Filtering noise reduction device and method for self-adaptive carrier frequency point and bandwidth
By dividing the receiver bandwidth into N segments and using a cascaded noise cancellation module to filter each segment of the spectrum for adaptive noise reduction, the problem of signal-to-noise ratio (SNR) degradation in multi-stage ORU cascades is solved, achieving effective noise reduction and SNR improvement under unknown carrier frequency and bandwidth.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- WUHAN GEWEI ELECTRONICS TECH
- Filing Date
- 2025-12-30
- Publication Date
- 2026-04-10
AI Technical Summary
In multi-level ORU cascaded scenarios, ORU0 and ORU1 cannot know the carrier frequency and bandwidth information, which leads to a decrease in signal-to-noise ratio after data merging and affects demodulation performance.
An adaptive carrier frequency and bandwidth filtering and noise reduction method is adopted. The receiver bandwidth is divided into N segments. Each segment of the spectrum is filtered by a cascaded noise cancellation module. Noise is judged and subtracted, and the signal data is retained, thus achieving adaptive noise reduction.
It effectively reduces noise, improves the signal-to-noise ratio, and enhances demodulation performance when the carrier frequency and bandwidth are unknown.
Smart Images
Figure CN121841384A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of communications, and more particularly to an adaptive carrier frequency and bandwidth filter and noise reduction device and method thereof. Background Technology
[0002] In the uplink reception of a 5G system, the received data needs to be filtered and denoised. Given the frequency and bandwidth information of the received carrier, a pre-designed FIR filter that matches the carrier bandwidth can be used to filter the received signal, thereby reducing the noise of the received data.
[0003] However, in some scenarios, the ORU (Open Radio Unit) does not know the carrier's frequency and bandwidth information, such as... Figure 1 The illustrated multi-level ORU cascading application scenario shows that ORU0 and ORU1 serve different cells. Their received carrier frequencies fc0 and fc1, as well as their carrier bandwidth, are dynamically scheduled by the ODU. ORU0 is unaware of the location and bandwidth of fc0, and ORU1 is also unaware of the specific frequency location and bandwidth of fc1. Both ORU0 and ORU1 simply receive all signals within their maximum designed receive bandwidth, such as 100MHz.
[0004] In this cascading scenario, ORU1 first transmits the received data from fc1 to ORU0 via the eCPRI interface, and ORU0 then transmits fc0 and fc1 to ODU via the eCPRI interface.
[0005] To save eCPRI data transmission bandwidth, ORU0 needs to merge the data from fc0 and fc1 before transmitting the merged data to ODU.
[0006] Directly adding and combining the data from fc0 and fc1 will increase the noise floor of the combined data and decrease the signal-to-noise ratio (SNR) of each carrier data. Let the signal power in fc0 be s0 and the noise be n0, and the signal power in fc1 be s1 and the noise be n1. Before combining, the SNR of fc0 is s0 / n0, and the SNR of fc1 is s1 / n1; after combining, the SNR of fc0 is s0 / (n0+n1), and the SNR of fc1 is s1 / (n0+n1). This decrease in SNR leads to a decline in demodulation performance. Summary of the Invention
[0007] The main objective of this invention is to provide an adaptive carrier frequency and bandwidth filter and its method, which can effectively reduce noise and improve the signal-to-noise ratio even when the carrier frequency and bandwidth are unknown.
[0008] The technical solution adopted in this invention is: An adaptive carrier frequency and bandwidth filtering and noise reduction method is provided, comprising the following steps: The receiver's entire receiving bandwidth is divided into N segments to obtain N segmented spectra, where N is a positive integer; N noise power thresholds are calculated based on the receiver's noise figure and N segmented spectrum. N cascaded noise cancellation modules are then set up based on the N segmented spectrum and N noise power thresholds. The carrier data is input to N cascaded noise cancellation modules. After the i-th noise cancellation module filters out the i-th segment of the spectrum, the i-th segment of the spectrum is obtained. The average power of the filtered data is calculated and compared with the i-th preset noise power threshold. If it is determined to be noise, the noise is subtracted from the original carrier data. If the i-th segment of the spectrum contains signal data, it is retained. The input signal of the i-th noise cancellation module is directly output as the input signal of the (i+1)-th noise cancellation module, where i is a positive integer and 1≤i≤N.
[0009] Following the above technical solution, the entire receiving bandwidth of the receiver is divided into N equal parts to obtain N segmented spectrums.
[0010] Following the above technical solution, the entire receiving bandwidth of the receiver is specifically divided into non-equal interval spectrum segments.
[0011] Following the above technical solution, when performing non-equal interval spectrum segmentation, a wide interval is first used for coarse spectrum segmentation. If the signal data is in one of the segmented spectrums after coarse segmentation spectrum filtering, then the segmented spectrum is further subdivided into equal intervals, and then multiple cascaded noise cancellation modules are set up accordingly.
[0012] Following the above technical solution, before subtracting noise from the original carrier data, the original carrier data is delayed accordingly to compensate for the time delay of the filtering process.
[0013] The present invention also provides an adaptive carrier frequency and bandwidth filtering and noise reduction device, comprising N cascaded noise cancellation modules, which are specifically constructed according to the adaptive carrier frequency and bandwidth filtering and noise reduction method described in the above technical solution.
[0014] Following the above technical solution, each noise cancellation module includes: A buffer unit is used to buffer the input original carrier data; The filtering unit is used to filter the original carrier data according to the spectrum of the segment it belongs to; The comparison unit is used to calculate the average power of the filtered data and compare it with the preset noise power threshold of the segment. If the average power is less than or equal to the preset noise power threshold, the filtered data is noise; otherwise, it contains signal data. The delay unit is used to delay the input original carrier data in order to align it with the filtered data; The noise cancellation unit is used to subtract the noise from the original carrier data after the time delay when the filtered data is noisy; otherwise, it directly outputs the original carrier data after the time delay to the next noise cancellation module.
[0015] Following the above technical solution, the segmented spectrum of different noise cancellation modules is an equally spaced spectrum.
[0016] Following the above technical solution, the segmented spectrum of different noise cancellation modules is a non-equally spaced spectrum.
[0017] Following the above technical solution, when the spectrum is not equally spaced, the filter noise reduction device includes cascaded M1 coarse noise cancellation modules and cascaded M2 fine noise cancellation modules. Specifically, the M1 coarse noise cancellation modules construct the spectrum by using wide intervals for coarse segmentation. Specifically, the M2 fine noise cancellation modules construct the spectrum by performing secondary equal-interval segmentation if the signal data is in one of the segmented spectrums after coarse segmentation spectrum filtering, where M1 and M2 are positive integers.
[0018] The beneficial effects of this invention are as follows: In order to achieve noise reduction even when the carrier frequency and bandwidth are unknown, this invention divides the entire receiving bandwidth into N segmented spectra and performs segmented filtering on the corresponding segmented spectra of the carrier data. If the data in the i-th segment of the spectrum after filtering is noise, this part of the noise is subtracted from the original carrier data; if the i-th segment of the spectrum contains signal data, it is retained. It can be seen that in all segments, the data segments with noisy spectra are deleted from the original carrier data. Thus, by using frequency segment scanning filtering, the noise reduction effect is adaptively achieved even when the carrier frequency and bandwidth are unknown.
[0019] Furthermore, multiple scanning filtering methods can be used. For example, a coarse segmentation scan can be performed first using a wider bandwidth to eliminate some noise and obtain a segment of the coarse segment containing the useful signal. Then, a second fine segmentation scan can be performed on the segment data containing the signal in the coarse segment to reduce noise using a narrower bandwidth.
[0020] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description
[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0022] Figure 1 This is a schematic diagram illustrating an application scenario of multi-level ORU cascading in existing technologies; Figure 2 This is a schematic diagram of how an FIR filter filters a carrier when the carrier frequency and bandwidth are known, based on existing technology. Figure 3 This is a flowchart of an embodiment of the filtering and noise reduction method for adaptive carrier frequency and bandwidth according to the present invention; Figure 4 This is a schematic diagram of an embodiment of the present invention, showing equally spaced segmented scanning filtering. Figure 5 yes Figure 4 A schematic diagram of the filtering frequency band of the first frequency band filtering unit; Figure 6 It was through Figure 5 A schematic diagram of the filtered data from the filtering unit in the diagram; Figure 7 This is a schematic diagram of the data obtained by subtracting the original carrier data from the filtered noise data; Figure 8 This is a schematic diagram of the original carrier data after two noise reduction steps according to an embodiment of the present invention; Figure 9 This is a schematic diagram of the carrier data X before noise cancellation in an embodiment of the present invention, which flows through N noise cancellation modules to obtain the noise-cancelled data Y in the entire bandwidth; Figure 10 This is a schematic diagram of the data processing logic of the noise cancellation module in an embodiment of the present invention. Detailed Implementation
[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0024] It should be noted that the illustrations provided in the embodiments of the present invention are only schematic representations of the basic concept of the present invention. Therefore, the illustrations only show the components related to the present invention and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.
[0025] In this invention, it should also be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. Furthermore, the terms "first" and "second" are used only for descriptive and distinguishing purposes and should not be construed as indicating or implying relative importance.
[0026] Furthermore, it should be noted that the features of the various embodiments of the present invention can be combined or integrated in whole or in part, and as those skilled in the art will understand, they can interact and operate in different ways. Each embodiment can be implemented independently of each other or in association with one another.
[0027] Existing FIR (Finite Impulse Response) filters can filter out out-of-band signals while having virtually no impact on signals within the filter's passband. Given the carrier frequency and bandwidth, an FIR filter can be designed to filter the carrier, thereby reducing noise outside the carrier bandwidth. For example... Figure 2 As shown, the top image represents the carrier spectrum before filtering, and the bottom image represents the carrier spectrum after filtering. After filtering, the noise outside the bandwidth is significantly reduced. When multiple carriers with this denoising effect are combined, the noise data at other carrier positions has been suppressed to a sufficiently low level, thus causing virtually no further interference to other carriers.
[0028] Furthermore, with a fixed frequency bandwidth, the received noise floor of different ORUs (Open Radio Units) is roughly the same, so the power can be used to determine whether a certain frequency range contains noise.
[0029] The formula for receiver noise floor is: Where -174 is the thermal noise power spectral density at room temperature (290K), B is the system bandwidth (Hz), and NF is the noise figure. For a single ORU, NF is a fixed value, so when the bandwidth B is fixed, the noise power is also a fixed value. Therefore, if the received data is filtered, and if there is no useful signal in the filter passband, only noise, then its power value is relatively fixed. Therefore, for scenarios where the useful signal power is higher than the noise power, the power of the filtered data can be used to determine whether the filtered data contains a useful signal.
[0030] To achieve similar results even without knowing the carrier frequency and bandwidth, this invention proposes a spectrum scanning noise reduction method, namely, an adaptive carrier frequency and bandwidth filtering noise reduction method, such as... Figure 3 As shown, it includes the following steps: S1. Divide the entire receiving bandwidth of the receiver into N segments to obtain N segmented spectra, where N is a positive integer; S2. Calculate N noise power thresholds based on the receiver's noise figure and N segmented spectrums, and set up N cascaded noise cancellation modules based on the N segmented spectrums and N noise power thresholds; S3. Input the carrier data into N cascaded noise cancellation modules. After the i-th noise cancellation module filters out the i-th segment of the spectrum, the i-th segment of the spectrum is obtained and its average power is calculated. S4. Compare the average power of the i-th segment of the filtered spectrum data with the i-th preset noise power threshold. If it is less than or equal to the threshold, it is noise; otherwise, it contains signal data. S5. If it is determined to be noise, then subtract the noise from the original carrier data; S6. If the i-th segment of spectrum data contains signal data, then retain it and directly output the input signal of the i-th noise cancellation module as the input signal of the (i+1)-th noise cancellation module, where i is a positive integer and 1≤i≤N.
[0031] In one embodiment of the present invention, the entire receiving bandwidth can be divided into N equal intervals, and the spectrum of each interval is filtered. If the filtered data of the nth segment of the spectrum is noise, this noise is subtracted from the original data; if the nth segment of the spectrum contains signal data, it is retained. The final result is that, for all segments, the data segments with noisy spectra are subtracted from the original data, thereby achieving an adaptive noise reduction effect. Figure 4 As shown, the top left is the data before noise reduction, the bottom left is the data after subtracting the first segment of noise, the top right is the data after subtracting the second segment of noise, and the bottom right is the data after subtracting the third segment of noise.
[0032] The following is an example of the noise cancellation process for the first frequency band: The filter for the first frequency band is as follows Figure 5 As shown, the filtered data, such as Figure 6 As shown, at the frequency domain location containing the useful signal, the signal has been suppressed to the noise floor by the filter. Figure 6 (below 100dB position in the image).
[0033] The data after noise removal is shown in Figure 7, where the upper figure is the source data (i.e., the original input carrier data), and the lower figure is the data after subtracting the noise data obtained by filtering from the source data.
[0034] By doing this, once the entire frequency segment has been scanned, the noise in segments that do not contain signals can be completely removed, while the data in segments that contain signals can be left unchanged.
[0035] The effect after the last two eliminations is as follows: Figure 8 As shown. For the highest frequency position, since the carrier is not usually located at this position, noise cancellation is not required at this position. For the carrier edge positions, there is still some noise that has not been cancelled. This is related to the filter used and the number of spectrum segments. If this part of the noise needs to be reduced, the number of spectrum segments can be increased, and the corresponding filter should also be changed to match the segment bandwidth. In this embodiment, the effective bandwidth is divided into 12 segments. Segments 7 and 8 are retained because they contain signal power, while the remaining segments have no signal and are subtracted.
[0036] like Figure 9 As shown, the carrier data before noise cancellation is X. Each time X passes through a noise cancellation module, noise in a segment of the spectrum is eliminated, and finally, the noise-cancelled data Y within the entire bandwidth is obtained.
[0037] Each noise cancellation module includes a buffer unit, a filtering unit, a comparison unit, a delay unit, and a noise cancellation unit.
[0038] in: The buffer unit is used to buffer the input original carrier data; the filtering unit is used to filter the original carrier data according to the spectrum of the segment. The comparison unit is used to calculate the average power of the filtered data and compare it with the preset noise power threshold of the segment. If the average power is less than or equal to the preset noise power threshold, the filtered data is noise; otherwise, it contains signal data. The delay unit is used to delay the input original carrier data in order to align it with the filtered data; The noise cancellation unit is used to subtract the noise from the original carrier data after the time delay when the filtered data is noisy; otherwise, it directly outputs the original carrier data after the time delay to the next noise cancellation module.
[0039] Each noise cancellation module eliminates noise in a specific frequency spectrum; their functional structures are identical, such as... Figure 10 As shown, the only difference lies in the coefficients of the filter (i.e., the filtering unit). The data processing logic of the noise cancellation module is as follows: Figure 10 As shown, C(i) is the input, which is also the output data of the previous noise cancellation module. If i=1, it is the first noise cancellation module, and its input is X. The module output is C(i+1), which is also the input of the (i+1)th noise cancellation module. If i=N, this module is the last noise cancellation module, and its output is the final noise cancellation data Y.
[0040] Specifically, the buffer unit buffers the data to be processed, denoted as buf(i,m)=C(i,tm), where i is the noise cancellation module number, with a value of 1≤i≤N, and N is the number of spectrum segments; m is the buffer data index, with a value of 0~M-1, and M is the filter coefficient length, such as 31; t is the current time; the buffer size is determined by the length of the filter coefficients used.
[0041] 1. The cache is initialized with all zeros, buf(i,m)=0; 2. Cache update: a) buf(i,m) = buf(i,m+1); 0 <= m <M-1 b)buf(i,M-1)=C(i,t) The filtering unit performs complex convolution operations. Each time the buffer is updated with a new data item, the filtering unit calculates the output using the following formula:
[0042] Where m is the index of the cached data in the buffer buf; M is the length of the buffer, which is also the length of the filter coefficients; and i is the number of the noise cancellation module. For cached data that will soon be used in convolution operations, These are the filter coefficients that will be involved in the convolution.
[0043] 1. Calculation and The product and cross product of the real and imaginary parts II(m)=real(buf(i,m))·real(coef(i,m)) QQ(m)=imag(buf(i,m))·imag(coef(i,m)) IQ(m)=real(buf(i,m))·imag(coef(i,m)) QI(m)=imag(buf(i,m))·real(coef(i,m)) 2. Calculate the real and imaginary parts of a complex multiplication. Real(S_one(m)) = II(m) - QQ(m) Imag(S_one(m)) = IQ(m) + QI(m) To reduce multiplication calculations, symmetrical frequency band division can be used during frequency band allocation. This way, in addition to obtaining the filter calculation value for one frequency band as described above, the filter calculation value for its symmetrical frequency band can also be obtained. Real(SS_one(m))=II(m)+QQ(m) Imag(SS_one(m)) = -IQ(m) + QI(m) 3. Accumulate to obtain the filtered output value:
[0044] Filter output values for symmetrical frequency bands:
[0045] Where 0≤i<N, if N is even, then there are an even number of spectrum segments, which is even symmetric; if N is odd, then the middle segment i and N-1-i are the same segment, and repeated elimination should be avoided when performing noise cancellation.
[0046] The comparator unit can first perform average power calculation: 1. Calculate the power value of a single sample point. ; 2. Averaging: Where Q is the alpha smoothing coefficient, and its value can be 128, 256, 512, etc. The power value is smoothed and is initially set to 0. It is updated once for each sample point.
[0047] Then compare the average power value with the preset threshold value thr (i.e., the preset noise power threshold of the segment). If If the noise cancellation unit outputs the original data C(i,t+d), where d is the number of delayed samples; otherwise, the noise cancellation unit outputs C(i,t+d)-s(i,t), and the noise cancellation for the symmetrical frequency band is C(i,t+d)-s(N-1-i,t).
[0048] Because the filtering convolution operation introduces a delay of half the filter coefficient length, the delay unit is used to align the main signal data with the filtered noise data in terms of delay, also applying a corresponding delay to the main signal. If the filter coefficient length is coeLen, then the delay value d = floor(coeLen / 2). For example, if coeLen = 31, then d = 15. If the convolution operation has other processing delays, these processing delays should also be added to the delay value in the delay module.
[0049] The above embodiment divides the entire bandwidth into equal segments. In other embodiments of the present invention, the segmentation can be more flexible in practical applications: (1) Segmentation with arbitrary bandwidth can be used, for example, the entire frequency band can be divided into N segments with different bandwidths, denoted as N, ... , i=1,...,N. But when judging whether the filtered data is noise, the threshold value used by the index will be different because the bandwidth of the noise contained in each segment is different. It can be calculated according to the formula accordingly; (2) Multiple scans can be performed. For example, a wider bandwidth is used for coarse segmentation scanning to eliminate some noise and obtain a segment of the coarse segment where the useful signal is located. Then, the segment data containing the signal in the coarse segment is scanned for the second fine segmentation and noise reduction with a narrower bandwidth. That is, when the spectrum is not equally spaced, the filter noise reduction device includes M1 coarse noise elimination modules and M2 subdivision noise elimination modules cascaded together. Specifically, the M1 coarse noise elimination modules use a wide interval to construct the spectrum coarse segmentation; the M2 subdivision noise elimination modules are constructed by performing a second equal interval spectrum subdivision after coarse segmentation spectrum filtering if the signal data is in one of the segment spectrums. M1 and M2 are positive integers.
[0050] It should be noted that, depending on the implementation needs, the various steps / components described in this application can be broken down into more steps / components, or two or more steps / components or parts of the operation of steps / components can be combined into new steps / components to achieve the purpose of this invention.
[0051] The order of the steps in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.
[0052] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.
Claims
1. A filtering and noise reduction method that adapts to carrier frequency and bandwidth, characterized in that, Includes the following steps: The receiver's entire receiving bandwidth is divided into N segments to obtain N segmented spectra, where N is a positive integer; N noise power thresholds are calculated based on the receiver's noise figure and N segmented spectrum. N cascaded noise cancellation modules are then set up based on the N segmented spectrum and N noise power thresholds. The carrier data is input to N cascaded noise cancellation modules. After the i-th noise cancellation module filters out the i-th segment of the spectrum, the i-th segment of the spectrum is obtained. The average power of the filtered data is calculated and compared with the i-th preset noise power threshold. If it is determined to be noise, the noise is subtracted from the original carrier data. If the i-th segment of the spectrum contains signal data, it is retained. The input signal of the i-th noise cancellation module is directly output as the input signal of the (i+1)-th noise cancellation module, where i is a positive integer and 1≤i≤N.
2. The adaptive carrier frequency and bandwidth filtering and noise reduction method according to claim 1, characterized in that, Specifically, the receiver's entire receiving bandwidth is divided into N equal segments to obtain N segmented spectrums.
3. The adaptive carrier frequency and bandwidth filtering and noise reduction method according to claim 1, characterized in that, Specifically, the entire receiving bandwidth of the receiver is divided into non-equal interval spectrum segments.
4. The adaptive carrier frequency and bandwidth filtering and noise reduction method according to claim 3, characterized in that, When performing non-equal interval spectrum segmentation, a wide interval is first used for coarse spectrum segmentation. If the signal data is in one of the spectrum segments after coarse segmentation spectrum filtering, then the spectrum segment is further subdivided into equal interval segments, and then multiple cascaded noise cancellation modules are set up accordingly.
5. The adaptive carrier frequency and bandwidth filtering and noise reduction method according to claim 1, characterized in that, Before subtracting noise from the original carrier data, the original carrier data is delayed accordingly to compensate for the time delay of the filtering process.
6. A filter and noise reduction device that adapts to carrier frequency and bandwidth, characterized in that, It includes N cascaded noise cancellation modules, which are specifically constructed according to the adaptive carrier frequency and bandwidth filtering and noise reduction method described in claim 1.
7. The adaptive carrier frequency and bandwidth filter noise reduction device according to claim 6, characterized in that, Each noise cancellation module includes: A buffer unit is used to buffer the input original carrier data; The filtering unit is used to filter the original carrier data according to the spectrum of the segment it belongs to; The comparison unit is used to calculate the average power of the filtered data and compare it with the preset noise power threshold of the segment. If the average power is less than or equal to the preset noise power threshold, the filtered data is noise; otherwise, it contains signal data. The delay unit is used to delay the input original carrier data in order to align it with the filtered data; The noise cancellation unit is used to subtract the noise from the original carrier data after the time delay when the filtered data is noisy; otherwise, it directly outputs the original carrier data after the time delay to the next noise cancellation module.
8. The adaptive carrier frequency and bandwidth filter noise reduction device according to claim 7, characterized in that, The segmented spectra of different noise cancellation modules are equally spaced spectra.
9. The adaptive carrier frequency and bandwidth filter noise reduction device according to claim 7, characterized in that, The segmented spectra of different noise cancellation modules are non-equally spaced spectra.
10. The adaptive carrier frequency and bandwidth filter noise reduction device according to claim 8, characterized in that, When the spectrum is not equally spaced, the filter noise reduction unit includes M1 cascaded coarse noise cancellation modules and M2 cascaded fine noise cancellation modules. Specifically, the M1 coarse noise cancellation modules construct the spectrum by using wide intervals for coarse segmentation. Specifically, the M2 fine noise cancellation modules construct the spectrum by performing secondary equal-interval segmentation if the signal data is in one of the segmented spectrums after coarse segmentation spectrum filtering, where M1 and M2 are positive integers.