CN109342813A - A kind of sinusoidal signal frequency estimation method based on DFT and dichotomy - Google Patents
A kind of sinusoidal signal frequency estimation method based on DFT and dichotomy Download PDFInfo
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- CN109342813A CN109342813A CN201811578917.4A CN201811578917A CN109342813A CN 109342813 A CN109342813 A CN 109342813A CN 201811578917 A CN201811578917 A CN 201811578917A CN 109342813 A CN109342813 A CN 109342813A
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Abstract
The sinusoidal signal frequency estimation method based on DFT and dichotomy that the invention proposes a kind of, the following steps are included: first using the corresponding sampling frequency index of N point DFT spectral line maximum value as the estimated value of integer part, then it is iterated using dichotomy and searches for the estimated value for determining fractional part, finally by the estimated value of determining residual error is solved equation, to obtain the fine estimation of frequency.This method can obtain the fine estimation of single sine wave signal frequency, and performance is better than existing method, and the mean square error of estimation is limited closer to carat Metro.
Description
Technical field
The present invention relates to the technical field of signal processing more particularly to it is a kind of based on the sinusoidal signal of DFT and dichotomy frequency
Rate estimation method.
Background technique
In radar/Signal processing of sonar, spectrum estimation, signal of communication processing, passive location and Speech processing,
Accurate Frequency Estimation has great meaning.Such as moving-target radial motion speed, nothing can be estimated using Doppler frequency
Line communication system needs to carry out frequency or frequency deviation accurate estimation to achieve the purpose that Frequency Synchronization, using Doppler frequency and
Single passive location may be implemented in its change rate.The realization of these technological means all be unable to do without the accurate estimation to frequency.Cause
This, always is the research hotspot in field of signal processing to the estimation of sine wave signal frequency under noise conditions.To by noise
The sine wave signal of pollution carries out Frequency Estimation, and current existing algorithm can be generally divided into two classes: one kind is in time domain based on letter
Number phase information；In addition one kind is in frequency domain based on DFT (Discrete Fourier Transform, DFT) interpolation.It is based on
Although the Time-Domain algorithm of linear fit equivalent maximal possibility estimation under the conditions of high s/n ratio, has optimal estimation performance,
It needs to carry out phase unwrapping, and is only applicable to the signal that signal-to-noise ratio is greater than 10dB.Other algorithms based on phase information are not
It can be close to the carat Metro lower limit (Cramer-Rao Lower Bound, CRLB) of Frequency Estimation.Based on two DFT spectral line interpolations
AM algorithm have 1.0147 times of carat Metros limit least mean-square error (minimum mean square error, MSE),
Although the frequency estimating methods based on dichotomizing search can also obtain accurate frequency estimation, successive ignition is needed, and high
Performance under the conditions of signal-to-noise ratio can deviate a carat Metro limit.
Summary of the invention
In order to obtain more accurate frequency estimation, the sinusoidal signal based on DFT and dichotomy that the invention proposes a kind of
Frequency estimating methods, comprising the following steps:
Step 1: to the single sine wave signal polluted by additive white Gaussian noise with fsUniform sampling is carried out, is obtained N number of
Dis-crete sample values x0,x1,…,xN-1, signal frequency is f=(m+ δ) fs/ N, m are integer, and 0≤m < N-1, δ are decimal, | δ |
≤ 0.5, N are positive integer；
Step 2: to the N number of dis-crete sample values x sampled0,x1,…,xN-1Carry out N point DFT transformObtain frequency spectrum X, X=[X [0] X [1] ... X [N-1]]；
Calculate the amplitude of frequency spectrum X | X |, | X |=[| X [0] | | X [1] | ... | X [N-1] |]；
Step 3: the estimated value of integer m is determinedNote
Step 4: it setsIf
Step 5: it setsD=0.5, i=1；Dichotomy iterative search number q is set, and q is just whole more than or equal to 3
Number；
Step 6: d=d/2；
Judge Y1And Y-1Size；
If Y1> Y-1, then Y-1=Y0,
Otherwise Y1=Y0,
This step is repeated until i > q；
Step 7: the estimated value of frequency f is calculatedWherein
Further, q is equal to 4.
Compared with prior art, the present invention beneficial effect is:
(1) present invention can accurately estimate the frequency of the single sine wave signal polluted by additive white Gaussian noise
(2) present invention can obtain better performance, and for mean square error closer to carat Metro lower limit, operand is far low
In conventional dichotomy, there is good engineering application value.
Detailed description of the invention
Fig. 1 is the specific flow chart of one embodiment of the invention.
Fig. 2 is the performance comparison figure that one embodiment of the invention and dichotomy, AM method change with signal-to-noise ratio.
Fig. 3 is that the present invention changes with dichotomy, AM method with fractional part (signal-to-noise ratio 5dB, integer part 14)
Performance comparison figure.
Specific embodiment
Present invention is further described in detail with reference to the accompanying drawing.
Various aspects with reference to the accompanying drawings to describe the present invention in the disclosure, shown in the drawings of the embodiment of many explanations.
It is not intended to cover all aspects of the invention for embodiment of the disclosure.It should be appreciated that a variety of designs and reality presented hereinbefore
Those of apply example, and describe in more detail below design and embodiment can in many ways in any one come it is real
It applies, this is because conception and embodiment disclosed in this invention are not limited to any embodiment.In addition, disclosed by the invention one
A little aspects can be used alone, or otherwise any appropriately combined use with disclosed by the invention.
Single sine wave signalReception signal after being polluted by additive white Gaussian noise isWherein,A、f、The respectively amplitude, frequency of signal and initial
Phase, w (t) are that mean value is 0, variance σ2White Gaussian noise.The signal-to-noise ratio of signal is defined as ρ=A2/σ2.Sample frequency is
1MHz, discrete sampling points are 128, and signal frequency integer part is 14, fractional part 0.35, the list that present embodiment uses
The specific steps of one sine-wave frequency estimation method are as shown in Figure 1:
S1, setting dichotomy iterative search number q, wherein q is the positive integer more than or equal to 3；
S2, to the N point discrete data x sampled0,x1,…,xN-1Carry out N point DFT transformK=
0,1 ..., N-1 obtain frequency spectrum X, wherein X=[X [0] X [1] ... X [N-1]]；
S3, the amplitude for calculating frequency spectrum X described in S2, obtain | X |=[| X [0] | | X [1] | ... | X [N-1] |]；
S4, the estimated value for determining integer mNote
S5, calculatingNote
S6, calculatingNote
S7, settingD=0.5, i=1；
S8, the size for judging i, q, if i > q, goes to S15, otherwise go to S9；
S9, d=d/2；
S10, judge the Y1And Y-1Size, if Y1> Y-1, then S11 is gone to；Otherwise S12 is gone to；
S11、Y-1=Y0,Go to S13；
S12、Y1=Y0,Go to S13；
S13、
S14, i=i+1 go to S8；
S15, calculating
S16, calculating
S17, calculating
S18, calculating
S19, the estimated value for calculating frequency f
It is preferred that q is 4.
Fig. 2 is the performance comparison that the present invention changes with dichotomy, AM method with signal-to-noise ratio, and abscissa is the noise of signal
Than unit dB, ordinate is root-mean-square error, unit Hz.Traditional dichotomy not only needs more iterative search
Number, and mean square deviation error can deviate carat Metro limit with the increase of signal-to-noise ratio；Section is compared in entire signal-to-noise ratio, AM method
Performance is all not so good as method of the invention；The present invention only needs 3 iterative search, can obtain excellent performance.
Fig. 3 is under the conditions of signal-to-noise ratio is 5dB, integer part is 14, and the present invention and dichotomy, AM method are with fractional part
The performance comparison situation of variation, abscissa are the value of fractional part, and ordinate is root-mean-square error.In contrast, in decimal
In the entire variation range of part from -0.5 to 0.5, the present invention is limited closer to carat Metro than other methods, iteration of the present invention
Number is more, and precision is higher, but when practical application, and satisfied estimation effect can be obtained after 3 iteration, therefore, has work
Journey application value.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all in spirit of the invention and
Within principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (2)
1. a kind of sinusoidal signal frequency estimation method based on DFT and dichotomy, which comprises the following steps:
Step 1: to the single sine wave signal polluted by additive white Gaussian noise with fsUniform sampling is carried out, is obtained N number of discrete
Sampled value x0,x1,…,xN-1, signal frequency is f=(m+ δ) fs/ N, m are integer, and 0≤m < N-1, δ are decimal, | δ |≤
0.5, N is positive integer；
Step 2: to the N number of dis-crete sample values x sampled0,x1,…,xN-1Carry out N point DFT transformk
=0,1 ..., N-1 obtain frequency spectrum X, X=[X [0] X [1] ... X [N-1]]；
Calculate the amplitude of frequency spectrum X | X |, | X |=[| X [0] | | X [1] | ... | X [N-1] |]；
Step 3: the estimated value of integer m is determinedNote
Step 4: it setsIf
Step 5: it setsD=0.5, i=1；Dichotomy iterative search number q is set, and q is the positive integer more than or equal to 3；
Step 6: d=d/2；
Judge Y1And Y-1Size；
If Y1> Y-1, then Y-1=Y0,I=i+1；
Otherwise Y1=Y0,I=i+1；
This step is repeated until i > q；
Step 7: the estimated value of frequency f is calculatedWherein
2. the sinusoidal signal frequency estimation method according to claim 1 based on DFT and dichotomy, which is characterized in that q etc.
In 4.
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Cited By (4)
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| CN110133738A (en) * | 2019-05-14 | 2019-08-16 | 东南大学 | The frequency estimating methods of proton magnetometer free induction decay signal based on IpDFT |
| CN112162152A (en) * | 2020-08-31 | 2021-01-01 | 南京亿杰明信息技术有限公司 | Sine wave coherent pulse train signal frequency estimation method based on phase straight line fitting |
| CN114578093A (en) * | 2022-03-10 | 2022-06-03 | 中国计量科学研究院 | Laser Doppler velocimeter speed measurement method based on mixed basis FFT |
| CN114923690A (en) * | 2022-04-18 | 2022-08-19 | 南京航空航天大学 | High-precision bearing fault characteristic frequency estimation diagnosis method |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110133738A (en) * | 2019-05-14 | 2019-08-16 | 东南大学 | The frequency estimating methods of proton magnetometer free induction decay signal based on IpDFT |
| CN110133738B (en) * | 2019-05-14 | 2020-06-09 | 东南大学 | IpDFT-based frequency estimation method for free induction attenuation signal of proton magnetometer |
| CN112162152A (en) * | 2020-08-31 | 2021-01-01 | 南京亿杰明信息技术有限公司 | Sine wave coherent pulse train signal frequency estimation method based on phase straight line fitting |
| CN112162152B (en) * | 2020-08-31 | 2024-01-26 | 南京亿杰明信息技术有限公司 | Sine wave coherent pulse train signal frequency estimation method based on phase straight line fitting |
| CN114578093A (en) * | 2022-03-10 | 2022-06-03 | 中国计量科学研究院 | Laser Doppler velocimeter speed measurement method based on mixed basis FFT |
| CN114578093B (en) * | 2022-03-10 | 2023-08-18 | 中国计量科学研究院 | Laser Doppler velocimeter speed measurement method based on mixed-base FFT |
| CN114923690A (en) * | 2022-04-18 | 2022-08-19 | 南京航空航天大学 | High-precision bearing fault characteristic frequency estimation diagnosis method |
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