skin's reflection and absorption of light are small, and the camera will introduce more noise when imaging. These factors will bring certain challenges to the measurement of physiological indicators. During the detection process, the subject's head movement due to blinking, talking, breathing or other reasons will cause changes in the reflected light of the facial skin, which in turn affects the camera's capture of the periodic color changes of the facial skin. How to eliminate this influence is also an important challenge faced by heart rate detection based on rPPG.

[0005] Under the same lighting environment, the factors that cause color changes in the face area will include the signal component caused by the blood pulse signal in the facial skin area compared to the surrounding background area, while both will have the same signal component of periodic changes in regional color caused by changes in lighting. Summary of the invention

[0006] 1. Technical issues to be resolved

[0007] In view of the deficiencies in the prior art, the present invention provides a non-contact real-time heart rate detection method based on an RGB-NIR camera to solve the problems mentioned in the prior art.

[0008] (II) Technical solution

[0009] To achieve the above objectives, the present invention is implemented through the following technical solutions:

[0010] A non-contact real-time heart rate detection method based on RGB-NIR camera, comprising the following steps:

[0011] S1, use RGB-NIR camera to collect face images;

[0012] S2. Use OpenCV to locate, identify and obtain the feature points of each face in each frame image, and divide it into several facial regions; then establish a background model based on Gaussian kernel density estimation, and obtain several background regions according to the facial regions;

[0013] S3, obtaining an original signal based on the facial region, and using the original signal after filtering as an original heart rate signal; obtaining a background signal based on the background reference region;

[0014] S4, empirical mode decomposition to obtain eigenmode components;

[0015] S5. Perform similarity analysis on the intrinsic mode components using an orthogonal projection transformation algorithm to extract a heart rate signal curve;

[0016] S6, performing peak value statistics on the heart rate signal curve to estimate the heart rate value;

[0017] S7. Collect data in real time, and repeat the above steps to obtain the real-time heart rate.

[0018] Furthermore, in said S1,

[0019] Open the RGB-NIR camera to capture a video containing a face, and obtain an RGB version and a NIR version of the video; use a slicing operation based on a sliding window on the timeline to divide the original video into short videos of 10 seconds.

[0020] Further, in said S2,

[0021] Create a face detector based on the DNN model in OpenCV, perform face detection on each frame of the RGB version of the video and obtain the face area, use the DLib library to obtain facial feature points, and divide the face area into four facial areas based on the obtained facial feature points: forehead area, left face area, right face area and jaw area. The facial area is divided into RGB version and NIR version; establish a background model based on Gaussian kernel density estimation, with the face area particle as the center, and use the search algorithm to select four background areas around the face area as reference areas;

[0022] Using the detected facial feature points, calculate the Euclidean distance between the facial feature points of the previous and next frames. If it is less than the preset threshold Dist, it can be considered to be the same face, and the face tracking is achieved accordingly;

[0023] Otherwise, the current heart rate estimation process is terminated, and S2 is repeated again with the current frame as the first frame; further, the facial regions of interest are extracted according to the facial feature points: forehead (a), left cheek (b), right cheek (c) and lower lip center (d);

[0024] The specific background extraction method is as follows: let x1,x2,…,x N is the gray value of a pixel in the most recent N frames, x t is the pixel value of the pixel at the current time t, then the probability density function of the pixel is:

[0025]

[0026] Among them, formula (1) is actually to use the Gaussian kernel function at the sample points x1, x2, ..., x N If we use a continuous function in the form of interpolation, we can get the background points according to the following formula:

[0027]

[0028] Among them, T is the threshold, M t In (x, y), 0 represents background points and 1 represents foreground target points.

[0029] Then the background area is extracted from the current short video as the reference area.

[0030] Furthermore, in said S3,

[0031] The original signal extraction is based on the facial area, extracting the G and N channel values ​​and performing an averaging operation, and making the obtained G channel and N channel sequences correspond to the input time axis one by one to obtain a set of original signals;

[0032] The background signal extraction is based on the background area, extracting the R, G, B and N channel values ​​and performing an averaging operation, and the obtained R, G, B and N channel sequences are matched one by one with the input time axis to obtain a set of background signals;

[0033] The specific process of obtaining the original heart rate signal and background signal is:

[0034] Firstly, the RGB image and NIR image at the same time are spatiotemporally fused to obtain the mean value sequences of the G and N channels of the facial region and the reference region before and after the fusion.

[0035] Then, the time axis is obtained according to the set value, and the nonlinear least squares method is used to fit the above sequence to obtain a one-dimensional signal curve on the time axis;

[0036] Finally, a bandpass filter is used to filter the original signal and the background signal curve to eliminate obvious noise, and then the filtered original signal is used as the original heart rate signal, and the filtered reference area signal is used as the background signal.

[0037] Further, in S4 and S5,

[0038] The BVP signal curve extraction is to decompose the original heart rate signal and the background signal into the superposition of each independent component by using the empirical mode separation method to obtain multiple IMFs, and then obtain the BVP signal curve by orthogonal projection operation;

[0039] The specific steps to obtain the heart rate signal curve are:

[0040] Firstly, the original heart rate signal and the background signal are subjected to blind source signal separation based on empirical mode decomposition, and a number of separated IMF components and a residual component are obtained for each signal;

[0041] Then, the orthogonal projection transformation algorithm is used to perform similarity analysis on the separated IMF components, and the IMF component with the lowest similarity between the original heart rate signal group and the background signal group is extracted, and the IMF is used as the BVP signal curve.

[0042] Further, in said S6,

[0043] The heart rate information estimation is to perform a fast Fourier transform on the BVP signal curve in the time domain, calculate the maximum value of the frequency domain response, and calculate the estimated heart rate through the peak value and the corresponding frequency value in the frequency domain.

[0044] (III) Beneficial effects

[0045] The present invention provides a method for estimating heart rate information by using a face skin area and a background reference area based on an RGB-NIR camera, so as to improve the accuracy of heart rate detection results under conditions of ambient light changes;

[0046] Accurate heart rate measurement is achieved using remote photoplethysmography; compared with existing technologies, it has the following advantages:

[0047] First, the extraction results are calculated based on RGB and NIR images, and the influence of lighting is eliminated to a certain extent by comparing the face image with the environmental background, so the accuracy is improved compared with the existing technology;

[0048] Second, select cameras suitable for medical health and home environments, and expand the use scenarios to health monitoring, which is in line with the principle of "prevention is better than cure" for cardiovascular diseases. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is the overall flow chart of the present invention;

[0050] Figure 2 is a schematic diagram of extracting a facial region of interest according to the present invention;

[0051] Figure 3 This is an example of an eigenmode function obtained by decomposing the original heart rate signal curve based on empirical mode decomposition of the present invention;

[0052] Figure 4 This is an example of IMF function similarity and heart rate estimation obtained by decomposing the facial skin area and background area. DETAILED DESCRIPTION

[0053] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. In addition, for the convenience of description below, the referenced "upper", "lower", "left", and "right" are the same as the upper, lower, left, and right directions of the drawings themselves. The "first", "second", etc. below are distinguished for the description and have no other special meanings.

[0054] A non-contact real-time heart rate detection method based on RGB-NIR camera, comprising the following steps:

[0055] S1, use RGB-NIR camera to collect face images;

[0056] Open the RGB-NIR camera to capture a video containing a face, and obtain an RGB version and a NIR version of the video; use the slicing operation based on the sliding window on the timeline to divide the original video into short videos of 10 seconds;

[0057] Specifically, the camera frame rate is initialized to f, the current frame count fcount = 0, the server queue queue is cleared, and the Boolean value isBlocked = false is set to indicate that signal transmission is possible;

[0058] When the camera is turned on and starts collecting data, fcount will count each frame of the image and obtain the currently collected image in real time based on the rtsp protocol;

[0059] The image processing in the following steps will only involve processing the images from 0 to 10*f in the current queue.

[0060] S2. Use OpenCV to locate, identify and obtain the feature points of each face in each frame image, and divide it into several facial regions; then establish a background model based on Gaussian kernel density estimation, and obtain several background regions according to the facial regions;

[0061] Create a face detector based on the DNN model in OpenCV, perform face detection on each frame of the RGB version of the video and obtain the face area, use the DLib library to obtain facial feature points, and divide the face area into four facial areas based on the obtained facial feature points: forehead area, left face area, right face area and jaw area. The facial area is divided into RGB version and NIR version; establish a background model based on Gaussian kernel density estimation, with the face area particle as the center, and use the search algorithm to select four background areas around the face area as reference areas;

[0062] The specific background extraction method is as follows: let x1,x2,…,x N is the gray value of a pixel in the most recent N frames, x t is the pixel value of the pixel at the current time t, then the probability density function of the pixel is:

[0063]

[0064] Among them, formula (1) is actually to use the Gaussian kernel function at the sample points x1, x2, ..., x N If we use a continuous function in the form of interpolation, we can get the background points according to the following formula:

[0065]

[0066] Among them, T is the threshold, M t In (x, y), 0 represents background points and 1 represents foreground target points.

[0067] Then extract the background area from the current short video as the reference area; the background area should meet the following conditions:

[0068] First, it does not overlap with any pixels in the facial area;

[0069] Second, the fluctuation of pixel changes in the area should be as small as possible.

[0070] The above background area is the video background obtained by the background modeling method of Gaussian kernel density estimation. Then, with the centroid of the face area as the center, the search starts from 12 o'clock, 3 o'clock, 6 o'clock and 9 o'clock in a clockwise direction, and finally four background areas are obtained. The size of each background area is 20×20, and the default initial distance between the centroid of the face area and the center of the background area is max(Width face ,Height face )+40.

[0071] The specific steps for selecting the reference area are as follows:

[0072] (1) Obtain the image width weight and height height, and create a dictionary type CoveredMap to record the area covered by the face;

[0073] (2) Traverse each frame image, record the centroid coordinates [c_x, c_y] and face radius R of the face in the current frame image, and add a record in CoveredMap as [key = [c_x, c_y], value = R]; the center point of the temples on both sides of the face is taken as the centroid, and the straight-line distance from the centroid to the chin is taken as the radius;

[0074] (3) Obtain a coordinate [p_x, p_y] in the image through a random number, and calculate the distance Dp between the coordinate and the key in CoveredMap in turn. If Dp is greater than R, exit the current judgment;

[0075] If Dp is always less than R, the current coordinate can be considered as a potential reference area selection point, record PotentialPoints[i] = [p_x, p_y], and update CoveredMap record [key = [p_x, p_y], value = D]; repeat this step k times to obtain an array PotentialPoints containing k potential reference area selection points;

[0076] Where D and k are input constants;

[0077] (4) Traverse each frame of the image, select a point for each potential reference area, and calculate whether its G channel value fluctuates by more than ±10%. If so, discard the point and remove it from PotentialPoints; the coordinates in the final PotentialPoints are considered to be the center point of the reference area.

[0078] Specifically:

[0079] For each frame, the DNN model is loaded using the readNetFromCaffe method in OpenCV: res10_300x300_ssd_iter_140000.caffemodel, and the face target in the frame image is located.

[0080] Then use the detector method of the frontal_face_detector class in the Dlib library to obtain the coordinates of the 68 feature points in the face area of ​​the frame image, recorded as [face_point1(x,y),…,face_point68(x,y)].

[0081] Using the detected facial feature points, calculate the Euclidean distance between the facial feature points of the previous and next frames. If it is less than the preset threshold Dist, it can be considered as the same face, and the face tracking is achieved accordingly. Otherwise, the current heart rate estimation process is terminated, and step 2 is repeated again with the current frame as the first frame; further extract the facial region of interest (forehead (a), left cheek (b), right cheek (c) and lower lip center (d)) based on the facial feature points;

[0082] Note: The region of interest mentioned in this application may also be referred to as the facial region.

[0083] S3, obtaining an original signal based on the facial region, and using the original signal after filtering as an original heart rate signal; obtaining a background signal based on the background reference region;

[0084] The original signal extraction is based on the facial area, extracting the G and N channel values ​​and performing an averaging operation, and making the obtained G channel and N channel sequences correspond to the input time axis one by one to obtain a set of original signals;

[0085] The background signal extraction is based on the background area, extracting the R, G, B and N channel values ​​and performing an averaging operation, and the obtained R, G, B and N channel sequences are matched one by one with the input time axis to obtain a set of background signals;

[0086] The specific process of obtaining the original signal and the background signal is:

[0087] Firstly, the RGB image and NIR image at the same time are spatiotemporally fused to obtain the mean value sequences of the G and N channels of the facial region and the reference region before and after the fusion.

[0088] Then, the time axis is obtained according to the set value, and the nonlinear least squares method is used to fit the above sequence to obtain a one-dimensional signal curve on the time axis;

[0089] Finally, a bandpass filter is used to filter the original signal and the background signal curve to eliminate obvious noise, and then the filtered original signal is used as the original heart rate signal, and the filtered reference area signal is used as the background signal.

[0090] Specifically,

[0091] For a frame of RGB video and NIR video at the same time, the following processing is performed:

[0092] (1) Use bilateral filter (BF) and weighted least squares filter (WLS) to filter the NIR image to obtain processed images Y1 and Y2; subtract them from the original image I_nir to obtain detail layer images Y3 and Y4, that is, I_nir-Y1=Y3, I_nir-Y2=Y4; average Y3 and Y4 to obtain the detail information Y_nir of the NIR image;

[0093] (2) Convert the RGB image to the YCbCr space, perform weighted least squares filtering on the Y layer, and obtain the RGB image information Y_rgb;

[0094] (3) Add Y_nir and Y_rgb to obtain the Y layer of the fused image in the YCbCr space, that is, Y_nir+Y_rgb=Y;

[0095] (4) Recombine the Y and CbCr layers of the original image and convert them into RGB space to obtain the fused RGB-NIR image.

[0096] For the fused RGB+NIR image and the original image, the following operations are performed:

[0097] (1) For the original RGB image, extract the G channel values ​​of the facial area and the background area respectively and calculate the average to obtain the sequences G_face and G_back;

[0098] (2) For the original NIR image, it needs to be converted to RGB space and then processed in the same way to obtain the sequences N_face and N_back;

[0099] (3) For the fused RGB-NIR image, G-N_face and G-N_back are obtained.

[0100] According to the frame rate, the relative time of each frame image with respect to the first frame can be calculated, and the time series Time = [t(1)....t(30)] is obtained, which corresponds one-to-one with the above sequence G_face = [Gf(1)...Gf(30)], and the coordinate point set G_face_node = [Gf-t(1)...Gf-t(30)] is obtained. The preset y = func(x) = A*x^5+B*x^4+C*x^3+D*x^2+E*x+F, and the coefficients are obtained based on the nonlinear least squares method to obtain the function y = func_Gf(x) of the optimal fitting curve; similarly, for the sequence G_back, N_face, N_back, G-N_face, G-N_back, func_? can be calculated. (x) Perform mean processing on func_Gf, func_Nf, and func_GNf to obtain the BVP signal curve func_face; perform mean processing on func_Gb, func_Nb, and func_GNb to obtain the background signal curve func_back; use a bandpass filter to filter the above one-dimensional signal curve to obtain filtered func_face_fil and func_back_fil.

[0101] S4, obtaining intrinsic mode components by empirical mode decomposition; S5, performing similarity analysis on the intrinsic mode components using an orthogonal projection transformation algorithm, and extracting a BVP signal curve;

[0102] The BVP signal curve extraction is to decompose the original heart rate signal and the background signal into the superposition of each independent component by using the empirical mode separation method to obtain multiple IMFs, and then obtain the BVP signal curve by orthogonal projection operation;

[0103] The specific steps to obtain the heart rate signal curve are:

[0104] Firstly, the original heart rate signal and the background signal are subjected to blind source signal separation based on empirical mode decomposition, and a number of separated IMF components and a residual component are obtained for each signal;

[0105] Then, the orthogonal projection transformation algorithm is used to perform similarity analysis on the separated IMF components, and the IMF component with the lowest similarity between the original heart rate signal group and the background signal group is extracted, and the IMF is used as the heart rate signal curve.

[0106] Specifically,

[0107] Performing EMD processing on each filtered signal curve will obtain k separated IMF components and a residual component. The separated component curve sequence is recorded as IMFS = [IMF (1) .... IMF (k)];

[0108] Where k is a certain value and the IMFS result is uniquely determined;

[0109] For each IMF(i) obtained by decomposing the BVP signal, the similarity with all IMFs in the IMFS obtained by decomposing the background signal is calculated, and the final similarity similar(i) is calculated based on the voting mechanism. The IMF(j) with the lowest similarity can be considered to contain the most heart rate information and is recorded as the heart rate signal curve Characteristic_curve.

[0110] S6, performing peak value statistics on the BVP signal curve to estimate the heart rate value;

[0111] The heart rate information estimation is to perform a fast Fourier transform on the BVP signal curve in the time domain, calculate the maximum value of the frequency domain response, and calculate the estimated heart rate through the peak value and the corresponding frequency value in the frequency domain;

[0112] Scan the heart rate signal curve Characteristic_curve, count the number of peaks P, where the number of peaks is the number of heartbeat fluctuations within 10 seconds, and return the estimated heart rate Heart_rate=P / 10 within 10 seconds.

[0113] S7, real-time data collection, repeating the above steps (S1-S5) to obtain the real-time heart rate.

[0114] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A non-contact real-time heart rate detection method based on RGB-NIR camera, characterized in that: The steps include: S1, use RGB-NIR camera to collect face images; S2. Use OpenCV to locate, identify and obtain the feature points of each face in each frame image, and divide it into several facial regions; then establish a background model based on Gaussian kernel density estimation, and obtain several background regions according to the facial regions; S3, obtaining an original signal based on the facial region, and using the original signal after filtering as an original heart rate signal; Obtaining a background signal based on a background reference region; S4, empirical mode decomposition to obtain eigenmode components; S5. Use the orthogonal projection transformation algorithm to perform similarity analysis on the intrinsic mode components and extract the BVP signal curve; S6, performing peak value statistics on the BVP signal curve to estimate the heart rate value; S7, real-time data collection, repeating the above steps to obtain the real-time heart rate; In said S3, The original signal extraction is based on the facial area, extracting the G and N channel values ​​and performing an averaging operation, and making the obtained G channel and N channel sequences correspond to the input time axis one by one to obtain a set of original signals; The background signal extraction is based on the background area, extracting the R, G, B and N channel values ​​and performing an averaging operation, and the obtained R, G, B and N channel sequences are matched one by one with the input time axis to obtain a set of background signals; The specific process of obtaining the original signal and the background signal is: Firstly, the RGB image and NIR image at the same time are spatiotemporally fused to obtain the mean value sequences of the G and N channels of the facial region and the reference region before and after the fusion. Then, the time axis is obtained according to the set value, and the nonlinear least squares method is used to fit the above sequence to obtain a one-dimensional signal curve on the time axis; Finally, a bandpass filter is used to filter the original signal and background signal curves to eliminate obvious noise, and then the filtered original signal is used as the original heart rate signal, and the filtered reference area signal is used as the background signal; In said S4 and S5, The BVP signal curve extraction is to decompose the original heart rate signal and the background signal into the superposition of each independent component by using the empirical mode separation method to obtain multiple IMFs, and then obtain the BVP signal curve by orthogonal projection operation; The specific steps to obtain the heart rate signal curve are: Firstly, the original heart rate signal and the background signal are subjected to blind source signal separation based on empirical mode decomposition, and a number of separated IMF components and a residual component are obtained for each signal; Then, the orthogonal projection transformation algorithm is used to perform similarity analysis on the separated IMF components, and the IMF component with the lowest similarity between the original heart rate signal group and the background signal group is extracted, and the IMF is used as the heart rate signal curve.

2. A non-contact real-time heart rate detection method based on an RGB-NIR camera as claimed in claim 1, characterized in that: In said S1, Open the RGB-NIR camera to capture a video containing a face, and obtain an RGB version and a NIR version of the video; use a slicing operation based on a sliding window on the timeline to divide the original video into short videos of 10 seconds.

3. A non-contact real-time heart rate detection method based on RGB-NIR camera as claimed in claim 1, characterized in that: In said S2, Create a face detector based on the DNN model in OpenCV, perform face detection on each frame of the RGB version of the video and obtain the face area, use the DLib library to obtain facial feature points, and divide the face area into four facial areas based on the obtained facial feature points: forehead area, left face area, right face area and jaw area. The facial area is divided into RGB version and NIR version; establish a background model based on Gaussian kernel density estimation, with the face area particle as the center, and use the search algorithm to select four background areas around the face area as reference areas; Using the detected facial feature points, calculate the Euclidean distance between the facial feature points of the previous and next frames. If it is less than the preset threshold Dist, it can be considered to be the same face, and the face tracking is achieved accordingly; Otherwise, the current heart rate estimation process is terminated, and S2 is repeated again with the current frame as the first frame; further, the facial regions of interest are extracted according to the facial feature points: the forehead, the left cheek, the right cheek and the center of the lower lip.

4. The non-contact real-time heart rate detection method based on RGB-NIR camera as claimed in claim 1, characterized in that: In said S2, The specific background extraction method is as follows: let x1,x2,…,x N is the gray value of a pixel in the most recent N frames, x t is the pixel value of the pixel at the current time t, then the probability density function of the pixel is: Among them, formula (1) is actually to use the Gaussian kernel function at the sample points x1, x2, ..., x N If we use a continuous function in the form of interpolation, we can get the background points according to the following formula: Among them, T is the threshold, M t In (x, y), 0 represents background points and 1 represents foreground target points; Then the background area is extracted from the current short video as the reference area.

5. The non-contact real-time heart rate detection method based on RGB-NIR camera as claimed in claim 1, characterized in that: In said S6, The heart rate estimation is to perform a fast Fourier transform on the BVP signal curve in the time domain, calculate the maximum value of the frequency domain response, and calculate the estimated heart rate through the peak value and the corresponding frequency value in the frequency domain.

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