CN106546817B - A Frequency Estimation and Energy Estimation Method with Feedback Function - Google Patents
A Frequency Estimation and Energy Estimation Method with Feedback Function Download PDFInfo
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- CN106546817B CN106546817B CN201611006338.3A CN201611006338A CN106546817B CN 106546817 B CN106546817 B CN 106546817B CN 201611006338 A CN201611006338 A CN 201611006338A CN 106546817 B CN106546817 B CN 106546817B
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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
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Abstract
本发明属于频率估计和能量估计领域，涉及一种具有反馈功能的频率估计和能量估计方法。本发明方法使用反馈的模式，第一次Chirp_z变换粗略估计出f0得到新的分辨率和带宽，根据第一次变换得到的参数进行第二次变换得到新的f0和能量，并且每次得到f0后都替换原来的f0，这样提高了频率估计和能量估计的精度。而且可以对f0进行追踪；因此，本发明的方法可以实现高效高精度的频率和能量估计。
The invention belongs to the field of frequency estimation and energy estimation, and relates to a frequency estimation and energy estimation method with feedback function. The method of the present invention uses the feedback mode, the first Chirp_z transformation roughly estimates f0 to obtain new resolution and bandwidth, and the second transformation is performed according to the parameters obtained by the first transformation to obtain new f0 and energy, and each time f0 is obtained Then replace the original f0, which improves the accuracy of frequency estimation and energy estimation. Moreover, f0 can be tracked; therefore, the method of the present invention can achieve efficient and high-accuracy frequency and energy estimation.
Description
Technical field
The invention belongs to Frequency Estimations and energy to estimate field, be related to a kind of Frequency Estimation and energy with feedback function
Estimation method.
Background technique
Frequency and energy estimation are the important contents of Digital Signal Processing, and current high-precision Frequency Estimation has been applied successfully
In radar detection, sonar seismic monitoring, bridge vibration detection and electronic communication, therefore, high-precision Frequency Estimation is calculated
The research of method receives universal attention.
In terms of Frequency Estimation, Li little Jie et al. is paper " high-precision under low signal-to-noise ratio answers sinusoidal frequency algorithm for estimating "
In propose and determine coherent integration length and maximum likelihood (M L) estimation method without winding sequence, but the party in conjunction with FF T
Method calculation amount is larger.One kind orrection phase place in a manner of scrambling is disclosed application No. is the TaiWan, China patent of TW091122918 to lock
Surely estimate that the phase-locking device of frequency and the technical solution of method, this method generate one according to the situation that data in input signal changes
Frequency estimation carries out a scrambling step for the frequency estimation and updates the frequency estimation multiplied by a pre-set ratio, and
The frequency of the clock pulse is adjusted according to the updated frequency estimation.
In many practical applications, the interested range that a narrowband is often only occupied in entire frequency spectrum of people,
In order to solve the problems, such as only to carry out careful observation to the range of a narrowband, the concept of frequency spectrum refinement is proposed.Common frequency spectrum
The method of refinement has ZFFT and Chirp_z transformation.The essence of ZFFT is a broadband signal by becoming after bandpass filter
One narrow band signal so as to reduce sample frequency by choosing pumping (i.e. resampling), and then can be reached with the FFT of base point
To high frequency resolution.The available more accurate spectrum peak position of ZFFT, reaches precise measurement.But this method needs to store
The memory headroom of intermediate data is huge to limit maximum refinement multiple, and low-pass filter special type limits precision and maximum refinement times
Number, this method will be very big to all analysis sites progress frequency displacement calculation amount and frequency content adjustment is more complex.
Summary of the invention
In order to solve the problems, such as that ZFFT exists, feedback function is had based on Chirp_z transformation the invention proposes a kind of
High-efficiency high-accuracy spectrum estimation and energy state postulate, in the big probable value of the frequency and bandwidth of knowing signal can quickly, it is high
Precision estimates signal frequency and signal energy, and consumption resource is less, since this method has feedback function, estimation
Precision is higher, and can track to the frequency of signal.
Be utilized in the present invention Chirp_z transformation, Chirp-z transformation be Lawrence Rabiner in 1975 to voice
Put forward when signal is analyzed, it the unit circle of z-plane can be become a helix gradually from unit origin to
In unit circle.Signal spectrum analysis can be realized on the helix on z-plane, may begin at any point, end at another
Arbitrary point.Therefore can to signal energy concentrate frequency band in spectral sample it is intensive, and sampled in other frequency bands it is sparse, and
The direct calculation method for carrying out Chirp_z transformation is converted into convolution form by the derivation of equation, so as to be carried out using FFT,
Greatly reduce calculation amount to achieve the purpose that further save resource, improve calculating speed.
Shown in the total formula such as formula (1) of Chirp_z transformation:
Wherein
A0Indicate the radius length of starting sample point, usual A0≤1；
θ0Indicate starting sample point Z0Phase angle, θ0=2 π f1/fs, wherein f1=fc- B/2 is the initial frequency point of refinement, fsFor
Signal sampling frequencies；
Indicate the sub-multiple angle between two consecutive pointsWherein f2=fc+B/2
For the end frequency point of refinement.
Due toIt can be transformed toWhereinTherefore Chirp_z transformation can be divided into the following steps realization:
1. selecting integer L one the smallest, it is set to meet L >=N+M-1, while meeting L=2m, wherein M is the point of refinement
Number；
2. the sequence for being N by length0 or arbitrary value are mended, is mended in present example(N≤n≤L-1) makes sequence length become L, therefore g (n) are as follows:
And the L point DFT of this sequence is sought using FFT method,
3. h (n) is asked according to formula,
The L point DFT of h (n) is sought with FFT method,
4. H (r) is multiplied with G (r), Q (r)=H (r) G (r) is obtained, Q (r) is L point frequency domain discrete series；
5. seeking the L point IDFT of Q (r) with FFT method, the circular convolution of h (n) He g (n) are obtained
In formula, preceding M value is equal to the linear convolution result [h (n) g (n)] of h (n) and g (n)；
6. finally obtaining the transformed result X (z of Chirp_zk):
The technical solution of the present invention is as follows:
A kind of Frequency Estimation and energy state postulate with feedback function, which comprises the following steps:
A. input signal information is obtained, signal intermediate frequency f is included at least0With signal bandwidth B；Flag bit i is set simultaneously, and just
Beginningization i=0；
B. according to the signal intermediate frequency f of acquisition0The Chirp_z that refinement points are M is carried out to signal with signal bandwidth B to convert,
Flag bit adds 1 simultaneously；
C. the peak value Y of frequency spectrum is obtained according to the transformed result of Chirp_zmaxAnd the points V at peak value, and by as follows
Formula is updated signal intermediate frequency:
f0=f0-B/2+(V-1)·B/(M-1) (7)
That counts V at peak value Y and peak value asks method as follows:
(i) result X (Z transformed to Chirp_zK) every bit seek amplitude, due to X (Zk)=ak+bkI, 0≤k
≤M-1(ak,bkFor arbitrary constant, i is imaginary unit), therefore can be according to formulaTo seek amplitude；
(ii) enables Ymax=Y1, V=1, m=1, wherein m is digit；
(iii) judges whether m≤M is true, executes step (iiii) if setting up, if invalid end loop, exports peak
Count V at value Y and peak value；
(iiii) enables m=m+1 judge YmaxWith YmSize, if YmIt is big then enable Ymax=Ym, otherwise V=m returns to step
(iii)；
D. judgement symbol position i >=it is 2 whether true, if so, calculating the energy Y of signal by following formulaenergy:
Yenergy=Ymax·ts (8)
Wherein ts=1/fs,fsFor the sample frequency of signal, f is exported0And YenergyReturn to step b；
If it is not, then entering step e；
E. level value is averaging to the result that Chirp_z in step b is converted and obtains the average level Z of noise；
F. according to the characteristic of the spectrum curve of FFT transform, it is assumed that
Ymax=Asinc (0) (9)
It enables
A (sinc (0)-sinc (x))=Z (10)
Wherein sinc (x)=sin (pi*x)/(pi*x) is sinc function, and pi is pi, and x is known variables, and A is normal
The value of number A can be found out by formula (9)；
X can be found out according to formula (10) according to the A found out in the average level Z and (9) formula obtained in step e, according to public affairs
Formula (11) obtains frequency resolution S:
S=xB/ (M-1) (11)
New bandwidth, which is found out, further according to formula (12) replaces original signal bandwidth B:
B=S (M-1) (12)
Return to step b.
Beneficial effects of the present invention are that the method for the present invention is converted using Chirp_z, frequency in the frequency band concentrated to signal energy
Spectrum sampling is intensive, and sparse, to use in this way when reaching identical resolution ratio with common FFT resource is sampled in other frequency bands
Less；And the direct calculation method for carrying out Chirp_z transformation is converted to so as to use by convolution form by the derivation of equation
FFT is carried out, and greatly reduces calculation amount to achieve the purpose that further save resource, improve calculating speed；Make this hair in this way
Bright method is more efficient；The method of the present invention roughly estimates f using the mode fed back, the transformation of first time Chirp_z0It obtains new
Resolution ratio and bandwidth obtain new f according to obtained second of transformation of parameter progress is converted for the first time0And energy, with newly obtaining
F0Replace original f0, and in order to achieve the purpose that tracking the step will recycle down always, improve in this way Frequency Estimation and
The precision of energy estimation；And it can be to f0It is tracked；Therefore, the frequency of high-efficiency high-accuracy may be implemented in method of the invention
Estimate with energy.
Detailed description of the invention
Fig. 1 is flow diagram of the invention.
Specific embodiment
With reference to the accompanying drawings and examples, the technical schemes of the invention are described in detail:
Since the method for the present invention can be applied in beacon detection, below by a method of the present invention in beacon detection
The example of application the specific implementation process of this method is illustrated.
Assuming that the expression formula of the beacon signal of input is x (n)=cos (2pifcT), signal intermediate frequency fc=
5.7MHz, bandwidth B=200KHz, sample frequency fs=200K, then satellite beacon receive process are as follows:
1) the step of x (n) being sampled, converted according to Chirp_z according to sample frequency carries out the signal after sampling
Chirp_z transformation, refinement points M=126；
2) peak value Ymax=1007.8 is obtained according to transformed result, at the 64th point, new f is obtained according to formula (7)0
For 5.7008MHz；
3) finding out noise average level is Z=95.9597；
4) obtaining x according to formula (9), formula (10) and formula (11) is 0.2442, and new resolution ratio S is 0.3907KHz；
New bandwidth B=48.8375 are obtained according to formula (12)；
5) according to B and f0Chirp_z transformation is carried out to x (n), obtains new peak value Ymax=1029.3 at the 63rd point；
6) mould for calculating Y calculates the energy Yenergy=5.7181e-005 of signal further according to formula (8), by formula
(7) signal intermediate frequency f is obtained0=5.70006MHz exports Yenergy and f0；
5) and 6) 7) repeat.
The present invention, which essentially consists in, is applied to Chirp_z transformation in Frequency Estimation and energy estimation and in the process of estimation
In used feedback, to reach higher precision and frequency-tracking.
Claims (1)
1. a kind of Frequency Estimation and energy state postulate with feedback function, which comprises the following steps:
A. input signal information is obtained, signal intermediate frequency f is included at least0With signal bandwidth B；Flag bit i is set simultaneously, and initializes i
=0；
B. according to the signal intermediate frequency f of acquisition0It carries out the Chirp_z that refinement points are M to signal with signal bandwidth B to convert, same to markers
Will position adds 1；
C. the points V at the peak value Y and peak value of frequency spectrum is obtained according to the transformed result of Chirp_z, and passes through following formula pair
Signal intermediate frequency is updated:
f0=f0-B/2+(V-1)·B/(M-1)
D. judgement symbol position i >=it is 2 whether true, if so, the mould of Y is asked to obtain Ymax, and signal is calculated by following formula
Energy Yenergy:
Yenergy=Ymax·ts
Wherein, ts=1/fs,fsFor the sample frequency of signal；Export f0And Yenergy, after return to step b；
If it is not, then entering step e；
E. level value is averaging to the result that Chirp_z in step b is converted and obtains the average level Z of noise；
F. according to the characteristic of the spectrum curve of FFT transform, it is assumed that
Ymax=Asinc (0)
It enables
A (sinc (0)-sinc (x))=Z
Wherein sinc (x)=sin (pi*x)/(pi*x) is sinc function, and pi is pi, and x is known variables, and A is constant；
Signal x can be obtained according to the average level Z obtained in step e, obtains frequency resolution S according to the following formula:
S=xB/ (M-1)
Signal bandwidth B is replaced further according to following formula:
B=S (M-1)
Return to step b.
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| CN108828312A (en) * | 2018-07-06 | 2018-11-16 | 厦门大学 | A method of reducing Frequency Estimation calculation amount |
| CN109599868B (en) * | 2018-11-28 | 2022-05-20 | 广州锐翔电力科技有限公司 | Control system and method for output current of active filter |
| CN110441746B (en) * | 2019-08-20 | 2021-07-09 | 北京环境特性研究所 | Time domain gate transformation method and device |
| CN110691051A (en) * | 2019-09-29 | 2020-01-14 | 天津大学 | GMSK signal frequency offset estimation algorithm based on FFT |
| CN112462140B (en) * | 2021-02-02 | 2021-04-13 | 成都能通科技有限公司 | Frequency tracking method for providing electric energy parameter analysis |
| CN113406386B (en) * | 2021-06-23 | 2023-04-25 | 中国电子科技集团公司第二十九研究所 | An Accurate Estimation Method of Signal Frequency Based on Digital Down-conversion |
| CN114814835B (en) * | 2022-04-24 | 2025-05-06 | 南京大学 | A vibration detection method and terminal based on millimeter wave radar |
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| CA2453711A1 (en) * | 2002-12-17 | 2004-06-17 | Queen's University At Kingston | Methods and systems for tracking of amplitudes, phases and frequencies of a multi-component sinusoidal signal |
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| CN102215187A (en) * | 2011-06-03 | 2011-10-12 | 涂亚庆 | Multistage stationary signal frequency domain related method of frequency estimation |
| CN102338827A (en) * | 2011-06-10 | 2012-02-01 | 中国矿业大学 | Method for analyzing electric network waveform distortions and automatically monitoring electric power harmonic parameters |
| DE102013217181A1 (en) * | 2012-10-26 | 2014-04-30 | Agilent Technologies, Inc. | Method and system for performing spectral analysis of a non-stationary signal in real time |
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