CN113987843A - Method for inhibiting Gibbs effect in digital signal processing system - Google Patents

Method for inhibiting Gibbs effect in digital signal processing system Download PDF

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CN113987843A
CN113987843A CN202111607787.4A CN202111607787A CN113987843A CN 113987843 A CN113987843 A CN 113987843A CN 202111607787 A CN202111607787 A CN 202111607787A CN 113987843 A CN113987843 A CN 113987843A
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吕磊
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Sichuan Innogence Technology Co Ltd
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Abstract

The invention discloses a method for inhibiting Gibbs effect in a digital signal processing system, which comprises the following steps: step 1: extending the head and the tail of the input signal to obtain an input signal with the head and the tail extended; step 2: designing an extended frequency domain roll-off window with the same sequence length as the extended input signal; and step 3: windowing; and 4, step 4: a transform domain operation; and 5: carrying out noise reduction processing on the transform domain signal to obtain a noise-reduced transform domain signal; step 6: inverse transform domain operation; and 7: removing a part corresponding to the extension signal from the extension roll-off signal after noise reduction to obtain a roll-off signal after noise reduction; and 8: and dividing the roll-off signal points subjected to noise reduction by the sampling points at the corresponding positions in the roll-off window of the extension frequency domain to obtain output signals subjected to noise reduction. The invention can effectively inhibit Gibbs effect in the noise reduction algorithm based on discrete Fourier transform, and obviously improve the overall performance of the digital signal processing system.

Description

Method for inhibiting Gibbs effect in digital signal processing system
Technical Field
The invention relates to the field of digital signal processing, in particular to a method for inhibiting Gibbs effect in a digital signal processing system.
Background
The digital signal processing method based on Discrete Fourier Transform (DFT) is widely applied in the present Generation, for example, the present Generation wireless Communication Technology represented by 4G (4 th Generation Mobile Communication Technology ), 5G (5 th Generation Mobile Communication Technology, 5th Generation Mobile Communication Technology) widely uses a channel estimation algorithm (also called transform domain channel estimation algorithm) based on DFT operation, specifically, a method is that a pilot receiving signal is extracted at an OFDM (Orthogonal Frequency Division Multiplexing) symbol pilot subcarrier position, LS (Least square) channel estimation is performed on the pilot receiving signal, the LS channel estimation result is transformed to the time domain by Inverse Discrete Fourier Transform (IDFT) to obtain a time domain channel response coefficient, noise reduction is performed on the time domain channel response coefficient and separation of time domain channel response coefficients of different ports (ports) is performed, and obtaining a time domain channel response coefficient after noise reduction, and converting the time domain channel response coefficient after noise reduction into a frequency domain through DFT to obtain a frequency domain channel estimation result after noise reduction.
In the DFT-based signal processing algorithm, if an input signal is discontinuous from the beginning to the end (after a period extension, the input signal is discontinuous), a large number of high-order components are generated after being converted into a transform domain through DFT operation and cannot be distinguished from each other by being superimposed on noise, and if the high-order components are deleted or suppressed as noise in the signal processing process, oscillation distortion is generated at the beginning and end boundaries of the original signal, which is called gibbs effect. The gibbs effect can significantly affect the performance of digital signal processing algorithms.
The patent of Huashi technology limited CN101155157A discloses a method for estimating a transform domain channel, which comprises a method for inhibiting Gibbs effect, the method replaces the frequency domain channel estimation result after noise reduction with an LS channel estimation result at the head and tail positions of a frequency domain, and the same scheme is also used in the patent of Beijing northern flame technology limited CN 104935534A. The method does not inhibit the generation of the Gibbs effect, but replaces the signal generating the distorted oscillation position with the input signal, and has the following problems:
1, if the input signal quality is poor, the system performance is greatly lost;
2, since the area of the gibbs oscillation influence cannot be estimated, the range of replacement is often required to be large, which further aggravates the influence on the system performance.
Disclosure of Invention
It is an object of the present invention to overcome the deficiencies of the prior art and to provide a method of suppressing the gibbs effect in a digital signal processing system.
The purpose of the invention is realized by the following technical scheme:
a method of suppressing the gibbs effect in a digital signal processing system, comprising the steps of:
step 1: extending the head and the tail of the input signal to obtain an input signal with the head and the tail extended; the extension is as follows: designing a head extension signal and a tail extension signal, and then respectively adding the head extension signal and the tail extension signal to the head and the tail of the input signal;
step 2: designing an extended frequency domain roll-off window with the same sequence length as the extended input signal; the extended frequency domain roll-off window should have the following characteristics: a, the amplitude of the middle part is high, and the amplitudes of the two ends are low; b, the amplitude of the first sampling point and the amplitude of the last sampling point are equal to or close to zero;
and step 3: performing point multiplication on the extended input signal and an extended frequency domain roll-off window to obtain an extended roll-off input signal;
and 4, step 4: converting the input signal after the roll-off extension into a transform domain through inverse discrete Fourier transform to obtain a transform domain signal;
and 5: carrying out noise reduction processing on the transform domain signal to obtain a noise-reduced transform domain signal;
step 6: performing discrete Fourier transform operation on the denoised transform domain signal to obtain a denoised extension roll-off signal;
and 7: removing a part corresponding to the extension signal from the extension roll-off signal after noise reduction to obtain a roll-off signal after noise reduction;
and 8: and dividing the roll-off signal points subjected to noise reduction by the sampling points at the corresponding positions in the roll-off window of the extension frequency domain to obtain output signals subjected to noise reduction.
Further, the design of the head and tail extension signals needs to consider smooth connection with the input signal.
Further, the extending includes copying a first sample of the input signal by LExtAs a header extension signal, for converting the input signal into the most significant signalCopy of the latter sample point LExtAnd taking the number of the extension signals as tail extension signals, wherein LExt is the number of the extension signals.
Furthermore, the extended frequency domain roll-off window may be specifically designed as a trapezoidal window, the values of the first LExt samples are incremented from 0 to 1 at equal intervals, the values of the last LExt samples are decremented from 1 to 0 at equal intervals, and the remaining samples are 1.
Further, said LExtThe size configuration needs to be matched with the design of the roll-off window of the extension frequency domain, and the matching specifically comprises the following steps: if the roll-off speed of the roll-off window in the extension frequency domain is high, i.e. the roll-off slope angle is greater than or equal to 60 degrees, L isExtCan be smaller; if the roll-off speed of the roll-off window in the extension frequency domain is slow, i.e. the roll-off slope inclination angle is less than 60 degrees, LExtShould be configured to be relatively large.
Further, step 8 is followed by a step of head and tail signal replacement, where the head and tail signal replacement specifically includes: and replacing the head and tail sampling points of the output signal after noise reduction with input signals at corresponding positions.
The invention has the beneficial effects that:
1) in the invention, any input information can be converted into a head and tail continuous signal during windowing, and two ends of the signal are 0 after windowing, so that the signal is a continuous signal after period extension; this fundamentally suppresses the gibbs effect;
2) according to the method, the residual noise amplification effect during removal of the roll-off window is reduced through head-to-tail extension operation, and the residual noise is amplified when the roll-off window is removed at a position with a small roll-off window amplitude;
in conclusion, the invention can effectively inhibit Gibbs effect in the DFT-based noise reduction algorithm and obviously improve the overall performance of the digital signal processing system.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a diagram of a result of performance simulation in the embodiment.
Detailed Description
It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In this embodiment, as shown in fig. 1, a method for suppressing gibbs effect in a digital signal processing system includes the following steps:
(1) head and tail extension: and extending the head and the tail of the input signal to obtain an extended input signal, wherein the extension method is to design a head extended signal and a tail extended signal, and then add the head extended signal and the tail extended signal to the head and the tail of the input signal respectively. The design of the head and tail extension signals needs to consider smooth connection with the input signal (the energy of high-order components generated in a transform domain after the extension signals are spliced with the original signal is small (the energy of the high-order components is less than 1% of the total energy of the original signal)), and the specific extension signal design method is not limited in this text.
An example of a method is: copying L a first sample of an input signalExtA header extension signal; copying L the last sample of the input signalExtA signal as tail extension signal, wherein LExtThe number of spread signals.
LExtThe configuration of (2) needs to be matched with the design of a subsequent extended frequency domain roll-off window, and if the roll-off speed of the latter is high (the roll-off slope is greater than or equal to 60 degrees), L isExtCan be smaller; otherwise, LExtShould be configured to be of a relatively large value,the specific optimal configuration can be obtained from simulation evaluation;
Figure 758944DEST_PATH_IMAGE001
Figure 775441DEST_PATH_IMAGE002
wherein k represents an input signal sample index;
Figure 538998DEST_PATH_IMAGE003
representing the input signal (LS channel estimation result);
r represents a base station antenna index;
p represents a pilot port index;
n represents the pilot sequence length;
Figure 513907DEST_PATH_IMAGE004
a first sample representing an input signal;
Figure 402229DEST_PATH_IMAGE005
representing the last sample of the input signal;
Figure 425680DEST_PATH_IMAGE006
represents a header extension signal;
Figure 715847DEST_PATH_IMAGE007
indicating tail extension signals, both of length LExt；
Figure 861657DEST_PATH_IMAGE008
Representing the stretched input signal.
(2) Designing an extended frequency domain roll-off window: the extended frequency domain roll-off window is a real or complex sequence, and the length of the sequence is the same as that of the extended input signal. The extended frequency domain roll-off window has 2 characteristics:
firstly, the amplitude of the middle part is high, and the amplitudes of the two ends are low;
second, the amplitudes of the first and last samples are equal to or close to zero.
An example of an extended frequency domain roll-off window is a trapezoidal window: front LExtThe values of the sample points are increased from 0 to 1 at equal intervals, and finally LExtThe number of the samples decreases from 1 to 0 at equal intervals, and the remaining samples are 1. The specific extended frequency domain roll-off window design method is not constrained herein.
Of course, the extended frequency domain roll-off window may also be a circular arc window, an oval window, etc., as long as the above-mentioned characteristics are satisfied.
(3) Windowing treatment: the extended input signal is point-multiplied with an extended frequency domain roll-off window to obtain an extended roll-off input signal;
Figure 565171DEST_PATH_IMAGE009
wherein, wfRepresenting an extended frequency domain roll-off window;
Figure 923471DEST_PATH_IMAGE010
which represents the input signal after the stretching,
Figure 599303DEST_PATH_IMAGE011
representing the windowed input signal; wherein, wfIs shown as
Figure 853698DEST_PATH_IMAGE012
LExtRepresenting the frequency domain extrapolation length.
(4) Transform domain operation: converting the input signal after the roll-off into a transform domain through IDFT to obtain a transform domain signal;
Figure 716612DEST_PATH_IMAGE013
wherein the content of the first and second substances,
Figure 890322DEST_PATH_IMAGE014
representing a transform domain signal and IDFT () representing an inverse discrete fourier transform.
(5) Transform domain noise reduction: carrying out noise reduction processing on the transform domain signal to obtain a noise-reduced transform domain signal;
Figure 155081DEST_PATH_IMAGE015
where β represents the transform domain noise reduction threshold.
(6) Inverse transform domain operation: performing DFT operation on the noise-reduced transform domain signal to obtain a noise-reduced extension roll-off signal;
Figure 377115DEST_PATH_IMAGE016
wherein the content of the first and second substances,
Figure 727325DEST_PATH_IMAGE017
representing the extended roll-off signal after noise reduction; DFT () represents a discrete fourier transform operation.
(7) Removing the extension signal: removing a part corresponding to the extension signal from the extension roll-off signal after noise reduction to obtain a roll-off signal after noise reduction;
(8) removing the roll-off window: dividing the roll-off signal points subjected to noise reduction by the sampling points at the corresponding positions in the roll-off window of the extension frequency domain (namely, the remaining sampling points after the positions of the extension signals are removed), and obtaining output signals subjected to noise reduction;
Figure 693007DEST_PATH_IMAGE018
(9) head and tail signal replacement: the output signal after noise reduction is L from head to tailsubInput with individual sample points replaced by corresponding positionsSignal (this step is not necessary).
In this example, we performed performance simulation experiments on the invention, the results of which are shown in fig. 2, wherein L issub=0, it can be seen that the invention can effectively suppress the gibbs effect and significantly improve the transform domain channel estimation accuracy.
The invention really inhibits the generation of Gibbs effect, obviously reduces the distortion and oscillation of the head and tail positions of the output signals after noise reduction, does not need to replace signals (or only needs to replace a small amount of signals, and depends on the scene requirement), thus better realizing the noise reduction effect and improving the system performance:
in the step (3), the windowing operation can convert any input signal into a head-tail continuous signal (two ends of the signal after windowing are 0, so that the signal after period extension is a continuous signal), thereby fundamentally inhibiting the Gibbs effect;
the extension operation in the step (1) can reduce the residual noise amplification effect in the step (8) (at the position with smaller roll-off window amplitude, the residual noise is amplified by removing the roll-off window processing);
by integrating the points 2, the invention can effectively inhibit the Gibbs effect in the noise reduction algorithm based on DFT and obviously improve the overall performance of the digital signal processing system.
It should be noted that, for simplicity of description, the above-mentioned embodiments of the method are described as a series of acts or combinations, but those skilled in the art should understand that the present application is not limited by the order of acts described, as some steps may be performed in other orders or simultaneously according to the present application. Further, those skilled in the art should also appreciate that the embodiments described in the specification are preferred embodiments and that the acts and elements referred to are not necessarily required in this application.
In the above embodiments, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a ROM, a RAM, etc.
The above disclosure is only for the purpose of illustrating the preferred embodiments of the present invention, and it is therefore to be understood that the invention is not limited by the scope of the appended claims.

Claims (6)

1. A method of suppressing the gibbs effect in a digital signal processing system, comprising the steps of:
step 1: extending the head and the tail of the input signal to obtain an input signal with the head and the tail extended; the extension is as follows: designing a head extension signal and a tail extension signal, and then respectively adding the head extension signal and the tail extension signal to the head and the tail of the input signal;
step 2: designing an extended frequency domain roll-off window with the same sequence length as the extended input signal; the extended frequency domain roll-off window should have the following characteristics: a, the amplitude of the middle part is high, and the amplitudes of the two ends are low; b, the amplitude of the first sampling point and the amplitude of the last sampling point are equal to or close to zero;
and step 3: performing point multiplication on the extended input signal and an extended frequency domain roll-off window to obtain an extended roll-off input signal;
and 4, step 4: converting the input signal after the roll-off extension into a transform domain through inverse discrete Fourier transform to obtain a transform domain signal;
and 5: carrying out noise reduction processing on the transform domain signal to obtain a noise-reduced transform domain signal;
step 6: performing discrete Fourier transform operation on the denoised transform domain signal to obtain a denoised extension roll-off signal;
and 7: removing a part corresponding to the extension signal from the extension roll-off signal after noise reduction to obtain a roll-off signal after noise reduction;
and 8: and dividing the roll-off signal points subjected to noise reduction by the sampling points at the corresponding positions in the roll-off window of the extension frequency domain to obtain output signals subjected to noise reduction.
2. A method for suppressing gibbs in a digital signal processing system according to claim 1, wherein the head and tail extension signals are designed to take into account smooth transitions with the input signal.
3. The method of claim 1, wherein said extending comprises copying a first sample of the input signal by LExtAs a header extension signal, copying the last sample point of the input signal by LExtAnd taking the number of the extension signals as tail extension signals, wherein LExt is the number of the extension signals.
4. A method for suppressing gibbs effect in a digital signal processing system as claimed in claim 1, wherein the extended frequency domain roll-off window is specifically designed as a trapezoidal window, the values of the first LExt samples are incremented from 0 to 1 at regular intervals, the values of the last LExt samples are decremented from 1 to 0 at regular intervals, and the remaining samples are 1.
5. A method of suppressing Gibbs effect in a digital signal processing system according to claim 3 or 4, wherein said LExtThe size configuration needs to be matched with the design of the roll-off window of the extension frequency domain, and the matching specifically comprises the following steps: if the roll-off speed of the roll-off window in the extension frequency domain is high, i.e. the roll-off slope angle is greater than or equal to 60 degrees, L isExtCan be smaller; if the roll-off speed of the roll-off window in the extension frequency domain is slow, i.e. the roll-off slope inclination angle is less than 60 degrees, LExtShould be configured to be relatively large.
6. The method according to claim 1, wherein said step 8 is followed by a step of head-to-tail signal replacement, said head-to-tail signal replacement specifically being: and replacing the head and tail sampling points of the output signal after noise reduction with input signals at corresponding positions.
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