CN106018955A - Low-rate end frequency estimation method of rapid convolution adjustable filer group - Google Patents

Abstract

The invention belongs to the field of digital signal processing, and provides a low-rate end frequency estimation method of a rapid convolution adjustable filer group, for realizing the purposes of determining relative positions between an output frequency spectrum and an input frequency on a corresponding filter passband, estimating the frequency of high-rate input signals at a low-rate end, and substantially inhibiting an error diffusion effect. The technical scheme employed by the invention is as follows: the low-rate end frequency estimation method of the rapid convolution adjustable filer group is divided into the following two phases: 1, a rapid convolution phase: step 1, performing overlapping segmentation on input signals x(n); step 2, performing N-point fast Fourier transform (FFT) on each segment; step 3, observing FFT amplitude output corresponding to each sub-band; step 4, performing Lk-point inverse FFT on a result after the sub-band is weighed; and step 5, repeating the previous four steps to obtain P time domain output samples each with a length of L<S,k>; and a frequency spectrum correction phase. The method provided by the invention is mainly applied to digital signal processing.

Description

The low rate end frequency estimating methods of fast convolution tunable filter group

Technical field

The invention belongs to digital processing field.It is specifically related to digital filter design, signal sampling and filtering, Signal spectrum corrects, and digital signal parameters is recovered.

Background technology

Currently, the outstanding problem of wireless channel spectrum resource scarcity, Multicarrier Transmission Technology can improve frequency spectrum profit because of it By rate [1], it is prone to suppress the advantage such as multipath effect and frequency selective fading [2], it has also become main flow modulation system, such as orthogonal frequency Divide multiplexing (Orthogonal Frequency Division Multiplexing, OFDM), just start from the 4th third-generation mobile communication Become modulation technique indispensable in radio communication.In recent years, multiple multi-carrier filter group modulation skill is proposed both at home and abroad The implementation [3-5] of art.Process in the field such as [6,7], Audio Processing [8,9] sub-filter for adapting to signal of communication Bandwidth, mid frequency, output sampling rate do the demand of flexible configuration, and Harris proposes based on multiphase filter at document [10] The collocation method of group, and then by multiphase filtering and fast fourier transform FFT (Fast Fourier in document [11] Transform) bank of filters characteristic combines, and each subband does more flexible parameter configuration, but program existence cuts Disconnected distortion is not easy the defect eliminated；For overcoming this defect, document [12] proposes a kind of tunable filter based on fast convolution Group structure, this structure can arrange by adjusting parameter and eliminate and block distortion, it is ensured that the flexible configuration of sub band parameter and input Output sampling rate, the estimated accuracy of each subband bandwidth.

In multi-carrier communication, each subcarrier shares a carrier frequency and is wirelessly transferred, thus the recovery of carrier frequency is Very important problem.But, document [12] does not has to solve in its filter bank structure based on fast convolution, how from respectively The frequency parameter problem of two-forty input accurately estimated by the low rate outfan of sub-filter.It is true that in adjustable filtering In device group, owing to output sampling rate has occurred that change compared to input sampling rate, and each subband width, center are deposited In difference, therefore from low speed output observation end, the result of its frequency analysis and source ideal value can produce the biggest deviation. If the frequency values of transmitting terminal can be measured exactly at low rate observation end, then can ensure that local carrier is recovered.

The present invention is directed to this problem and done quantitative study, be deduced the adjustable filtering realizing frequency measurement at low rate end The parameter configuration condition of device group model, based on this condition derive subband output digital angular frequency, actual treat 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 bank of filters achieves Frequency Estimation.Test result indicate that, the relative estimation difference of this estimator is less than 0.001%.

List of references

[1] Hamamura M, Tachikawa S.Bandwidth efficiency improvement for multi- carrier systems[A].Proceedings of the15th 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, etc. the bispectrum line ratio compressed sensing restructing algorithm of band-limited signal [J]. signal processing, 2012,28 (6): 793-798.

Summary of the invention

For overcoming the deficiencies in the prior art, it is contemplated that realize on respective filter passband, it may be determined that output spectrum Relative position with incoming frequency；The frequency of two-forty input signal is estimated at low rate end；Error diffusion can be significantly inhibited Effect.The technical solution used in 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

1 input signal x (n) Overlapping Fragment of Step, every segment length is N, and overlap length is N_O, the most each section length N, Overlap length N between segmentation_O, non-overlapped length N of each segmentation_SMeet:

N=N_S+2N_O (1)

N point Fourier conversion FFT is made in each segmentation by Step 2. respectively, and according to actual needs, its FFT output is divided For M subband, the subband broadband occupied is respectively L₁～L_MIndividual FFT frequency resolution；

Step 3. observes the FFT amplitude output that each subband is corresponding, if observing, kth has the amplitude of maximum, then with one Comprise the window w of certain intermediate zone_kThe FFT input value of this subband is weighted；

Result after this subband is weighted by Step 4. is L_kInverse fast fourier transform IFFT (the Inverse Fast of point Fourier Transform), take the middle L of IFFT result_{S, k}Individual value is as the subband output being currently entered corresponding to segmentation；

Step 5. repeats above four steps, it is thus achieved that P a length of L_{S, k}Time domain output sample；

2) the Spectrum Correction stage

Step 6. is by obtained P a length of L_{S, k}Time domain output sample scrabble up a length of L_out=PL_{S, k}Time domain Sample；

The time domain samples that splicing is obtained by Step 7. is counted as L_outFFT；

Step 8. obtains the frequency estimation of output sequence by bispectrum line correction method

Step 9. utilize following equation obtain incoming carrier Frequency Estimation:

${\hat{f}}_0=\frac{2{\mathrm{\&pi;L}}_{k,0}+L_k{\widehat{\mathrm{\&omega;}}}_{out}}{2\mathrm{\&pi;}N}\&CenterDot;R_k{f}_{s,k}---\left(2\right)$

Wherein R_kFor sampling rate conversion factor, f_{S, k}For output sampling rate.

Each section length N, non-overlapped length N of each segmentation_S, subband width L_k, subband retain width L_{S, k}, input sample speed Rate f_sSampling rate f is exported with subband_{S, k}Meet following relation in proportion

$R_k=\frac{N}{L_k}=\frac{N_S}{L_{S,k}}=\frac{f_s}{f_{s,k}}---\left(3\right)$

If the parameter configuration condition of formula (3) is set up, then splice the L obtained_outIndividual time domain samples can be completely eliminated and splice The waveform truncation effect arrived, thus ensure that obtaining High-precision carrier at low rate outfan estimates.

Section length must strictly mate with subband width, and the matching condition that its concrete need meet is:

1)L_S=L_kN_SIt is integer that/N requires；

2)R_k=N/L_k=N_S/L_SRequirement is integer.

Assuming that X (m^*) it is peak value spectral line amplitude, g is the ratio of output signal peak value spectral line amplitude and second highest spectral line amplitude, That is:

$g=\frac{\left|X\left(m^{*}\right)\right|}{max\left\{\right|X(m^{*}-1)|,|X(m^{*}+1)\left|\right\}}---\left(10\right)$

Then its output signal frequency ω_outEstimated value be:

${\widehat{\mathrm{\&omega;}}}_{out}=(m^{*}\&PlusMinus;\frac{1}{g+1})\&CenterDot;\frac{2\mathrm{\&pi;}}{L_{out}}---\left(11\right)$

In formula (11), peak value is composed when the left side of second highest spectral line, symbol in formula (11) " ± " take "+"；When peak value is composed secondary During the right of high spectral line, the middle symbol of formula (11) " ± " take "-"；

The L of formula (11)_outCount for FFT, i.e. the number of samples of output signal, L_outAllow to comprise the multiple output of same subband The sample of segmentation, wushu (11) substitutes in formula (2), i.e. obtains final Frequency Estimation result.

The feature of the present invention and providing the benefit that:

Present invention tunable filter based on fast convolution group model, proposes to carry out the load of two-forty end at its low rate end The method that frequency is estimated, if for Frequency Estimation and Practical Project field, can produce following beneficial effect:

First, set up relative position model, frequency estimation accuracy is high

The present invention has analysed in depth the signal processing flow of this bank of filters, and has excavated suppression truncation effect and subband power Value and section length configuration relation, establish output spectrum and the incoming frequency relative position model in filter passband；Low Speed end achieves the frequency estimation algorithm of high-frequency input signal.Emulation experiment shows, the low rate end frequency that the present invention proposes The estimation technique, in the case of the 8 sections of samples only needing consumption output subband, its 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 of low rate end Meter is to the Frequency Estimation model of two-forty end frequency input signal, and combines estimation output letter based on the correction of bispectrum line spectrum The algorithm of number frequency, this algorithm greatly suppresses the mistake of the conversion ratio factor pair direct estimation of the tunable filter group of fast convolution The impact of difference diffusion, its Frequency Estimation relative error is only about 0.001%, has the highest estimated accuracy.Many at OFDM etc. In carrier communication, the recovery of local carrier and synchronization has bigger application prospect.

Accompanying drawing illustrates:

The design cycle of Fig. 1 tunable filter group low rate end frequency estimator.

Fig. 2 multi-sampling rate based on fast convolution tunable filter group model.

The sampling point number schematic symbol diagram of Fig. 3 not negative lap reserved block.

A () FFT processes block (b) IFFT and processes block.

The weights coefficient of Fig. 4 wave filter.

Fig. 5 frequency input signal and filter passband schematic diagram.

Fig. 6 output signal spectrum schematic diagram.

Fig. 7 peak value spectrum and second highest spectral line profile.

A () second highest spectral line is positioned at (b) second highest spectral line on the right side of peak value spectrum and is positioned on the left of peak value spectrum.

Fig. 8 L_{S, k}The frequency spectrum of output signal and waveform when=16.

(a) output signal spectrum (b) signal output waveform.

Fig. 9 L_{S, k}The frequency spectrum of output signal and waveform when=14.

(a) output signal spectrum (b) signal output waveform.

Figure 10 L_{S, k}The frequency spectrum of output signal and waveform when=12.

(a) output signal spectrum (b) signal output waveform.

Figure 11 L_{S, k}The frequency spectrum of output signal and waveform when=10.

(a) output signal spectrum (b) signal output waveform.

Figure implemented by the hardware of Figure 12 present invention.

Figure 13 DSP internal algorithm flow chart.

Detailed description of the invention

The frequency estimator proposed according to the present invention has a following performance:

(1) on respective filter passband, it may be determined that the relative position of output spectrum and incoming frequency；

(2) combine the spectrum correction method of FFT bispectrum line ratio, the frequency of two-forty input signal can be estimated at low rate end；

(3) can significantly inhibit error diffusion effect, its 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 relating to this flow process can Tunable filter group model

Process shown in Fig. 1 is divided into the following two stage:

1) the fast convolution stage

1 input signal x (n) Overlapping Fragment of Step, every segment length is N, and overlap length is N_O.The most each section length N, Overlap length N between segmentation_O, non-overlapped length N of each segmentation_SMeet

N=N_S+2N_O (1)

N point FFT is made in each segmentation by Step 2. respectively, and according to actual needs, its FFT output is divided into M subband (the subband broadband occupied is respectively L₁～L_MIndividual FFT frequency resolution).

Step 3. observes the FFT amplitude output that each subband is corresponding, if observing, kth has the amplitude of maximum, then with one Comprise the window w of certain intermediate zone_kThe FFT input value of this subband is weighted.

Result after this subband is weighted by Step 4. is L_kThe IFFT of point, takes the middle L of IFFT result_{S, k}Individual value is as working as Subband output corresponding to front input segmentation；

Step 5. repeats above four steps, it is thus achieved that P a length of L_{S, k}Time domain output sample.

2) the Spectrum Correction stage

Step 6. is by obtained P a length of L_{S, k}Time domain output sample scrabble up a length of L_out=PL_{S, k}Time domain Sample.

The time domain samples that splicing is obtained by Step 7. is counted as L_outFFT.

Step 8. obtains the frequency estimation of output sequence by bispectrum line correction method

Step 9. utilizes following equation to obtain the Frequency Estimation (f of incoming carrier_{S, k}For output sampling rate)

${\hat{f}}_0=\frac{2{\mathrm{\&pi;L}}_{k,0}+L_k{\widehat{\mathrm{\&omega;}}}_{out}}{2\mathrm{\&pi;}N}\&CenterDot;R_k{f}_{s,k}---\left(2\right)$

In the present invention, can calculate accurate estimating carrier frequencies value for guarantee formula (2), it it is critical only that each section length Length N that N, each segmentation retain_S, subband width L_k, subband retain width L_{S, k}, input sample speed f_sWith subband output sampling Speed f_{S, k}Meet following relation in proportion

$R_k=\frac{N}{L_k}=\frac{N_s}{L_{S,k}}=\frac{f_s}{f_{s,k}}---\left(3\right)$

If the parameter configuration condition of formula (3) is set up, then splice the L obtained_outIndividual time domain samples can be completely eliminated and splice The waveform truncation effect arrived, thus ensure that can obtain High-precision carrier at low rate outfan estimates.

2 tunable filter group models based on fast convolution

2.1 model structures and signal processing

The structure of the adjustable analysis filterbank of multi-sampling rate based on fast convolution that document [12] is given as in figure 2 it is shown, Can be seen that from this figure, the signal processing of this model is as follows: sampling rate is f_sSequence segmentation one by one be input to this model In, each input fragmented packets contains N number of sampling point, and input segmentation front and back allows part data overlap, and (overlapping number of samples is N_OAs shown in Fig. 3 (a))；Then, input sample is the FFT of N point and transforms to frequency domain；Then, a length of L is used_kWeights to Amount w_k, k=1 ..., M, the result on frequency band corresponding to FFT output weights concurrently；Finally, after to each subband frequency domain weighting Result be L_kThe IFFT of point, takes the middle L of IFFT result_{S, k}Individual value exports (i.e. as the subband being currently entered corresponding to segmentation L_{S, k}The sample of individual taking-up is the not lap of output, as shown in Fig. 3 (b)).Above procedure piecewise one by one is carried out, and The not lap that each subband of each segmentation is exported is stitched together, and i.e. obtains whole filter result of this subband.

Obviously, the structural model of Fig. 2 is especially suitable for doing two-forty wideband input signal sweetly disposition: the most only need to set each Subband weight vector w_kLength L_k, input and export non-overlapped parameter N of sample_SAnd L_{S, k}, each son can be adjusted easily Width, amplitude-frequency response characteristic and the sample rate of band, to meet the specific requirement of communication system.

2.2 subband weights configurations

Document [12] is pointed out, frequency domain fast convolution tunable filter group is from convolution model based on overlap-save method Develop and come.And overlap-save method be also segment data input, it is necessary to segmentation parameter is done appropriate setting just can eliminate cut Disconnected effect.Accordingly, if the frequency domain weight w of each subband_kIt is set to step response, the impulse response that its inverse fourier transform is corresponding H (n) necessarily unlimited support decays at a slow speed, and this will introduce the biggest truncated error；Thus each subband weights sequence must be given Row w_k, k=1 ..., M, the intermediate zone of configuration certain length, as shown in Figure 4.

Due to w_kHaving intermediate zone, impulse response h (n) corresponding with its Fourier inversion is just able to rapid decay, from And be conducive to eliminating the convolution of overlap-save method block distortion.The existence of this intermediate zone, also results in the output of each subband Compared to input, certain amplitude distortion occurs.Thus, tunable filter group based on fast convolution can only obtain approximation completely Reconstruction property.

2.3 fragment length parameter and the relation of sample rate conversion

Input in Fig. 2 is by following decimation factor R with the conversion of output sampling rate_kDetermine:

$R_k=\frac{N}{L_k}=\frac{N_S}{L_{S,k}},k=1,...,M---\left(4\right)$

Each length parameter in formula (1) as it is shown on figure 3, N is the length of the segmentation of long list entries, N_SIt is the most non-overlapped The length of part, L_kIt is the IFFT process block length of kth subband, L_{S, k}It is the length of non-overlapped part therein, meets

$\{\begin{array}{c}N=N_S+2N_o\\ L_k=L_{S,k}+2L_{o,k}\end{array}---\left(5\right)$

The lap i.e. inputted and export all is symmetrically distributed in both sides.

Further, according to formula (4), formula (5), the data segment of definition overlap accounts for the scale factor of total section length and is

$R_o=\frac{2N_O}{N}=\frac{N-N_S}{N}=\frac{2L_{O,k}}{L_k}=\frac{L_k-L_{S,k}}{L_k}---\left(6\right)$

Comparison expression (4), formula (6) are found out, when decimation factor R_kWhen determining, overlap factor R_ODetermine the most therewith.It is to say, Lap and the length of non-overlapped part in overlap-save method, with the ratio of sample rate conversion, all determined by the same factor. Therefore, the conversion ratio R required by Practical Project_kConstraint, section length must strictly mate with subband width length, and it is concrete Need meet matching condition be:

1)L_S=L_kN_SIt is integer that/N requires；

2)R_k=N/L_k=N_S/L_SRequirement is integer.

Therefore length L of two above conditional decision output IFFT_kMust be N/gcd (N, N_S) multiple, wherein gcd () represents greatest common divisor (Greatest Common Divider).Such as, if N_S=3N/4, N_SWith the grand duke of N because of Number is N/4, then L_kIt must be the integral multiple of 4；For another example, if N_S=4N/5, N_SN/5 with the greatest common factor of N, then L_kMust It must be the integral multiple of 5.So being arranged in of output sampling rate is heavily dependent on N_SValue with N.

It addition, be the truncation effect suppressing each subband output sequence, the overlap factor R in formula (6)_ONeed to meet above two Individual configuration condition, this is also to ensure that the premise of frequency estimation algorithm precision of the present invention.

3 low rate end frequency estimation algorithms

3.1 Frequency Estimation models

Analyze in conjunction with above, the Frequency Estimation model of fast convolution tunable filter group structure can be set up.Assume input Signal frequency f₀(being positioned at position as shown in solid in Fig. 5) belongs to kth subband B_k, the weight vector w of this subband_kUse dotted line table Show and (include common L_kIndividual weights), its initial frequency point is f_{K, 0}, cut-off frequency point isFig. 6 is the output signal frequency of this subband The schematic diagram of spectrum, if the digital angular frequency of output signal is ω_out。

In conjunction with Fig. 5, Fig. 6, due to frequency f of input signal₀At B_kRelative position and ω_outPhase in numerical frequency axle Position should be met concordance, therefore following formula is set up

$\frac{{\mathrm{\&omega;}}_{out}}{2\mathrm{\&pi;}}=\frac{f_0-f_{k,0}}{B_k}---\left(7\right)$

Make subband B_kStarting point be numbered L_{K, 0}, f in formula (7)_{K, 0}It is represented by

f_{K, 0}=L_{K, 0}×f_s/N (8)

Assuming that the sampling rate of kth subchannel is f_{S, k}, then the sample rate conversion relation shown in convolution (4), can release Estimated value f of frequency input signal₀Estimated value with output numeral angular frequencyBetween relation be

${\hat{f}}_0=\frac{2{\mathrm{\&pi;L}}_{k,0}+L_k{\widehat{\mathrm{\&omega;}}}_{out}}{2\mathrm{\&pi;}N}\&CenterDot;R_k{f}_{s,k}---\left(9\right)$

In formula (7), the beginning label L of subfilter passband_{K, 0}, passband spectral line number L_k, output sub-band sample rate f_{S, k}, sampling Rate conversion factor R_kIt is all the parameter value that pre-sets of system, thus the output numeral angular frequency that can observe_outEstimation be Crucial.

Obviously, Fig. 6 frequency values corresponding to output peak value spectral line be can be used directly as ω_outEstimation, and then according to formula (9) calculateBut so can introduce error because of fence effect.The more important thing is, formula (9) can be seen that, turned by sampling rate Change factor R_kImpact, ω_outEstimation difference can be further magnified, thus reduce frequency input signal f₀Estimated accuracy.With Lower employing bispectrum line ratio spectrum correction method can solve this problem.

3.2 estimations based on double spectrum line ratio methods

Owing to there is spectrum leakage problem, the output spectrum of Fig. 6 can be seen that, the actual frequency of output signal should be positioned at peak value Between spectrum and second highest spectral line.Therefore, peak value spectrum is directly used to estimate that frequency input signal can exist 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, it is simply that use The ratio of peak value spectrum and second highest spectral line obtains observing frequency ω accurately_outValue, and then improve frequency input signal f₀Estimation Precision.

There are two kinds of situations, as shown in Figure 7 in the distribution of output peak value spectrum and second highest spectral line.

Assuming that the ratio that g is output signal peak value spectral line amplitude and second highest spectral line amplitude, i.e.

$g=\frac{\left|X\left(m^{*}\right)\right|}{max\left\{\right|X(m^{*}-1)|,|X(m^{*}+1)\left|\right\}}---\left(10\right)$

Then its output signal frequency ω_outEstimated value be^[8]

${\widehat{\mathrm{\&omega;}}}_{out}=(m^{*}\&PlusMinus;\frac{1}{g+1})\&CenterDot;\frac{2\mathrm{\&pi;}}{L_{out}}---\left(11\right)$

In formula (11), peak value compose when the left side of second highest spectral line, as shown in Fig. 7 (a), in formula (11) symbol take "+"；Work as peak Value spectrum is when the right of second highest spectral line, and as shown in Fig. 7 (b), the middle symbol of formula (11) takes "-".

The L of formula (11)_outCount for FFT, i.e. the number of samples of output signal, in reality is measured, if overlap factor R_O The parameter meeting formula (6) arranges condition, then truncation effect can be suppressed.For improving precision, L_outAllow to comprise same subband many The sample of individual output segmentation.And then wushu (11) substitutes in formula (9), i.e. can get final Frequency Estimation result.

4 Frequency Estimation emulation experiments

Experiment parameter arranges as follows, input sampling rate f_s=100MHz, by frequency f₀Value is the complex exponential of 7.25MHz Signal is input in the fast convolution tunable filter group of Fig. 2, does Frequency Estimation at its low data rate outfan.In Fig. 2, FFT Section length N=1536, length N of the most non-overlapped part_S=3N/4=1152.Make the sampling rate conversion factor R of system_k= 96, then according to formula (4), it may be determined that output IFFT processes block length L_k=N/R=16.Its subband weight vector w_kBy rolloff-factor Raised cosine sampling for α=1 obtains, its beginning label L_{K, 0}=100 (obtain by the output of each subband is done energy comparison Arrive).

Respectively by length L of non-overlapped part_{S, k}It is set to 16,14,12,10, then the overlap factor R of outfan_O=L_k- L_{S, k}/L_kIt is respectively 0,1/8,1/4,3/8, by L_outIt is set as the splicing total length of the non-overlapped output in continuous P=8 time of this subband (i.e. L_out=PL_{S, k}=8L_{S, k})。

Fig. 8-Figure 11 sets forth output signal real part waveform y (n) and amplitude spectrum | the Y (m) | thereof of above 4 kinds of situations (i.e. | Y (ω) | is at 2 π m/L_out, m=0 ..., L_out-1, value).

By Fig. 8 (b)-Figure 11 (b) Suo Shi, only work as L_{S, k}=12, R_OWhen=1/4, the waveform of output signal is continuous print； Work as L_{S, k}When taking other values, owing to being unsatisfactory for the configuration condition shown in the formula (6) that the present invention derives, so continuous print can not be obtained Output waveform and the output spectrum (showing that output FFT spectrum is many bunches of spectral peaks) comprising single peak value spectral line.

Table 1 lists works as L_{S, k}When=16,14,12,10, respectively with direct method and bispectrum line correction method, the observation measured frequency Rate valueAnd give its respective frequencies estimated valuePercentage error (i.e.)。

The different L of table 1_{S, k}Estimate incoming frequency under value and actually enter frequency contrast

As can be seen from Table 1, L is worked as_{S, k}When=12 (meet the present invention derives such as the configuration condition of formula (6) time), its input Signal frequency estimation difference is much smaller compared to other situations.It is in particular in: after Spectrum Correction, its frequency estimation accuracy Than other L_{S, k}Situation improves 2～3 orders of magnitude.

The hardware that the most just the present invention relates to realizes illustrating.

In fig. 12, first the input signal of simulation is sampled, the digital signal after sampling is carried out segmentation, each Segment data and filter coefficient are stored in external RAM (random access memory), then they are input in real time in DSP, warp Cross DSP internal core algorithm, signal is carried out FFT, filtering, IFFT, extracts, connect and correction etc. processes, signal frequency is entered Row is estimated, finally drives display and display module thereof to demonstrate frequency values by output.

Wherein, the DSP (Digital Signal Processor, digital signal processor) of Figure 12 is core devices, During frequency reconfiguration, complete following major function:

(1) call internal core algorithm, complete the FFT of each section of input signal, filtering, IFFT, extract, connect and correction etc. Process；

(2) frequency input signal is estimated by frequency relative to position model；

(3) by output during Frequency Estimation fructufy to driving and display module.

It may be noted that owing to have employed digitized method of estimation, thus determine the complexity of Figure 12 system, real-time levels and The principal element of stability is not the peripheral connection of hardware in figure, but the core that DSP internal program memory is stored is estimated Calculating method.

The internal algorithm flow process of DSP device is as shown in figure 13.

The core algorithm of " the low rate end frequency estimator of fast convolution tunable filter group " that the present invention will be proposed Implant in DSP device, complete high accuracy, low complex degree, efficient Frequency Estimation based on this.

Figure 13 flow process is divided into following several step:

(1) first each parameter value of estimator is set according to analysis above；

(2) then DSP reads input signal from I/O end, and segmentation is saved in internal RAM；

(3) according to the algorithm main-process stream of Fig. 1, each segment data of parallel processing, calculate frequency estimation；

(4) Frequency Estimation result is preserved.

It may be noted that realize owing to have employed DSP so that the design of whole spectral estimator becomes the most flexibly and fast, can root According to being actually needed in spectral estimator design process, the parameter in flexible transformation formula (9), it is allowed to finally meet requirement of engineering. Meet requirement of engineering eventually.

Claims (2)

1. a low rate end frequency estimating methods for fast convolution tunable filter group, is characterized in that, be divided into following two rank Section:

1) the fast convolution stage

1 input signal x (n) Overlapping Fragment of Step, every segment length is N, and overlap length is N_O, between the most each section length N, segmentation Overlap length N_O, non-overlapped length N of each segmentation_SMeet:

N=N_S+2N_O (1)

N point Fourier conversion FFT is made in each segmentation by Step 2. respectively, and according to actual needs, its FFT output is divided into M Subband, the subband broadband occupied is respectively L₁～L_MIndividual FFT frequency resolution；

Step 3. observes the FFT amplitude output that each subband is corresponding, if observing, kth has the amplitude of maximum, then comprise with one The window w of certain intermediate zone_kThe FFT input value of this subband is weighted；

Result after this subband is weighted by Step 4. is L_kInverse fast fourier transform IFFT (the Inverse Fast of point Fourier Transform), take the middle L of IFFT result_S,kIndividual value is as the subband output being currently entered corresponding to segmentation；

Step 5. repeats above four steps, it is thus achieved that P a length of L_S,kTime domain output sample；

2) the Spectrum Correction stage

Step 6. is by obtained P a length of L_S,kTime domain output sample scrabble up a length of L_out=PL_S,kTime domain samples；

The time domain samples that splicing is obtained by Step 7. is counted as L_outFFT；

Step 8. obtains the frequency estimation of output sequence by bispectrum line correction method

Step 9. utilize following equation obtain incoming carrier Frequency Estimation:

${\hat{f}}_0=\frac{2{\mathrm{\&pi;L}}_{k,0}+L_k{\widehat{\mathrm{\&omega;}}}_{out}}{2\mathrm{\&pi;}N}\&CenterDot;R_k{f}_{s,k}---\left(2\right)$

Wherein R_kFor sampling rate conversion factor, f_s,kFor output sampling rate.

Each section length N, non-overlapped length N of each segmentation_S, subband width L_k, subband retain width L_S,k, input sample speed f_s Sampling rate f is exported with subband_s,kMeet following relation in proportion

$R_k=\frac{N}{L_k}=\frac{N_S}{L_{S,k}}=\frac{f_s}{f_{s,k}}---\left(3\right)$

If the parameter configuration condition of formula (3) is set up, then splice the L obtained_outIndividual time domain samples can be completely eliminated what splicing obtained Waveform truncation effect, thus ensure that obtaining High-precision carrier at low rate outfan estimates.

2. the low rate end frequency estimating methods of fast convolution tunable filter group as claimed in claim 1, is characterized in that, point Segment length must strictly be mated with subband width, and the matching condition that its concrete need meet is:

1)L_S=L_kN_SIt is integer that/N requires；

2)R_k=N/L_k=N_S/L_SRequirement is integer；

Assuming that X (m^*) it is peak value spectral line amplitude, g is the ratio of output signal peak value spectral line amplitude and second highest spectral line amplitude, it may be assumed that

$g=\frac{\left|X\left(m^{*}\right)\right|}{max\left\{\right|X(m^{*}-1)|,|X(m^{*}+1)\left|\right\}}---\left(10\right)$

Then its output signal frequency ω_outEstimated value be:

${\widehat{\mathrm{\&omega;}}}_{out}=(m^{*}\&PlusMinus;\frac{1}{g+1})\&CenterDot;\frac{2\mathrm{\&pi;}}{L_{out}}---\left(11\right)$

In formula (11), peak value is composed when the left side of second highest spectral line, symbol in formula (11) " ± " take "+"；When peak value is composed in second highest spectrum During the right of line, the middle symbol of formula (11) " ± " take "-"；

The L of formula (11)_outCount for FFT, i.e. the number of samples of output signal, L_outAllow to comprise the multiple output segmentation of same subband Sample, wushu (11) substitutes in formula (2), i.e. obtains final Frequency Estimation result.