CN105301354B - Harmonic frequency signal method of estimation in multiplying property of one kind and additive noise - Google Patents
Harmonic frequency signal method of estimation in multiplying property of one kind and additive noise Download PDFInfo
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Abstract
The invention discloses harmonic frequency signal method of estimation in multiplying property of one kind and additive noise, it comprises the following steps：Calculate circulation covariance；Construction circulation covariance matrix；Eigenvalues Decomposition；Build noise subspace matrix；Calculate spatial spectrum；Calculate frequency estimation.Harmonic frequency signal method of estimation in the multiplying property and additive noise of the present invention, can improve the precision and frequency resolution of Frequency Estimation, and be easily achieved.
Description
Technical field
The present invention relates to harmonic frequency signal estimation side in field of signal processing, more particularly to multiplying property of one kind and additive noise
Method.
Background technology
In multiplying property and additive noise background, the Parameter Estimation Problem of harmonic signal has a wide range of applications in multiple fields,
Its main purpose is the frequency for the harmonic component number harmonic that harmonic signal is estimated from the signal by noise pollution.
At present, the method for estimation of harmonic frequency signal mainly has Cyclic Statistics method (Li Hong in multiplying property and additive noise
It is big, Cheng Qian life " the Cyclic Statistics method of Harmonic retrieval in multiplying property and additive noise ", electronic letters, vol, volume 26, the 7th phase,
1998) and general covariance matrix method (is " humorous in multiplying property and additive noise based on general covariance matrix forever for poplar generation
Ripple recovers ", signal transacting, volume 28, the 2nd phase, 2012).Cyclic Statistics method is to be based on Cyclic Statistics, using quick
Fourier transformation and peak value searching method are realized.Due to being influenceed by Rayleigh limit, the estimated accuracy and frequency of Cyclic Statistics method
Rate resolution ratio is not high.General covariance matrix method estimates the frequency of harmonic wave using the constant technology of Subspace Rotation, but it is realized
Process is more complicated, and the resolution ratio of Frequency Estimation is not also high.
The content of the invention
The present invention provides harmonic frequency signal method of estimation in multiplying property of one kind and additive noise, with reach computational accuracy it is high,
Frequency resolution height and the purpose being easily achieved.
The present invention realizes above-mentioned purpose using following technical scheme.Harmonic frequency signal is estimated in multiplying property of one kind and additive noise
Meter method, it comprises the following steps：
Step 1：Calculate circulation covariance；
Step 2：Construction circulation covariance matrix；
Step 3：Eigenvalues Decomposition；
Step 4：Build noise subspace matrix；
Step 5：Calculate spatial spectrum；
Step 6：Calculate frequency estimation.
It is described calculate circulation covariance method be：If N number of data measurement of harmonic signal is x (1), x (2) ..., x
(N), P is harmonic component number, for integer M of the span in [P+1, N/2], calculates circulation covariance c (α),
α=0,1,2 ..., M-1：
Wherein () * represents to take conjugate operation.
The method of the construction circulation covariance matrix C is：
The method of the Eigenvalues Decomposition is：Eigenvalues Decomposition is carried out to circulation covariance matrix C, by the characteristic value of gained
λ is denoted as by order from big to small1,λ2,…,λM, corresponding feature value vector is denoted as e1,e2,…,eM。
The method of the structure noise subspace matrix Z is：Z=[eP+1,eP+2,…,eM]。
It is described calculate spatial spectrum method be：A given positive integer K (span for (2P, M]), makes ωk=2 π (k-
1)/K；K=1,2 ..., K, first calculate β (ωk)：
Then spatial spectrum W (ω are calculated by following formulak)：
Wherein ()HRepresent conjugate transposition computing.
It is described calculate frequency estimation method be：Spatial spectrum W (ω are found out successivelyk) P peak value, find out first first
Corresponding ω values are designated as ω by big peak value1, next is found out second largest peak value and corresponding ω values is designated as into ω2, by parity of reasoning, finally
Find out the big peak values of P and corresponding ω values are designated as ωP；Calculate the estimate of harmonic frequency signalFor：
M=1,2 ..., P.
The second largest peak value is the peak value for being only second to the described first big peak value.
Harmonic frequency signal method of estimation in the multiplying property and additive noise of the present invention, the advantage is that：Frequency can be improved to estimate
The precision and frequency resolution of meter, and be easily achieved.
Brief description of the drawings
Fig. 1 is the flow chart of the present invention.
Embodiment
The principle and feature of the present invention are described below in conjunction with the accompanying drawings, the given examples are served only to explain the present invention, and
It is non-to be used to limit the scope of the present invention.
As shown in figure 1, harmonic frequency signal method of estimation in multiplying property of one kind and additive noise, comprises the following steps：
Step 1：Calculate circulation covariance 101；
If N number of data measurement of harmonic signal is x (1), x (2) ..., x (N), P are harmonic component number, for one
Integer M of the span in [P+1, N/2], calculate circulation covariance c (α), α=0,1,2 ..., M-1：
Wherein () * represents to take conjugate operation.
Step 2：Construction circulation covariance matrix 102；
Construction circulation covariance matrix 102C method is：
Step 3：Eigenvalues Decomposition 103；
Eigenvalues Decomposition 103 is carried out to circulation covariance matrix C, the characteristic value of gained is denoted as by order from big to small
λ1,λ2,…,λM, corresponding feature value vector is denoted as e1,e2,…,eM；
Step 4：Build noise subspace matrix 104；
Structure noise subspace matrix 104Z method is：Z=[eP+1,eP+2,…,eM]。
Step 5：Calculate spatial spectrum 105；
Calculate spatial spectrum 105 method be：A given positive integer K (span for (2P, M]), makes ωk=2 π (k-
1)/K；K=1,2 ..., K, first calculate β (ωk)：
Then spatial spectrum W (ω are calculated by following formulak)：
Wherein ()HRepresent conjugate transposition computing.
Step 6：Calculate frequency estimation 106；
Calculate frequency estimation 106 method be：Spatial spectrum W (ω are found out successivelyk) P peak value, find out first first
Corresponding ω values are designated as ω by big peak value1, next is found out second largest peak value and corresponding ω values is designated as into ω2.First big peak value is most
Big peak value.Second largest peak value is only second to the first big peak value.By parity of reasoning, finally finds out the big peak values of P and remembers corresponding ω values
For ωP.Calculate the estimate of harmonic frequency signalFor：M=1,2 ..., P.
Claims (5)
1. harmonic frequency signal method of estimation in multiplying property of one kind and additive noise, it is characterised in that it comprises the following steps：
Step 1：Calculate circulation covariance：It is described calculate circulation covariance method be：If N number of data measurement of harmonic signal
For x (1), x (2) ..., x (N), P are harmonic component number, for integer M of the span in [P+1, N/2], are calculated
Circulate covariance c (α), α=0,1,2 ..., M-1：
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Wherein ()*Expression takes conjugate operation；
Step 2：Construction circulation covariance matrix：The method of the construction circulation covariance matrix C is：
Step 3：Eigenvalues Decomposition；
Step 4：Build noise subspace matrix；
Step 5：Calculate spatial spectrum；
Step 6：Calculate frequency estimation:It is described calculate frequency estimation method be：Spatial spectrum W (ω are found out successivelyk) P
Peak value, the first big peak value is found out first corresponding ω values are designated as ω1, next is found out second largest peak value and is designated as corresponding ω values
ω2, by parity of reasoning, finally finds out the big peak values of P and corresponding ω values are designated as into ωP；Calculate the estimate of harmonic frequency signalFor：M=1,2 ..., P.
2. harmonic frequency signal method of estimation in multiplying property according to claim 1 and additive noise, it is characterised in that described
The method of Eigenvalues Decomposition is：Eigenvalues Decomposition is carried out to circulation covariance matrix C, the characteristic value of gained is pressed from big to small
Order is denoted as λ1,λ2,…,λM, corresponding feature value vector is denoted as e1,e2,…,eM。
3. harmonic frequency signal method of estimation in multiplying property according to claim 2 and additive noise, it is characterised in that described
Structure noise subspace matrix Z method is：Z=[eP+1,eP+2,…,eM]。
4. harmonic frequency signal method of estimation in multiplying property according to claim 1 and additive noise, it is characterised in that described
Calculate spatial spectrum method be：Given positive integer K, K a span for (2P, M], make ωk=2 π (k-1)/K, k=1,
2 ..., K, first calculate β (ωk)：
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Then spatial spectrum W (ω are calculated by following formulak)：
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Wherein ()HRepresent conjugate transposition computing.
5. harmonic frequency signal method of estimation in multiplying property according to claim 1 and additive noise, it is characterised in that described
Second largest peak value is the peak value for being only second to the described first big peak value.
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| CN106291101B (en) * | 2016-10-14 | 2018-12-18 | 九江学院 | Harmonic frequency signal estimation method in a kind of multiplying property and additive noise with super-resolution |
| CN112882111B (en) * | 2021-01-18 | 2022-05-03 | 吉林大学 | Magnetic resonance response signal parameter extraction method and system based on cyclic correlation |
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| CN1609630A (en) * | 2004-10-21 | 2005-04-27 | 上海交通大学 | Method for extracting harmonic signal under chaos interference |
| US7672407B2 (en) * | 2006-06-27 | 2010-03-02 | Intel Corporation | Mitigation of interference from periodic noise |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1609630A (en) * | 2004-10-21 | 2005-04-27 | 上海交通大学 | Method for extracting harmonic signal under chaos interference |
| US7672407B2 (en) * | 2006-06-27 | 2010-03-02 | Intel Corporation | Mitigation of interference from periodic noise |
Non-Patent Citations (5)
| Title |
|---|
| Harmonics in Multiplicative and Additive Noise:Parameter Estimation Using Cyclic Statistics;Georgios B 等;《IEEE TRANSACTIONS ON SIGNAL PROCESSING》;19950930;第43卷(第9期);第2217-2221页 * |
| Performance Analysis of Cyclic Statistics for the Estimation of Harmonics in Multiplicative and Additive Noise;Mounir Ghogho 等;《IEEE TRANSACTIONS ON SIGNAL PROCESSING》;19991231;第47卷(第12期);第3235-3249页 * |
| 乘性和加性噪声中二维谐波的参数估计;杨世永 等;《信号处理》;20050831(第4A期);第1-4页 * |
| 乘性和加性噪声中谐波恢复的循环统计量方法;李宏伟 等;《电子学报》;19980731;第26卷(第7期);第105-111，116页 * |
| 乘性和复加性噪声中复谐波的循环估计的性能分析;毛用才 等;《电子科学学刊》;19971130;第19卷(第6期);第773-779页 * |
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