CN106018955B - The low rate end frequency estimating methods of fast convolution tunable filter group - Google Patents
The low rate end frequency estimating methods of fast convolution tunable filter group Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/16—Spectrum analysis; Fourier analysis
- G01R23/165—Spectrum analysis; Fourier analysis using filters
- G01R23/167—Spectrum analysis; Fourier analysis using filters with digital filters
Abstract
The invention belongs to digital processing fields, to realize on respective filter passband, it may be determined that the relative position of output spectrum and input frequency；The frequency of high-speed input signal is estimated at low rate end；Error diffusion effect can be significantly inhibited.The technical solution adopted by the present invention is that the low rate end frequency estimating methods of fast convolution tunable filter group are divided into following two stages：1) fast convolution stage Step 1 is input signal x (n) Overlapping Fragments；Step 2. makees N point Fouriers to each segmentation and converts FFT respectively；Step 3. observes the corresponding FFT amplitudes output of each subband；Result after Step 4. weights the subband is LkThe inverse fast fourier transform of point；Step 5. repeats above four steps, and it is L to obtain P lengthS,kTime domain export sample；2) the Spectrum Correction stage.Present invention is mainly applied to Digital Signal Processing.
Description
Technical field
The invention belongs to digital processing fields.More particularly to digital filter design, signal sampling and filtering,
Signal spectrum corrects, and digital signal parameters are restored.
Background technology
Currently, the problem of wireless channel spectrum resource scarcity, protrudes, and Multicarrier Transmission Technology can improve frequency spectrum profit because of it
With rate [1], it is easy to inhibit the advantages such as multipath effect and frequency selective fading [2], it has also become mainstream modulation system, such as orthogonal frequency
Divide multiplexing (Orthogonal Frequency Division Multiplexing, OFDM), since the 4th third-generation mobile communication
Just become modulation technique indispensable in wireless communication.In recent years, a variety of multi-carrier filter group modulation are proposed both at home and abroad
The implementation [3-5] of technology.It is handled in the fields such as [6,7], audio frequency process [8,9] to sub-band filter to adapt to signal of communication
Bandwidth, centre frequency, the output sampling rate of device do the demand of flexible configuration, and Harris proposes to filter based on multiphase in document [10]
The configuration method of wave device group, and then by multiphase filtering and Fast Fourier Transform FFT (Fast Fourier in document [11]
Transform filter group characteristic) combines, and more flexible parameter configuration is done to each subband, however program presence is cut
Disconnected distortion is not easy the defect eliminated；To overcome the defect, document [12] to propose a kind of tunable filter based on fast convolution
Group structure, the structure can be eliminated by adjusting parameter setting and block distortion, ensure that flexible configuration and the input of sub-band parameter
The estimated accuracy of output sampling rate, each subband bandwidth.
In multi-carrier communication, each subcarrier shares a carrier frequency and is wirelessly transferred, thus the recovery of carrier frequency is
Extremely important problem.However, document [12] is without solving in its filter bank structure based on fast convolution, how from each
The low rate output end of sub-filter accurately estimates the frequency parameter problem of high-speed input terminal.In fact, in adjustable filtering
In device group, since output sampling rate has occurred that variation compared to input sampling rate, and each subband width, center are deposited
In difference, therefore observation end is exported from low speed, the result and source ideal value of frequency analysis will produce very big deviation.
If the frequency values that transmitting terminal is accurately measured at end can be observed in low rate, it can ensure that local carrier is restored.
The present invention has done quantitative study for the problem, is deduced and realizes the adjustable filtering of frequency measurement at low rate end
The parameter configuration condition of device group model, based on this condition derive subband output digital angular frequency, actually wait for frequency measurement value and
The relational expression of filter internal parameter configuration, further combined with bispectrum line frequency correction method [13], adjustable based on fast convolution
The low rate end of filter group realizes Frequency Estimation.The experimental results showed that the opposite evaluated error of the estimator is no more than
0.001%.
Bibliography
[1] Hamamura M, Tachikawa S.Bandwidth efficiency improvement for multi-
carrier systems[A].Proceedings of the 15th IEEE International Symposium on
Personal, Indoor and Mobile Radio Communications (PIMRC) [C] .Sep. 5-8,2004.
[2] Goldsmith A.Wireless Communications [M] .Cambridge University Press,
2005.
[3] Medjahdi Y, Le Ruyet D, Roviras D, et al.New Types of Air Interface
Based on Filter Banks for Spectrum Sharing and Coexistence[M]//Di Benedetto M
G, Cattoni A F, Fiorina J, et al.Cognitive Radio and Networking for
Heterogeneous Wireless Networks.Springer International Publishing.2015:1-35.
[4] Shao K, Ji X, Zhuang L, et al.Time-domain modified DFT modulated
filter banks for multi-carrier transceiver systems[J].The Journal of China
Universities of Posts and Telecommunications, 2014,21 (2)：57-62.
[5] Rahimi S, Champagne B.Oversampled perfect reconstruction DFT
modulated filter banks for multi-carrier transceiver systems[J].Signal
Processing, 2013,93 (11)：2942-2955.
[6] Farhang-Boroujeny B, Kempter R.Multicarrier communication
techniques for spectrum sensing and communication in cognitive radios[J]
.Communications Magazine, IEEE, 2008,46 (4)：80-85.
[7] Bogucka H, Wyglinski A M, Pagadarai S, et al.Spectrally agile
multicarrier waveforms for opportunistic wireless access[J].Communications
Magazine, IEEE, 2011,49 (6)：108-115.
[8] Cvetkovic Z, Johnston J.Nonuniform oversampled filter banks for
audio applications[A].Proceedings of the the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers [C] .Pacific Grove, CA, USA, Oct. 29-
Nov.1,2000.IEEE.
[9]Smith J O.Audio FFT filter banks[A].Proceedings of the the 12th
International Conference on Digital Audio Effects (DAFx-09) [C] .Como, Italy,
September 1-4,2009.
[10] Harris F J, Dick C, Rice M.Digital receivers and transmitters using
polyphase filter banks for wireless communications[J].Microwave Theory and
Techniques, IEEE Transactions, 2003,51 (4)：1395-1412.
[11] Harris F, McGwier R, Egg B.A versatile multichannel filter bank
with multiple channel bandwidths[A]. Proceedings of the the Fifth
International Conference on Cognitive Radio Oriented Wireless Networks&
Communications (CROWNCOM) [C] .Cannes, France, June 9-11,2010.
[12] Renfors M, Yli-Kaakinen J, Harris F J.Analysis and Design of
Efficient and Flexible Fast-Convolution Based Multirate Filter Banks[J]
.Signal Processing, IEEE Transactions, 2014,62 (15)：3768-3783.
[13] Huang Xiangdong, Zhu Qingqing, cuckoo is refined, waits the bispectrum line ratio compressed sensing restructing algorithm of band-limited signals
[J] signal processings, 2012,28 (6)： 793-798.
Invention content
In order to overcome the deficiencies of the prior art, the present invention is directed to realize on respective filter passband, it may be determined that output spectrum
With the relative position of input frequency；The frequency of high-speed input signal is estimated at low rate end；Error diffusion can be significantly inhibited
Effect.The technical solution adopted by the present invention is the low rate end frequency estimating methods of fast convolution tunable filter group, be divided into
Lower two stages：
1) the fast convolution stage
Step 1 is N, overlap length N input signal x (n) Overlapping Fragments, per segment lengthO, i.e., each section length N,
Overlap length N between segmentationO, be respectively segmented non-overlapping length NSMeet：
N=NS+2NO (1)
Step 2. makees N point Fouriers to each segmentation and converts FFT respectively, and according to actual needs, its FFT is exported and is divided
For M subband, the subband broadband occupied is respectively L1~LMA FFT frequency resolutions；
Step 3. observes the corresponding FFT amplitudes output of each subband, if observing there is maximum amplitude k-th, with one
Include the window w of certain intermediate zonekThe FFT input values of the subband are weighted；
Result after Step 4. weights the subband is LkInverse fast fourier transform IFFT (the Inverse Fast of point
Fourier Transform), take the intermediate L of IFFT resultsS, kThe subband output corresponding as current input segmentation of a value；
Step 5. repeats above four steps, and it is L to obtain P lengthS, kTime domain export sample；
2) the Spectrum Correction stage
Obtained P length is L by Step 6.S, kTime domain output sample scrabble up length be Lout=PLS, kTime domain
Sample；
It is L that the time domain samples that Step 7. obtains splicing, which do points,outFFT；
Step 8. obtains the frequency estimation of output sequence by bispectrum line correction method
Step 9. obtains the Frequency Estimation of incoming carrier using following equation：
Wherein RkFor sampling rate conversion factor, fS, kFor output sampling rate.
Each section length N, respectively it is segmented non-overlapping length NS, subband width Lk, subband retain width LS, k, input sample speed
Rate fsWith subband output sampling rate fS, kMeet following relationship in proportion
If the parameter configuration condition of formula (3) is set up, the L splicedoutA time domain samples, which can completely eliminate, to be spliced
The waveform truncation effect arrived, to ensure to obtain High-precision carrier estimation in low rate output end.
Section length must be matched strictly with subband width, and the matching condition that need to specifically meet is：
1)LS=LkNS/ N requirements are integers；
2)Rk=N/Lk=NS/LS,kIt is required that being integer.
It is assumed that X (m*) it is peak value spectral line amplitude, g is the ratio of output signal peak value spectral line amplitude and time high spectral line amplitude,
I.e.：
Then its output signal frequency ωoutEstimated value be：
In formula (11), peak value is composed at the left side of secondary high spectral line, and symbol " ± " takes "+" in formula (11)；When peak value is composed secondary
When the right of high spectral line, the middle symbol " ± " of formula (11) takes "-"；
The L of formula (11)outIt counts for FFT, i.e. the number of samples of output signal, LoutAllow to include the multiple outputs of same subband
The sample of segmentation, wushu (11) substitute into formula (2) to get to final Frequency Estimation result.
The features of the present invention and advantageous effect are：
The present invention is based on the tunable filter group model of fast convolution, propose to carry out the load at high-speed end at its low rate end
The method of frequency estimation can generate following advantageous effect if being used for Frequency Estimation and Practical Project field：
First, relative position model is established, frequency estimation accuracy is high
The present invention has analysed in depth the signal processing flow of the filter group, and has excavated inhibition truncation effect and weighed with subband
Value and section length configuration relation establish output spectrum and input relative position model of the frequency in filter passband；Low
Rate end realizes the frequency estimation algorithm of high-frequency input signal.Emulation experiment shows low rate end proposed by the present invention frequency
The estimation technique, in the case where only needing 8 sections of samples of consumption output subband, Frequency Estimation relative error is about 0.1%.
Second, in conjunction with bispectrum line correction method, it is suppressed that error diffusion effect
The present invention proposes in the tunable filter group structure of fast convolution, estimates according to the output sample at low rate end
The Frequency Estimation model of high-speed end frequency input signal is counted, and combines the estimation corrected based on bispectrum line spectrum and exports letter
The algorithm of number frequency, the algorithm greatly suppress the mistake of the conversion ratio factor pair direct estimation of the tunable filter group of fast convolution
The influence of difference diffusion, Frequency Estimation relative error are only about 0.001%, have very high estimated accuracy.It is more in OFDM etc.
In carrier communication, the recovery of local carrier with it is synchronous in have larger application prospect.
Description of the drawings：
The design cycle of Fig. 1 tunable filter group low rates end frequency estimator.
Multi-sampling rate tunable filter group models of the Fig. 2 based on fast convolution.
The sampling point number schematic symbol diagram of Fig. 3 not negative lap reserved blocks.
(a) FFT process blocks (b) IFFT process blocks.
The weight coefficient of Fig. 4 filters.
Fig. 5 frequency input signals and filter passband schematic diagram.
Fig. 6 output signal spectrum schematic diagrames.
Fig. 7 peak values are composed and time high spectral line profile.
(a) secondary high spectral line is located at peak value spectrum right side (b) secondary high spectral line and is located at peak value spectrum left side.
Fig. 8 LS, kThe frequency spectrum and waveform of output signal when=16.
(a) output signal spectrum (b) signal output waveform.
Fig. 9 LS, kThe frequency spectrum and waveform of output signal when=14.
(a) output signal spectrum (b) signal output waveform.
Figure 10 LS, kThe frequency spectrum and waveform of output signal when=12.
(a) output signal spectrum (b) signal output waveform.
Figure 11 LS, kThe frequency spectrum and waveform of output signal when=10.
(a) output signal spectrum (b) signal output waveform.
The hardware of Figure 12 present invention implements figure.
Figure 13 DSP internal algorithm flow charts.
Specific implementation mode
The frequency estimator proposed according to the present invention has following performance：
(1) on respective filter passband, it may be determined that the relative position of output spectrum and input frequency；
(2) it combines FFT bispectrum line ratios to compose correction method, the frequency of high-speed input signal can be estimated at low rate end；
(3) error diffusion effect can be significantly inhibited, Frequency Estimation relative error is only about 0.001%.
The present invention adopts the following technical scheme that
The design main-process stream of 1 tunable filter group low rate end frequency estimator
Fig. 1 gives the design cycle of the present invention, and Fig. 2 is that the multi-sampling rate based on fast convolution being related to the flow can
Tunable filter group model
Process shown in Fig. 1 can be divided into following two stages：
1) the fast convolution stage
Step 1 is N, overlap length N input signal x (n) Overlapping Fragments, per segment lengthO.I.e. each section length N,
Overlap length N between segmentationO, be respectively segmented non-overlapping length NSMeet
N=NS+2NO (1)
Step 2. makees N point FFT respectively to each segmentation, and according to actual needs, its FFT outputs are divided into M subband
(the subband broadband occupied is respectively L1~LMA FFT frequency resolutions).
Step 3. observes the corresponding FFT amplitudes output of each subband, if observing there is maximum amplitude k-th, with one
Include the window w of certain intermediate zonekThe FFT input values of the subband are weighted.
Result after Step 4. weights the subband is LkThe IFFT of point, takes the intermediate L of IFFT resultsS, kA value, which is used as, to be worked as
The corresponding subband output of preceding input segmentation；
Step 5. repeats above four steps, and it is L to obtain P lengthS, kTime domain export sample.
2) the Spectrum Correction stage
Obtained P length is L by Step 6.S, kTime domain output sample scrabble up length be Lout=PLS, kTime domain
Sample.
It is L that the time domain samples that Step 7. obtains splicing, which do points,outFFT.
Step 8. obtains the frequency estimation of output sequence by bispectrum line correction method
Step 9. obtains the Frequency Estimation (f of incoming carrier using following equationS, kFor output sampling rate)
In the present invention, accurate estimating carrier frequencies value can be calculated for guarantee formula (2), key is each section length
N, the length N that each segmentation retainsS, subband width Lk, subband retain width LS, k, input sample rate fsIt exports and samples with subband
Rate fS, kMeet following relationship in proportion
If the parameter configuration condition of formula (3) is set up, the L splicedoutA time domain samples, which can completely eliminate, to be spliced
The waveform truncation effect arrived, to ensure that High-precision carrier estimation can be obtained in low rate output end.
The 2 tunable filter group models based on fast convolution
2.1 model structures and signal processing
The structure of the adjustable analysis filter group of the multi-sampling rate based on fast convolution that document [12] provides as shown in Fig. 2,
It can be seen that from the figure, the signal processing of the model is as follows：Sampling rate is fsSequence be segmented be input to the model one by one
In, each input segmentation includes N number of sampling point, and front and back input segmentation allows partial data overlapping (number of samples of overlapping is
NOAs shown in Fig. 3 (a))；Then, the FFT of N points is done to input sample and transforms to frequency domain；Then, it is L with lengthkWeights to
Measure wk, k=1 ..., M concurrently export the result on corresponding frequency band to FFT and weight；Finally, to each subband frequency domain weighting
Result afterwards is LkThe IFFT of point, takes the intermediate L of IFFT resultsS, kThe subband output corresponding as current input segmentation of a value
(i.e. LS, kThe sample of a taking-up is the not lap of output, as shown in Fig. 3 (b)).By above procedure, piecewise carries out one by one,
And the not lap for each subband output being segmented every time is stitched together, that is, obtains whole filter results of the subband.
Obviously, the structural model of Fig. 2 is very suitable for doing flexible processing to high-speed wideband input signal：It need to only set each
Subband weight vector wkLength Lk, output and input the non-overlapping parameter N of sampleSAnd LS, k, you can easily adjust each son
Width, amplitude-frequency response characteristic and the sample rate of band, to meet the specific requirement of communication system.
2.2 subband weights configure
Document [12] points out that frequency domain fast convolution tunable filter group is from the convolution model based on overlap-save method
It develops.And overlap-save method is also segment data input, it is necessary to do appropriately to set just to eliminate to segmentation parameter and cut
Disconnected effect.Accordingly, if the frequency domain weight w of each subbandkIt is set as step response, the corresponding impulse response of inverse fourier transform
Necessarily unlimited support decays at a slow speed h (n), this will introduce prodigious truncated error；Each subband weights sequence thus must be given
Arrange wk, k=1 ..., M configure the intermediate zone of certain length, as shown in Figure 4.
Due to wkWith intermediate zone, impulse response h (n) corresponding with its Fourier inversion is just able to rapid decay, from
And the convolution for being conducive to eliminate overlap-save method blocks distortion.The presence of the intermediate zone also results in each subband output
Occurs certain amplitude distortion compared to input.Thus, the tunable filter group based on fast convolution can only obtain approximate complete
Reconstruction property.
The relationship of 2.3 fragment length parameters and sample rate conversion
The conversion of input and output sampling rate in Fig. 2 is by following decimation factor RkIt determines：
Each length parameter in formula (1) is as shown in figure 3, N is the length of the segmentation of long list entries, NSIt is wherein non-overlapping
Partial length, LkIt is the IFFT processing block lengths of k-th of subband, LS, kIt is the length of non-overlapping part therein, meets
The lap output and input is all symmetrically distributed in both sides.
Further, according to formula (4), formula (5), the data segment for defining overlapping accounts for the scale factor of total section length and is
Comparison expression (4), formula (6) are found out, as decimation factor RkWhen determining, overlap factor ROAlso it determines therewith.That is,
The length of lap and non-overlapping part in overlap-save method, the ratio with sample rate conversion, is all determined by the same factor.
Therefore, the conversion ratio R required by Practical ProjectkConstraint, section length must match strictly with subband width length, specific
Need meet matching condition be：
1)LS=LkNS/ N requirements are integers；
2)Rk=N/Lk=NS/LS,kIt is required that being integer.
Therefore the length L of two above conditional decision output IFFTkMust be N/gcd (N, NS) multiple, wherein gcd
() represents greatest common divisor (Greatest Common Divider).For example, if NS=3N/4, NSWith the most grand duke of N because
Number is N/4, then LkIt must be 4 integral multiple；For another example, if NS=4N/5, NSGreatest common factor with N is N/5, then LkIt must
It must be 5 integral multiple.So the configuration of output sampling rate depends greatly on NSWith the value of N.
In addition, to inhibit the truncation effect of each subband output sequence, the overlap factor R in formula (6)OIt needs to meet above two
A configuration condition, this is also the premise for ensureing frequency estimation algorithm precision of the present invention.
3 low rate end frequency estimation algorithms
3.1 Frequency Estimation models
In conjunction with the above analysis, the Frequency Estimation model of fast convolution tunable filter group structure can be established.Assuming that input
Signal frequency f0(being located at such as position shown in solid Fig. 5) belongs to k-th of subband Bk, the weight vector w of the subbandkWith dotted line table
Show (including total LkA weights), initial frequency point is fK, 0, cutoff frequency point isFig. 6 is the output signal frequency of the subband
The schematic diagram of spectrum, if the digital angular frequency of output signal is ωout。
In conjunction with Fig. 5, Fig. 6, due to the frequency f of input signal0In BkRelative position and ωoutPhase in numerical frequency axis
Consistency should be met to position, therefore following formula is set up
Enable subband BkStarting point marked as LK, 0, the f in formula (7)K, 0It is represented by
fK, 0=LK, 0×fs/N (8)
It is assumed that the sampling rate of k-th of subchannel is fS, k, then sample rate transformational relation shown in convolution (4), can release
The estimated value f of frequency input signal0With the estimated value of the digital angular frequency of outputBetween relationship be
In formula (7), the beginning label L of subfilter passbandK, 0, passband spectral line number Lk, output subband sample rate fS, k, sampling
Rate conversion factor RkAll it is the pre-set parameter value of system, thus the output number angular frequency that can observeoutEstimation be
It is crucial.
Obviously, the corresponding frequency values of output peak value spectral line can be used directly as ω by Fig. 6outEstimation, and then according to formula
(9) it calculatesBut error can be introduced because of fence effect in this way.Importantly, can be seen that by formula (9), turned by sampling rate
Change factor RkIt influences, ωoutEvaluated error can be further magnified, to reduce frequency input signal f0Estimated accuracy.With
It is lower that this can be solved the problems, such as using bispectrum line ratio spectrum correction method.
3.2 estimations based on double spectrum line ratio methods
Leakage problem is composed due to existing, can be seen that by the output spectrum of Fig. 6, the actual frequency of output signal should be located at peak value
Between spectrum and secondary high spectral line.Therefore, it is directly composed using peak value to estimate that frequency input signal can have error.Here bispectrum is introduced
Line ratio method[13], it is generalized in the frequency input signal estimation of fast convolution tunable filter group.Specifically, being exactly to use
Peak value is composed obtains accurate observing frequency ω with the ratio of time high spectral lineoutValue, and then improve frequency input signal f0Estimation
Precision.
There are two kinds of situations for the distribution of output peak value spectrum and time high spectral line, as shown in Figure 7.
It is assumed that g is the ratio of output signal peak value spectral line amplitude and time high spectral line amplitude, i.e.,
Then its output signal frequency ωoutEstimated value be[8]
In formula (11), peak value is composed at the left side of secondary high spectral line, and as shown in Fig. 7 (a), symbol takes "+" in formula (11)；Work as peak
For value spectrum at the right of secondary high spectral line, as shown in Fig. 7 (b), the middle symbol of formula (11) takes "-".
The L of formula (11)outIt counts for FFT, i.e. the number of samples of output signal, in actually measuring, as long as overlap factor RO
Meet the parameter setting condition of formula (6), then truncation effect can be inhibited.To improve precision, LoutAllow more comprising same subband
The sample of a output segmentation.And then wushu (11) substitutes into formula (9), you can obtains final Frequency Estimation result.
4 Frequency Estimation emulation experiments
As follows, input terminal sampling rate f is arranged in experiment parameters=100MHz, by frequency f0Value is the complex exponential of 7.25MHz
Signal is input in the fast convolution tunable filter group of Fig. 2, and Frequency Estimation is done in its low data rate output end.In Fig. 2, FFT
Section length N=1536, wherein the length N of non-overlapping partS=3N/4=1152.Enable the sampling rate conversion factor R of systemk=
96, then according to formula (4), it may be determined that output IFFT processing block lengths Lk=N/R=16.Its subband weight vector wkBy rolloff-factor
It samples to obtain for the raised cosine of α=1, beginning label LK, 0=100 (are obtained by doing energy comparison to the output of each subband
To).
Respectively by the length L of non-overlapping partS, k16,14,12,10 are set as, then the overlap factor R of output endO=Lk-
LS, k/LkRespectively 0,1/8,1/4,3/8, by LoutIt is set as the splicing total length of the non-overlapping output in continuous P=8 time of the subband
(i.e. Lout=PLS, k=8LS, k)。
The output signal real part waveform y (n) and its amplitude spectrum of above 4 kinds of situations is set forth in Fig. 8-Figure 11 | Y (m) |
(i.e. | Y (ω) | in 2 π m/Lout, m=0 ..., Lout- 1, value).
By shown in Fig. 8 (b)-Figure 11 (b), only working as LS, k=12, ROWhen=1/4, the waveform of output signal is continuous；
Work as LS, kWhen taking other values, due to being unsatisfactory for configuration condition shown in the formula (6) that the present invention derives, so cannot obtain continuous
Output waveform and comprising single peak value spectral line output spectrum (show output FFT spectrum be more cluster spectral peaks).
Table 1, which lists, works as LS, kWhen=16,14,12,10, direct method and bispectrum line correction method are used respectively, the observation frequency measured
Rate valueAnd give its respective frequencies estimated valuePercentage error (i.e.)。
1 difference L of tableS, kEstimation inputs frequency and actually enters frequency comparison under value
As can be seen from Table 1, work as LS, kWhen=12 (meet the present invention derive as formula (6) configuration condition when), input
Signal frequency evaluated error is much smaller compared to other situations.It is in particular in：After Spectrum Correction, frequency estimation accuracy
Than other LS, kSituation improves 2~3 orders of magnitude.
Hardware realization of the present invention is illustrated below.
In fig. 12, the input signal of simulation is sampled first, the digital signal after sampling is segmented, each
Segment data and filter coefficient are stored in external RAM (random access memory), then they are input in DSP in real time, are passed through
Cross DSP internal core algorithms, the processing such as FFT, filtering, IFFT, extraction, connection and correction carried out to signal, to signal frequency into
Row estimation, finally shows by output driving and its display module shows frequency values.
Wherein, the DSP (Digital Signal Processor, digital signal processor) of Figure 12 is core devices,
During frequency reconfiguration, following major function is completed：
(1) internal core algorithm is called, FFT, filtering, IFFT, extraction, connection and the correction etc. of each section of input signal are completed
Process；
(2) frequency relative position model is used to estimate frequency input signal；
(3) by Frequency Estimation fructufy it is exported when to driving and display module.
It may be noted that as a result of digitized method of estimation, thus determine the complexities of Figure 12 systems, real-time levels and
The principal element of stability is not the periphery connection of hardware in figure, but the core that DSP internal program memories are stored is estimated
Calculating method.
The internal algorithm flow of DSP devices is as shown in figure 13.
The present invention is by the core algorithm of " the low rate end frequency estimator of fast convolution tunable filter group " that is proposed
It is implanted into DSP devices, based on this completion high-precision, low complex degree, efficient Frequency Estimation.
Figure 13 flows are divided into the following steps：
(1) first according to each parameter value of analysis setting estimator above；
(2) and then DSP reads input signal from the ends I/O, and is segmented and is saved in internal RAM；
(3) according to the algorithm main-process stream of Fig. 1, each segment data of parallel processing calculates frequency estimation；
(4) Frequency Estimation result is preserved.
It may be noted that being realized as a result of DSP so that entire spectral estimator design becomes more flexibly and fast, can root
According to the actual needs in spectral estimator design process, the parameter in flexible transformation formula (9) is allowed to finally meet requirement of engineering.
Meet requirement of engineering eventually.
Claims (2)
1. a kind of low rate end frequency estimating methods of fast convolution tunable filter group, characterized in that be divided into following two ranks
Section：
1) the fast convolution stage
Step 1 is N, overlap length N input signal x (n) Overlapping Fragments, per segment lengthO, i.e., between each section length N, segmentation
Overlap length NO, be respectively segmented non-overlapping length NSMeet：
N=NS+2NO (1)
Step 2. makees N point Fouriers to each segmentation and converts FFT respectively, and according to actual needs, its FFT outputs are divided into M
Subband, the subband broadband occupied is respectively L1~LMA FFT frequency resolutions；
Step 3. observes the corresponding FFT amplitudes output of each subband
The window w of certain intermediate zonekThe FFT input values of the subband are weighted；
Result after Step 4. weights the subband is LkInverse fast fourier transform IFFT (the Inverse Fast of point
Fourier Transform), take the intermediate L of IFFT resultsS,kThe subband output corresponding as current input segmentation of a value；
Step 5. repeats above four steps, and it is L to obtain P lengthS,kTime domain export sample；
2) the Spectrum Correction stage
Obtained P length is L by Step 6.S,kTime domain output sample scrabble up length be Lout=PLS,kTime domain samples；
It is L that the time domain samples that Step 7. obtains splicing, which do points,outFFT；
Step 8. obtains the frequency estimation of output sequence by bispectrum line correction method
Step 9. obtains the Frequency Estimation of incoming carrier using following equation：
Wherein RkFor sampling rate conversion factor, fs,kFor output sampling rate.
Each section length N, respectively it is segmented non-overlapping length NS, subband width Lk, subband retain width LS,k, input sample rate fs
With subband output sampling rate fs,kMeet following relationship in proportion
If the parameter configuration condition of formula (3) is set up, the Lo splicedutA time domain samples can completely eliminate what splicing obtained
Waveform truncation effect, to ensure to obtain High-precision carrier estimation in low rate output end.
2. the low rate end frequency estimating methods of fast convolution tunable filter group as described in claim 1, characterized in that point
Segment length must be matched strictly with subband width, and the matching condition that need to specifically meet is：
1)LS=LkNS/ N requirements are integers；
2)Rk=N/Lk=Ns/LS,kIt is required that being integer；
It is assumed that X (m*) is peak value spectral line amplitude, g is the ratio of output signal peak value spectral line amplitude and time high spectral line amplitude, i.e.,：
Then its output signal frequency ωoutEstimated value be：
In formula (11), peak value is composed at the left side of secondary high spectral line, and symbol " ± " takes "+" in formula (11)；When peak value spectrum is in secondary high spectrum
When the right of line, the middle symbol " ± " of formula (11) takes "-"；
The L of formula (11)outIt counts for FFT, i.e. the number of samples of output signal, LoutAllow comprising the multiple output segmentations of same subband
Sample, wushu (11) substitutes into formula (2) to get to final Frequency Estimation result.
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