CN107342750A - Fractional delay optimization method suitable for more Nyquist areas and its realize structure - Google Patents
Fractional delay optimization method suitable for more Nyquist areas and its realize structure Download PDFInfo
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- H03H17/0018—Realizing a fractional delay
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Abstract
Fractional delay optimization method suitable for more Nyquist areas and its structure is realized, belong to digital processing field.Fractional delay is carried out respectively to input data sequence to handle to obtain the first output data sequence and do Hilbert transform again after doing multiplication operation to obtain the second output data sequence, the first output data sequence is subtracted into the output data sequence after the second output data sequence obtains the fractional delay suitable for more Nyquist areas again, input data sequence is multiplied by zoom factor A=(1) by wherein multiplication operationNZThe π D of ceil [(NZ 1)/2] 2, wherein NZ represents the frequency fin of input data sequence relative to the Nyquist area residing for sample frequency fs, ceil represents the operation that rounded up to data (NZ 1)/2, and D represents the retardation of fractional delay filter.Traditional fractional delay filter can be expanded to high Nyquist area by the present invention using frequency band range, realize the fractional delay in more Nyquist areas, and simple in construction, it is easy to accomplish.
Description
Technical field
The present invention relates to digital processing field, particularly relates to a kind of fraction suitable for more Nyquist areas
Postpone the design of optimization method and the fractional delay filter suitable for more Nyquist areas.
Background technology
Fractional delay filter, it is that a kind of delay is non-integer sampling point also referred to as being continuous variable digital delay unit
Digital filter, be widely used in the fields such as voice coding and synthesis, digital communication, time delay estimation, sample rate conversion.
Fractional delay filter has had the design method of comparative maturity, such as based on polynomial design method
(Farrow structures), the design method based on Lagrange's interpolation, design method based on least square method etc..It is but logical
Cross the fractional delay filter that conventional method is designed to be disadvantageous in that, its application frequency band is in the first Nyquist area (0
~fs/2, fs represent the sample rate of data signal), refer to the frequency input signal (fin) that the wave filter can handle using frequency band
Scope, so when fin is more than fs/2, fractional delay filter cannot normal work, this significantly limit fraction and prolongs
The application of slow wave filter.
The content of the invention
The present invention in view of the deficiencies of the prior art, proposes that a kind of fractional delay suitable for more Nyquist areas optimizes
Method and the fractional delay filter suitable for more Nyquist areas so that fractional delay filter can work to more than fs/2
Frequency band range.
The technical scheme is that：
Suitable for the fractional delay optimization method in more Nyquist areas, comprise the following steps：
Step 1：Fractional delay is carried out to input data to handle to obtain the first output data；
Step 2：Input data is done and does Hilbert transform again after multiplication operation and obtains the second output data, it is described to multiply
Method operation is that input data is multiplied by into zoom factor A=(- 1)NZCeil [(NZ-1)/2] 2 π D, wherein NZ represent input number
According to frequency fin relative to the Nyquist area residing for sample frequency fs, ceil represents to round up to data (NZ-1)/2
Operation, D represent the retardation of fractional delay filter；
Step 3：First output data is subtracted into second output data to obtain described being applied to more Nyquists
Output data after the fractional delay in area.
During NZ=1, input signal is represented in the first Nyquist area, now 0≤fin<fs/2；During NZ=2, input is represented
Signal is in the second Nyquist area, now fs/2≤fin<fs；During NZ=3, input signal is represented in the 3rd Nyquist area, this
When fs≤fin<3fs/2；During NZ=4, represent input signal in the 4th Nyquist area 3fs/2≤fin<2fs, by that analogy.
Specifically, the fractional delay processing in the step 1, using the fractional delay filter of Farrow structures, it is passed
Defeated function isWherein N represents the rank of the wave filter
Number, h [n] are the unit impulse response of wave filter, are fitted h [n] by weighted least-squares method, a (n, m) is fitting used
Multinomial, the numbering of m representative polynomials.
Specifically, the fractional delay processing in the step 1 uses the fractional delay filter based on Lagrange's interpolation
Algorithm, its unit impulse response are
Wherein, N represents filter order.
Specifically, the unit impulse response of the Hilbert transform is
Spectrum Conversion operation is done to input data.
A kind of fractional delay filter suitable for more Nyquist areas, including fractional delay filter module, correcting module,
Hilbert transform module and computing module, the correcting module will input data therein and do multiplication operation, be multiplied by scaling because
Exported after son, the zoom factor A=(- 1)NZCeil [(NZ-1)/2] 2 π D, wherein NZ represent input data sequence xd
Relative to the Nyquist area residing for sample frequency fs, ceil represents to round up to data (NZ-1)/2 the frequency fin of [n]
Operation, D represent the retardation of fractional delay filter；
The fractional delay filter module connects input data, the output of the correcting module with the input of correcting module
End connects the input of the Hilbert transform module, and the first input end of the computing module links the fractional delay filter
The output data of ripple module, its second input connect the output data of the Hilbert transform module, the computing module
The data that the data of its first input end are subtracted to its second input obtain the fraction suitable for more Nyquist areas and prolonged
The output data of slow wave filter.
Specifically, the fractional delay filter module uses the fractional delay filter of Farrow structures, its transfer function
ForWherein N represents the exponent number of the wave filter, h
[n] is the unit impulse response of wave filter, is fitted h [n] by weighted least-squares method, a (n, m) is that fitting used is multinomial
Formula, the numbering of m representative polynomials.
Specifically, the unit impulse response of the Hilbert module is
The present invention operation principle be：
Make input dataOutput data xd *[n]=cos (ωinN), wherein inputting
The angular frequency of datain=2 π fin, Ts=1/fs, fin are the frequency of input data, and wherein fs is sample frequency, TsFor sampling
Cycle, when Δ T expressions carry out sampling discretization with sampling clock to data, relative to the time deviation of preferable sampling instant,
So to expect output data xd *[n], it is necessary to postponed by fractional delay filter to input signal
When input signal is in the first Nyquist area, by traditional fractional delay filter with regard to that can achieve the goal.
Input signal frequency-domain expression of input signal at the second Nyquist area is：
Wherein δ (ω) represents uni-impulse function.
The frequency-domain expression of output signal is：
As input data xd[n] is by after traditional fraction filtering wave by prolonging time device, having：
Contrast equation (2) and formula (3) are understood, if wanting the output y by fraction filtering wave by prolonging time deviced[n], which is equal to, it is expected school
Signal x after justd *[n], the then condition for needing to meet are：
Formula (4) represents, when input signal is in the second Nyquist area, in order to reach delay Δ T purpose, it is desirable to point
The delay and input signal angular frequency that number filtering wave by prolonging time device is realizedinIt is relevant.But due to the frequency of input signal can not be known,
So this point is difficult to accomplish.
Similarly, can be obtained in arbitrary Nyquist area：
In order to solve the problems, such as that fraction filtering wave by prolonging time device can not be applied to high Nyquist area, with input signal second how
Exemplified by area of Qwest, as follows, the second Nyquist area NZ=2, according to zoom factor A=(- 1 proposed by the present invention is specifically described
)NZThe π D calculating formulas of ceil [(NZ-1)/2] 2, the zoom factor A=2 π D in the second Nyquist area.
If Δ T is smaller, it can use first approximation to rewrite formula (1), can obtain：
Require that the delay D that fraction filtering wave by prolonging time device is realized is also smaller accordingly, therefore e±j2πDIt can be rewritten with first approximation
For：
ej2πD≈1+j2πD (7)
In order in constructive formula (7) j2 π D this, introduce Hilbert transform (Hilbert Transform), with reason
Exemplified by the Hilbert transform thought,
Meanwhile introduce the π D of zoom factor 2 in the second Nyquist area, then input signal xd[n]] pass through Hilbert transform
After being scaled with zoom factor, it can obtain：
Wherein j ωinΔT/TsCan be neglected with j2 π D product term, therefore, formula (9) can approximate abbreviation be：
YHd(jω)≈π[δ(ω-ωin+2π)·j2πD+δ(ω+ωin-2π)·(-j2πD)] (10)
Similarly, formula (3) is rewritten with first approximation, can obtained：
Subtracting formula (10) with formula (11) can obtain：
Contrast equation (12) and formula (2), it is found that after aforesaid operations, it is expected to correct if thinking that signal is equal to
Signal x afterwardsd *[n], the then condition for needing to meet are still formulaSolving traditional fraction filtering wave by prolonging time device can not apply
In the high Nyquist area the problem of.
Beneficial effects of the present invention are：Traditional fractional delay filter can be expanded to Gao Naikui using frequency band range
This special zone, realize the fractional delay in more Nyquist areas；And the present invention is simple in construction, it is easy to accomplish.
Brief description of the drawings
Fig. 1 is the structured flowchart of the fractional delay filter proposed by the present invention suitable for more Nyquist areas.
Fig. 2 is the output waveform of traditional fractional delay filter and the comparison diagram of actual delay waveform.
Fig. 3 is the output waveform of fractional delay filter and the comparison diagram of actual delay waveform in the present invention.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation describes, it is clear that described embodiment is only part of the embodiment of the present invention, rather than whole embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art are obtained every other under the premise of creative work is not made
Embodiment, belong to the scope of protection of the invention.
Fractional delay filter proposed by the present invention suitable for more Nyquist areas is as shown in figure 1, including fractional delay
Filtration module C, correcting module A, Hilbert transform module B and computing module E, wherein correcting module will input data therein
Multiplication operation is done, is exported after being multiplied by zoom factor, zoom factor A=(- 1)NZThe π D of ceil [(NZ-1)/2] 2, wherein NZ tables
Show input data sequence xdThe frequency fin of [n] is represented to data relative to the Nyquist area residing for sample frequency fs, ceil
(NZ-1)/2 round up operation, and D represents the retardation of fractional delay filter；Fractional delay filter module and correcting module
Input connection input data, correcting module output end connection Hilbert transform module input, computing module
First input end links the output data of fractional delay filter module, and its second input connects the defeated of Hilbert transform module
Go out data, the data that computing module subtracts the data of its first input end its second input obtain being applied to more Nyquists
The output data of the fractional delay filter in area.
Fractional delay filter module uses existing fractional delay filter, and the fractional delay filter module in embodiment one uses
The fractional delay filter of Farrow structures, its transfer function are
Wherein N represents the exponent number of the wave filter, and h [n] is the unit impulse response of wave filter, and h is fitted by weighted least-squares method
[n], a (n, m) are polynomial fitting used, the numbering of m representative polynomials, and polynomial solution refers to document
T.B.Deng.Symmetry-Based Low-ComplexityVariable Fractional-DelayFIR Filters
[C].Intemaiional Symposiumon Conmiunications and Information Technologies
(ISCIT),Sapporo,Japan,October 26-29,2004.Fractional delay processing in embodiment two, which uses, is based on glug
The fractional delay filter algorithm of bright day interpolation, its unit impulse response can refer to formula
The formula derives from non-integer filtering wave by prolonging time devices of document Guo Wei, Pan Zhongming, Du Jinbang, Wang Yue the section based on Lagrange interpolation
Algorithm [J] National University of Defense technology journal, 2009,01:90-94.
The unit impulse response of Hilbert module in the present embodiment is
The present embodiment is so that input signal is in the 4th Nyquist area as an example, it should be appreciated that although the present embodiment with
Input signal is exemplified by the 4th Nyquist area, but the application of the present invention can be in any Nyquist area.
In the present embodiment, fs=1GHz, fin=1.95GHz, xd[n]=0.9sin (2 π finn/fs), n=0,1,
2,3 ... so input signal is in the 4th Nyquist area, and the present embodiment is modeled using MATLAB simulation softwares, makes fraction prolong
The delay parameter D=0.01, now zoom factor corrector of slow wave filter multiplication factor A=4 π D.
For output signal, three signals can be obtained using three kinds of modes：xd1 *[n], xd2 *[n], xd3 *[n], wherein
xd1 *[n] represents the output signal obtained by traditional fractional delay filter, xd2 *[n] is represented by the fraction in the present invention
The output signal that delay filter obtains, xd3 *[n]=0.9sin (2 π fin (n-0.01)/fs), represent directly to believe input
Number delay 0.01 chronomere after output signal.
Signal xd1 *[n] and xd3 *The comparison of wave shape figure of [n] is as shown in Fig. 2 signal xd2 *[n] and xd3 *The comparison of wave shape of [n]
Figure is as shown in Figure 3；From Fig. 2 two waveforms contrast it can be found that traditional fractional delay filter in the 4th Nyquist
Area, which can not accurately realize, sets length of delay, is compared with the delay waveform of reality and larger deviation be present, from the contrast in Fig. 3
It can be found that the output waveform by the fractional delay filter in the present invention can be good at and actual delay waveform weight
Close, illustrate that the fractional delay filter in the present invention accurately realizes the length of delay set very much, can be by traditional fraction
The application of delay filter expands to high Nyquist area.
One of ordinary skill in the art can make various do not depart from originally according to these technical inspirations disclosed by the invention
The other various specific deformations and combination, these deformations and combination of invention essence are still within the scope of the present invention.
Claims (7)
1. suitable for the fractional delay optimization method in more Nyquist areas, it is characterised in that comprise the following steps：
Step 1：Fractional delay is carried out to input data to handle to obtain the first output data；
Step 2：Input data is done and does Hilbert transform after multiplication operation again and obtains the second output data, the multiplication behaviour
Zoom factor A=(- 1) is multiplied by as by input dataNZCeil [(NZ-1)/2] 2 π D, wherein NZ represent input data
Frequency fin represents the operation that rounded up to data (NZ-1)/2 relative to the Nyquist area residing for sample frequency fs, ceil,
D represents the retardation of fractional delay filter；
Step 3：By first output data subtract second output data obtain it is described suitable for more Nyquist areas
Output data after fractional delay.
2. the fractional delay optimization method according to claim 1 suitable for more Nyquist areas, it is characterised in that described
Fractional delay processing in step 1 uses the fractional delay filter of Farrow structures, and its transfer function is Wherein N represents the exponent number of the wave filter, and h [n] is wave filter
Unit impulse response, h [n] is fitted by weighted least-squares method, a (n, m) is polynomial fitting used, and m represents multinomial
The numbering of formula.
3. the fractional delay optimization method according to claim 1 suitable for more Nyquist areas, it is characterised in that described
Fractional delay processing in step 1 uses the fractional delay filter algorithm based on Lagrange's interpolation, its unit impulse response
For
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4. the fractional delay optimization method suitable for more Nyquist areas according to any one of claims 1 to 3, its feature
It is, the unit impulse response of the Hilbert transform is
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A kind of 5. fractional delay filter suitable for more Nyquist areas, it is characterised in that including fractional delay filter module,
Correcting module, Hilbert transform module and computing module, the correcting module will input data therein and do multiplication operation, multiply
To be exported after zoom factor A, the zoom factor A=(- 1)NZCeil [(NZ-1)/2] 2 π D, wherein NZ represent input number
According to the frequency fin of sequence relative to the Nyquist area residing for sample frequency fs, ceil represents to do upwards data (NZ-1)/2
Floor operation, D represent the retardation of fractional delay filter；
The fractional delay filter module connects input data with the input of correcting module, and the output end of the correcting module connects
The input of the Hilbert transform module is connect, the first input end of the computing module links the fractional delay filter mould
The output data of block, its second input connect the output data of the Hilbert transform module, the computing module by its
The data that the data of first input end subtract its second input obtain the fractional delay filter suitable for more Nyquist areas
The output data of ripple device.
6. the fractional delay filter according to claim 5 suitable for more Nyquist areas, its feature
It is, the fractional delay filter module uses the fractional delay filter of Farrow structures, and its transfer function isWherein N represents the exponent number of the wave filter, h [n]
For the unit impulse response of wave filter, h [n] is fitted by weighted least-squares method, a (n, m) is polynomial fitting used,
The numbering of m representative polynomials.
7. the fractional delay filter suitable for more Nyquist areas according to claim 5 or 6, it is characterised in that institute
The unit impulse response for stating Hilbert module is
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2
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110266287A (en) * | 2019-05-05 | 2019-09-20 | 深圳信息职业技术学院 | Cochlear implant fractional delay filter building method, storage medium and cochlear implant |
| CN111327297A (en) * | 2020-03-09 | 2020-06-23 | 华北电力大学 | Self-adaptive resampling method based on window function design |
| CN111327382A (en) * | 2020-02-25 | 2020-06-23 | 东南大学 | Channel simulation architecture with variable amplitude, time delay bandwidth and delay and method thereof |
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| US20090208033A1 (en) * | 2000-12-05 | 2009-08-20 | Ami Semiconductor, Inc. | Digital automatic gain control |
| CN102624357A (en) * | 2012-03-19 | 2012-08-01 | 上海交通大学 | Implementation structure of fractional delay digital filter |
| US20140070859A1 (en) * | 2012-09-05 | 2014-03-13 | IQ-Analog Corporation | System and Method for Frequency Multiplier Jitter Correction |
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| US20090208033A1 (en) * | 2000-12-05 | 2009-08-20 | Ami Semiconductor, Inc. | Digital automatic gain control |
| CN102624357A (en) * | 2012-03-19 | 2012-08-01 | 上海交通大学 | Implementation structure of fractional delay digital filter |
| US20140070859A1 (en) * | 2012-09-05 | 2014-03-13 | IQ-Analog Corporation | System and Method for Frequency Multiplier Jitter Correction |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110266287A (en) * | 2019-05-05 | 2019-09-20 | 深圳信息职业技术学院 | Cochlear implant fractional delay filter building method, storage medium and cochlear implant |
| CN110266287B (en) * | 2019-05-05 | 2023-06-23 | 深圳信息职业技术学院 | Method for constructing fractional delay filter of electronic cochlea, storage medium and electronic cochlea |
| CN111327382A (en) * | 2020-02-25 | 2020-06-23 | 东南大学 | Channel simulation architecture with variable amplitude, time delay bandwidth and delay and method thereof |
| CN111327382B (en) * | 2020-02-25 | 2022-03-08 | 东南大学 | Channel simulation architecture with variable amplitude, time delay bandwidth and delay and method thereof |
| CN111327297A (en) * | 2020-03-09 | 2020-06-23 | 华北电力大学 | Self-adaptive resampling method based on window function design |
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