CN105337587B - A kind of non-maximum extraction system synthesis filter group building method based on DFT - Google Patents
A kind of non-maximum extraction system synthesis filter group building method based on DFT Download PDFInfo
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Abstract
The invention belongs to soft radio applications fields, and in particular to a kind of non-maximum extraction system synthesis filter group building method based on DFT in broadband digital receive-transmit system, speech signal processing system and multi-carrier communications systems.A kind of non-maximum extraction system synthesis filter group building method based on DFT, utilize shift frequency module, it will need comprehensive M son band baseband complex signal and be multiplied by the complex-exponential-modulation factor respectively, and obtain that bandwidth will be equal, centre frequency signal spectrum distribution mode arranged at equal interval；The modulation data of M channel is passed through into Fourier transform module again, inverse discrete Fourier transformer inverse-discrete IDFT, data after being converted are carried out to M sub-channels；Data after IDFT are filtered, D times of interpolation is carried out, obtains data after M sub-channels interpolation；Finally pass through time delay module, summation module, synthesis goes out final echo signal.The present invention can obtain better stopband attenuation, reduce operand and hardware resource loss.
Description
Technical field
The invention belongs to soft radio applications fields, and in particular to at broadband digital receive-transmit system, voice signal
A kind of non-maximum extraction system synthesis filter group building method based on DFT in reason system and multi-carrier communications systems.
Background technology
With software radio system, communication system, video signal analysis, speech signal analysis, picture signal processing, thunder
Up to the rapid development in the fields such as signal processing, the treatment technology of digital signal has been to be concerned by more and more people.At digital signal
Reason is the basis of electronic warfare and communication, and electronic warfare and the two big battlefields that communication is modern information technologies war, in electronic warfare
Many technologies are equally applicable in the communications field.Key technology one of of the filter group technology as Digital Signal Processing, becomes
The research hotspot in soft radio applications fields.The research of synthesis filter group structure design and its building method is filter
The synthesis filter group structure design of important link in group technology, optimization can greatly improve system performance, reduce resource
Consumption has important practical significance to the soft radio applications field using filter bank structure design.
In terms of synthesis filter structure design, patent《A kind of building method of lattice structure synthesis filter group》(Shen
Please number：2010100290218) lattice structure construction synthesis filter group is used, image denoising field is used for, is tied with the present invention
Structure design is different；Document《Synthesis filter group optimization design and its application in image procossing》(Wuhan University Of Technology doctor
Paper, 2014) mainly one-dimensional, the two-dimension integrated filter group optimization design in image procossing is studied, it is all made of
Be lattice structure, it is different from structure of the invention design；Document《HDTV audio decoders synthesis filter group algorithm optimization and FPGA
It realizes》(electronic measurement technique, 2008) is realized mainly around the FPGA of the synthesis filter group butterfly structure in audio frequency process
Study on Problems does not provide the specific configuration method of synthesis filter group, different from the content of present invention；Document《Based on the channels M
The synthesis filter symmetry of LPPRFB and length selection method research》(Chinese journal of scientific instrument, 2009) is mainly around comprehensive
The research for closing the symmetry and length selection method of filter, is not directed to the building method of synthesis filter group, with this hair
Bright patent is different.
Invention content
The non-maximum extraction system synthesis filter group building method that it is an object of the invention to provide a kind of based on DFT.
The object of the present invention is achieved like this：
A kind of non-maximum extraction system synthesis filter group building method based on DFT will be needed comprehensive using shift frequency module
M of conjunction is sub to be with baseband complex signalBe multiplied by the complex-exponential-modulation factor respectively, obtain bandwidth it is equal,
Centre frequency signal spectrum distribution mode arranged at equal interval；The modulation data of M channel is passed through into Fourier transform module again,
Inverse discrete Fourier transformer inverse-discrete IDFT, data after being converted are carried out to M sub-channels；Then the data after IDFT are filtered
Wave carries out D times of interpolation using up-sampling, obtains data after M sub-channels interpolation；Finally pass through time delay module, summation module,
Synthesis goes out final echo signal.
Synthesis filter group construction meets following characteristic condition：
Wherein H (Z) is analysis filter group ptototype filter, and G (Z) is synthesis filter group ptototype filter, and K (Z) is
Intermediate treatment unit frequency responds, and X (Z) is the transform of input signal x (n), and Y (Z) is the transform of output signal y (n), and M is
The number of channel, D are to extract number；
Matrix form is defined as follows：
Matrix representations are：
Useful signal transfer function；
For useless signal aliasing transfer function；
When being zero：
Then have：
For effective transmission of realization signal, the frequency response K of the intermediate treatment part of analysis filter and synthesis filter
(Z) meet：
KM×M=EM×M
EM×MFor M rank unit matrixs；
The synthesis filter frequency response of m-th of channel is：
Synthesis filter group multiphase branching filter construction process is as follows：
(2) number of channel M=16 is set, number D=8 is extracted, normalization cut-off frequecy of passband is 0.065, stopband initial frequency
Respectively 0.114, filter order N=192, the coefficient * 10 of ptototype filter-6It is as follows：
H (n)=[- 6.728, -7.634, -0.111, -0.145, -0.176, -0.194, -0.192, -
0.159,......]1×196
(3) ptototype filter coefficient is converted into 16 × 12 array, according to design parameter in non-maximum extraction systemSynthesis filter multi-phase components Fk(Z2) multiphase filter that is equivalent in each branch interleaves 0 value, you can
Obtain 16 groups of multi-phase components Fk(Z2) (k=0,1 ... 15), wherein inserting each multi-phase components F after 0 valuek(Z2) it is 24 ranks.
The beneficial effects of the present invention are：A kind of non-maximum extraction system integrated filter based on DFT that the present invention announces
Device group building method, not only ptototype filter design is simple and identical in constraints, and the present invention can obtain
Better stopband attenuation reduces operand and hardware resource loss.This method pushes traditional maximum extraction system to applicability
Wider array of non-maximum extraction system, the synthesis filter group building method based on DFT provided is small with calculation amount, flexibility is high
The characteristics of.
Description of the drawings
Sub-channel signal frequency spectrum arrangement mode after Fig. 1 complex-exponential-modulations of the present invention
The non-maximum extraction system filter group block diagrams of Fig. 2
The general synthesis filter structures of Fig. 3
Fig. 4 synthesis filter group efficient configurations of the present invention
Fig. 5 ptototype filter frequency responses of the present invention
Specific implementation mode
With reference to the accompanying drawings of the specification, detailed description of the present invention specific embodiment.
The non-maximum extraction system synthesis filter group building method that the present invention provides a kind of based on DFT, the tool of use
Body technique scheme and its Structure and Process include mainly the following aspects：First with shift frequency module, M comprehensive son will be needed
It is with baseband complex signalIt is multiplied by the complex-exponential-modulation factor respectively, obtains that bandwidth is equal, center frequency
Rate signal spectrum distribution mode arranged at equal interval；The modulation data of M channel is passed through into Fourier transform module again, to M
Subchannel carries out inverse discrete Fourier transformer inverse-discrete (IDFT), data after being converted；Then the data after IDFT are filtered, then
D times of interpolation is carried out by up-sampling, obtains data after M sub-channels interpolation；Finally pass through time delay module, summation module, it is comprehensive
Go out echo signal.The present invention pushes traditional maximum extraction system to applicability wider array of non-maximum extraction system, not only prototype
Filter design is simple and identical in constraints, it is possible to reduce operand and hardware resource loss provide
Non- maximum extraction system synthesis filter group building method based on DFT has the characteristics that calculation amount is small, flexibility is high.
In order to complete above-mentioned purpose, specific technical solution and its Structure and Process that the present invention uses include mainly following
Aspect：First with shift frequency module, will need M comprehensive son band baseband complex signal isRespectively
It is multiplied by the complex-exponential-modulation factor, obtains that bandwidth as shown in Figure 1 is equal, centre frequency signal spectrum distribution side arranged at equal interval
Formula；The modulation data of M channel is passed through into Fourier transform module again, inverse discrete Fourier transformer inverse-discrete is carried out to M sub-channels
(IDFT), data after being converted；Then the data after IDFT are filtered, carry out D times of interpolation using up-sampling, obtains
Data after M sub-channels interpolation；Finally pass through time delay module, summation module, synthesis goes out final echo signal.
Filter group block diagram as shown in Figure 2, it is known that analysis filter group includes M bandpass filter, transform definition
For Hm(Z), m=0,1 ..., M-1.Bandpass filter bandwidth having the same, the centre frequency of each filter are expressed as
ωm, wherein ωm=2 π m/M, m=0,1 ..., M-1.The unit impact response of known ptototype filter is h (n)={ h
[0] ..., h [N-1], filter length N, i.e. 0≤n≤N-1, transform is：By DFT
Modulation, the bandpass filter of m-th of channel areCorresponding frequency response is：
Relationship between channel number M and extracting multiple D meets：It is extracted when working as M/D=1, i.e. M=D to maximize；Work as M/
When D=F (F is the integer more than 1), referred to as non-maximization is extracted.
The frequency response of the intermediate treatment part of defined analysis filter and synthesis filter is K (Z), the then mesh that synthesis goes out
Mark signal can be expressed as：
Formula (1) is expressed as matrix form, we can be defined as follows：
Above formula (1) matrix is expressed as：
In formula (2)：
Formula (3) is the entire transfer function table of M channel, D times of extraction and analysis filter group and synthesis filter group
Up to formula.
In formula (3)：
Formula (4) is useful signal transfer function.
Formula (5) is useless signal aliasing transfer function.
By formula (4) and formula (5), formula (3) can be expressed as：
When formula (5) is zero, i.e.,：
I.e.：
By the correlation theory modulated, formula (7) can be reduced to：
To realize that effective transmission of signal, formula (4) are necessary for the integer between analysis filter group and synthesis filter group
Postpone again, and the frequency response K (Z) of the intermediate treatment part of analysis filter and synthesis filter meets：
KM×M=EM×M (9)
In above formula：EM×MFor M rank unit matrixs.
To sum up, useful signal transmission function can be reduced to：
In order to realize that the nearly perfect reconstruction of signal, analysis filter group h (n) and synthesis filter group g (n) need to meet
The condition of formula (8) and (9), formula (8), (9) are known as signal Accurate Reconstruction condition.
It can be expressed as in the synthesis filter frequency response of the configuration aspects of analysis integrated filter group, m-th of channel：
In formula (11)：
Fk(Z) the multiphase component for being G (Z), P are the smallest positive integral more than N/M.
By above formula analysis it is found thatIt can be indicated with IFFT inverse fourier transforms.
Based on synthesis filter structure, D times is up-sampled after module is moved to bandpass filter group, then at this time m-th
The filter freguency response of channel can be expressed as：
General synthesis filter group structure, as shown in Figure 3.For M son band baseband complex signal, m=0,1,
2 ... M-1,For the shift frequency factor, D is up-sampling multiple, Gm(Z) it is m-th of channel ptototype filter frequency response.It should
Structure includes shift frequency module (101), up-sampling module (102), bandpass filtering modules block (103), summation module (104), the tradition
Synthesis filter Structure Calculation amount it is big, filter segment design is complicated, and hardware realization is not easy.
A kind of non-maximum extraction system synthesis filter group building method based on DFT, Structure and Process includes mainly
Several aspects：First with shift frequency module, will need M comprehensive son band baseband complex signal is
It is multiplied by the complex-exponential-modulation factor respectively, obtains that bandwidth as shown in Figure 1 is equal, centre frequency signal spectrum arranged at equal interval point
Mode for cloth；The modulation data of M channel is passed through into Fourier transform module again, discrete Fourier inversion is carried out to M sub-channels
(IDFT) is changed, data after being converted；Then the data after IDFT are filtered, carry out D times of interpolation using up-sampling, obtains
Data after to M sub-channels interpolation；Finally pass through time delay module, summation module, synthesis goes out echo signal.
Filter group block diagram as shown in Figure 2, it is known that analysis filter group includes M bandpass filter, transform definition
For Hm(Z), m=0,1 ..., M-1.Bandpass filter bandwidth having the same, the centre frequency of each filter are expressed as
ωm, wherein ωm=2 π m/M, m=0,1 ..., M-1.The unit impact response of known ptototype filter is h (n)={ h
[0] ..., h [N-1], filter length N, i.e. 0≤n≤N-1, transform is：M-th of letter
The bandpass filter in road isCorresponding frequency response is：
In the present embodiment, M=16, D=8.
The frequency response of the intermediate treatment part of defined analysis filter and synthesis filter is K (Z), the then mesh that synthesis goes out
Mark signal can be expressed as：
Formula (14) is expressed as matrix form, we can be defined as follows：
Above formula (14) matrix is expressed as：
In formula (15)：
Formula (16) is the entire transfer function of 16 channels, 8 times of extractions and analysis filter group and synthesis filter group
Expression formula.
In formula (16)：
Formula (17) is useful signal transfer function.
Formula (18) is useless signal aliasing transfer function.
By formula (17) and formula (18), formula (15) can be expressed as：
When formula (18) is zero, i.e.,：
I.e.：
By the correlation theory modulated, formula (21) can be reduced to：
Similarly, it is effective transmission of realization signal, formula (17) is necessary between analysis filter group and synthesis filter group
Integer delay, and the intermediate treatment part of analysis filter and synthesis filter frequency response K (Z) meet：
K16×16=E16×16 (23)
In above formula：E16×16For 16 rank unit matrixs.
To sum up, useful signal transmission function can be reduced to：
In order to realize that the nearly perfect reconstruction of signal, analysis filter group h (n) and synthesis filter group g (n) need to meet
The condition of formula (22) and (23), formula (22), (23) are known as signal Accurate Reconstruction condition.
It can be expressed as in the synthesis filter frequency response of the configuration aspects of analysis integrated filter group, m-th of channel：
By above formula analysis it is found thatIt can be indicated with IFFT inverse fourier transforms.Based on synthesis filter structure, by 8
Up-sampling module is moved to after bandpass filter group again, then the filter freguency response of m-th of channel can be expressed as at this time：
In formula (26)：
For the multiphase component of G (Z), P is the smallest positive integral more than N/16.
The present invention obtains efficient synthesis filter group structure, as shown in Figure 4.
A kind of non-maximum extraction system synthesis filter group building method of in the present invention based on DFT, include mainly with
Under several steps：
Step 1：Shift frequency module, needing M comprehensive son band baseband complex signal isMultiply respectively
With the complex-exponential-modulation factor, obtain that bandwidth as shown in Figure 1 is equal, centre frequency signal spectrum distribution side arranged at equal interval
Formula, wherein：The complex-exponential-modulation factor isE is natural number logarithm；J is imaginary number, meets j2=-1；π is pi；M is
Subchannel number；D is up-sampling multiple, m=0,1 ..., M-1, n=(- ∞, ∞).
Step 2：Complex-exponential-modulation module extracts when working as M/D=1, i.e. M=D to maximize；Work as M/D=F, (F is more than 1
Integer) when, referred to as non-maximization is extracted at this time, designs the non-maximization extraction system complex-exponential-modulation factorMeet with
Lower condition：
Step 3：Fourier transform module carries out IDFT inverse discrete Fourier transformer inverse-discretes to M sub-channels, obtains transformation number
According to；Wherein when sub-band channel number M meets M=2n, n=0, when 1,2..., IDFT modules can use IFFT Fourier transforms to replace,
Significantly reduce operand.When being calculated such as 16 point IDFT, when IDFT modules replace with IFFT modules, calculation amount comparison such as table
Shown in 1.
1 IDFT modules of table are compared with IFFT module calculation amounts
Step 4：The transformation data of filter module, M sub-channels are filtered by multiphase bandpass filtering group, obtain M
The filtered signal of subchannel；
In the design aspect of filter group, this example M=16, D=8, it is FIR filter to take ptototype filter, is used
Remez functions design filter, and normalization cut-off frequecy of passband is 0.065, and stopband initial frequency is respectively 0.114, filter
Exponent number is 192.Ptototype filter frequency response is as shown in Figure 5.
The coefficient (* 10 of ptototype filter-6) as follows：
H (n)=[- 6.728, -7.634, -0.111, -0.145, -0.176, -0.194, -0.192, -
0.159,......]1×196 (28)
Ptototype filter coefficient is converted into 16 × 12 array, then by extracting the correlation theory with interpolation it is found that comprehensive
Close filter multi-phase components Fk(Z2) multiphase filter that is equivalent in each branch interleaves 0 value.
I.e.：
F0(Z2)=[- 6.72*10-6 0 0.0002 0 -0.0006 0 -0.0001 0 0.0061 0 -0.0152 0
0.0839 0 -0.0162 0 0.0048 0 0.0004 0 -0.0007 0 0.0001 0]
F1(Z2)=[- 7.63*10-6 0 0.0002 0 -0.0005 0 -0.0008 0 0.007 0 -0.0129 0
0.0819 0 -0.0160 0 0.0033 0 0.0010 0 -0.0007 0 0.0001 0]
F2(Z2)=[- 0.11*10-6 0 0.0002 0 -0.0004 0 -0.0016 0 0.0076 0 -0.0091 0
0.0780 0 -0.0148 0 0.0018 0 0.0014 0 -0.0006 0 0.0001 0]
F3(Z2)=[- 0.14*10-6 0 0.0002 0 -0.0001 0 -0.002 0 0.0076 0 -0.0039 0
0.0723 0 -0.0127 0 0.0003 0 0.0017 0 -0.0005 0 0.7262 0]
F4(Z2)=[- 0.17*10-6 0.0002 0 0.0001 0 -0.0030 0 0.0071 0 0.0026 0
0.0651 0 -0.0100 0 -0.0010 0 0.0018 0 -0.0004 0 0.44*10-60]
F5(Z2)=[- 0.1949*10-6 0 0.0001 0 0.0004 0 -0.00350 0.0059 0 0.0103 0
0.0568 0 -0.0069 0 -0.0021 0 0.00170-0.0003 0 0.21*10-6 0]
F6(Z2)=[- 0.19*10-6 0 0.0001 0 0.0007 0 -0.0038 0 0.0042 0 0.0190 0
0.0476 0 -0.0038 0 -0.0030 0 0.0016 0 -0.0002 0 3.58*10-6 0]
F7(Z2)=[- 0.15*10-6 0 0.16*10-6 0 0.0011 0 -0.0038 0 0.0019 0 0.0283 0
0.0380 0 -0.0008 0 -0.0035 0 0.0014 0 -0.90*10-6 0 -8.59*10-6 0]
F8(Z2)=[- 8.59*10-6 0 -0.90*10-6 0 0.001 0 -0.0035 0 -0.0008 0 0.0380 0
0.0283 0 0.0019 0 -0.0038 0 0.0011 0 0.16*10-6 0 -0.15*10-6 0]
F9(Z2)=[3.58*10-6 0 -0.0002 0 0.0016 0 -0.0030 0 -0.0038 0 0.0476 0
0.0190 0 0.0042 0 -0.0038 0 0.0007 0 0.00010 -0.19*10-6 0]
F10(Z2)=[0.21*10-6 0 -0.0003 0 0.0017 0 -0.0021 0 -0.0069 0 0.0568 0
0.0103 0 0.0059 0 -0.0035 0 0.0004 0 0.00010 -0.19*10-6 0]
F11(Z2)=[0.44*10-6 0 -0.0004 0 0.0018 0 -0.0010 0 -0.0100 0 0.0651 0
0.0026 0 0.0071 0 -0.0030 0 0.0001 0 0.0002 0 -0.17*10-6 0]
F12(Z2)=[0.72*10-6 0 -0.0005 0 0.0017 0] 0.0003 0 -0.0127 0 0.0723 0 -
0.0039 0 0.0076 0 -0.0023 0 -0.0001 0 0.0002 0 -0.14*10-6 0]
F13(Z2)=[0.0001 0-0.0006 0 0.0014 0 0.0018 0-0.0148 0 0.0780 0-
0.0091 0 0.0076 0 -0.0016 0 -0.0004 0 0.0002 0 -0.11*10-6 0]
F14(Z2)=[0.0001 0-0.0007 0 0.0010 0 0.0033 0-0.0160 0 0.0819 0-
0.0129 0 0.0070 0 -0.0008 0 -0.0005 0 0.0002 0 -7.63*10-6 0]
F15(Z2)=[0.0001 0-0.0007 0 0.0004 0 0.0048 0-0.0162 0 0.0839 0-
0.0152 0 0.0061 0 -0.0001 0 -0.0006 0 0.0002 0 -6.72*10-6 0]
Step 5：Module is up-sampled, D times of interpolation is carried out to the filtered signal of M sub-channels, obtains M sub-channels interpolation
Data afterwards；Wherein, module is up-sampled compared with traditional synthesis filter structure for D times, position makes the present invention exist in the rear end of structure
It is carried out under low sampling rate, operand is reduced.Its theory is, it is assumed that M sub-channels sampling rates are fs, then D times up-sampling after M
Sub-channels sampling rate FsMeet Fs=Dfs, D times of channel sampling rate increase, i.e., The present invention reduces operands.
Step 6：Unit time delay module is delayed respectively to data after M sub-channels interpolation accordingly, realizes multiphase knot
Structure；
Step 7：Summation module carries out overlap-add, the data summed, i.e. comprehensive letter to M sub-channels signals
Road signal.
Claims (5)
1. a kind of non-maximum extraction system synthesis filter group building method based on DFT, it is characterised in that：Utilize shift frequency mould
Block, will need M comprehensive data packets complex signal isM=0,1 ... M-1 is multiplied by the complex-exponential-modulation factor respectively,
Obtain that bandwidth is equal, centre frequency signal spectrum distribution mode arranged at equal interval；Wherein：The complex-exponential-modulation factor isE is natural number logarithm；J is imaginary number, meets j2=-1；π is pi；M is subchannel number；D is up-sampling times
Number, m=0,1 ..., M-1, n=(- ∞, ∞)；The modulation data of M channel is passed through into Fourier transform module again, M is believed
Road carries out inverse discrete Fourier transformer inverse-discrete IDFT, data after being converted；Then the data after IDFT are filtered, using upper
Sampling carries out D times of interpolation, obtains data after M channel interpolation；Finally pass through time delay module, summation module, synthesis goes out final
Echo signal.
2. a kind of non-maximum extraction system synthesis filter group building method based on DFT according to claim 1, special
Sign is：Analysis filter group includes M channel, and transform is defined as Hm(Z), m=0,1 ..., M-1；Bandpass filtering utensil
There are identical bandwidth, the centre frequency of each filter to be expressed as ωm, wherein ωm=2 π m/M, m=0,1 ..., M-1；It is former
The unit impact response of mode filter is h (n)={ h [0] ..., h [N-1] }, filter length N, i.e. 0≤n≤N-1, Z
It is transformed to：It is modulated by DFT, the bandpass filter of m-th of channel is
Corresponding frequency response is：Wherein,Synthesis filter group indicates
For：AndRelationship between channel number M and extracting multiple D meet it is non-most
Bigization extraction condition, i.e.,：M/D=F, F are the positive integer more than 1.
3. a kind of non-maximum extraction system synthesis filter group building method based on DFT according to claim 1, special
Sign is that synthesis filter group construction meets following characteristic condition：
Wherein H (Z) is analysis filter group ptototype filter, and G (Z) is synthesis filter group ptototype filter, and K (Z) is centre
Processing unit frequency response, X (Z) are the transform of input signal x (n), and Y (Z) is the transform of output signal y (n), and M is channel
Number, D are to extract number；
Matrix form is defined as follows：
Matrix representations are：
Useful signal transfer function；
For useless signal aliasing transfer function；
When being zero：
Then have：
For effective transmission of realization signal, the frequency response K (Z) of the intermediate treatment part of analysis filter and synthesis filter is full
Foot：
KM×M=EM×M
EM×MFor M rank unit matrixs；
4. a kind of non-maximum extraction system synthesis filter group building method based on DFT according to claim 1, special
Sign is：The synthesis filter frequency response of m-th of channel is：
Fk(Z) the multiphase component for being G (Z),
P is the smallest positive integral more than N/M；When M meets M=2n, n=0, when 1,2..., IDFT modules can use IFFT Fourier transforms
It replaces.
5. a kind of non-maximum extraction system synthesis filter group building method based on DFT according to claim 1, special
Sign is that synthesis filter group multiphase branching filter construction process is as follows：
(1) Remez function design synthesis filter group ptototype filters, unit impact response h are utilized0(n)=h [0] ...,
H [N-1] }, filter length N, i.e. 0≤n≤N-1, transform is：The band logical of m-th of channel
Filter isWherein ωm=2 π k/K, k=0,1 ..., K-1, corresponding frequency response are：
(2) number of channel M=16 is set, number D=8 is extracted, normalization cut-off frequecy of passband is 0.065, stopband initial frequency difference
It is 0.114, filter order N=192, the coefficient * 10 of ptototype filter-6It is as follows：
H (n)=[- 6.728, -7.634, -0.111, -0.145, -0.176, -0.194, -0.192, -0.159 ...]1×196
(3) ptototype filter coefficient is converted into 16 × 12 array, according to design parameter in non-maximum extraction systemSynthesis filter multi-phase components Fk(Z2) multiphase filter that is equivalent in each branch interleaves 0 value, i.e.,
16 groups of multi-phase components F can be obtainedk(Z2), k=0,1 ... 15, wherein inserting each multi-phase components F after 0 valuek(Z2) it is 24 ranks.
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| CN108259024A (en) * | 2018-02-26 | 2018-07-06 | 中国人民解放军国防科技大学 | Design method of over-D sampling multiphase DFT filter bank |
| CN108416165B (en) * | 2018-03-26 | 2021-08-27 | 合肥工业大学 | High-noise-resistance local frequency estimation method suitable for elastic imaging |
| CN112039497A (en) * | 2020-08-21 | 2020-12-04 | 安徽蓝讯电子科技有限公司 | Multi-carrier sub-band filter of filter bank |
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