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Short interval frequency estimation method of undersampled waveform, and estimator

A technology of frequency estimation and undersampling, which is applied in the field of array signal analysis and processing, can solve the problems of increasing DFT and high computational complexity, and achieve the effects of improving anti-noise robustness, improving estimation accuracy, and reducing computational complexity

Inactive Publication Date: 2019-02-01
TIANJIN UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

The calculation complexity of the method of obtaining the remainder in this way is very high, which is due to the increase of the number of points of the DFT due to zero padding

Method used

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  • Short interval frequency estimation method of undersampled waveform, and estimator
  • Short interval frequency estimation method of undersampled waveform, and estimator
  • Short interval frequency estimation method of undersampled waveform, and estimator

Examples

Experimental program
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Embodiment 1

[0056] The embodiment of the present invention performs a comprehensive error analysis on the CRT-based frequency estimator in the prior art, and the error analysis consists of two parts: DFT resolution error and noise error.

[0057] To eliminate the DFT resolution error, existing CRT-based estimators only consider a special case, the signal frequency f 0 Exactly equal to an integer multiple Δf of the frequency resolution of the DFT, where the resolution error of the zero-filled DFT is negligible.

[0058] However, the signal frequency f 0 is more likely to be equal to a fractional multiple of Δf, i.e. the DFT resolution error is not negligible. Therefore, a spectral corrector should be introduced to reduce the resolution error.

[0059] In addition, the choice of spectral corrector is important because choosing an inappropriate corrector may introduce undesired corrector errors. Therefore, using the Candan spectral corrector [10][11] . Therefore, compared with the CRT-b...

Embodiment 2

[0068] Below in conjunction with specific calculation formulas, examples further introduce the scheme in embodiment 1, see the following description for details:

[0069] 1. Estimation model based on CRT

[0070] Suppose a high frequency signal model looks like this:

[0071] x(t)=α exp(j2πf 0 t)+ω(t) (1)

[0072] Among them, f 0 is the frequency to be measured, α is the amplitude, and ω(t) is additive white noise.

[0073] In order to estimate the frequency to be measured f 0 , L low-sampling-rate A / D converters are needed to discretize the high-frequency signal x(t). Suppose the sampling rate of the high-frequency signal x(t) is M 1 ~ M L , and the greatest common divisor of the sampling rate is M, let:

[0074] Γ i = M i / M, 1

[0075] Among them, Γ 1 ~Γ L Pairs of each other.

[0076] Assuming that the observation time is T, the undersampling sequence is:

[0077]

[0078] Further, in this embodiment of the present invention, M i Do DFT to get th...

Embodiment 3

[0136] The feasibility of the method in Embodiment 1 and 2 is verified below in conjunction with specific simulation experiments, see the following description for details:

[0137] In this part, the embodiment of the present invention compares the estimation method designed in the embodiment of the present invention with the original CRT estimation method in terms of anti-noise robustness and estimation accuracy. The parameters involved in formulas (1) to (4) are set as follows:

[0138] L=2,f 0 =120000.3Hz, M 1 =13600Hz, M 2 = 14400Hz (mutual prime integer is Γ 1 =17,Γ 2 =18, M 1 , M 2 The common divisor of M=800). If the observation interval is short T=0.05s, then the first channel and the second channel sample 680 and 720 respectively.

[0139] 1. Comparison of anti-noise robustness in the case of low signal-to-noise ratio

[0140] In the experiment, the SNR increases in [-34,-18], and for each SNR, 10,000 Monte Carlo experiments are performed in the embodiment of...

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Abstract

The invention discloses a short interval frequency estimation method of an undersampled waveform, and an estimator. The method comprises the following steps: discretizing original signals by using L paths of analog-to-digital converters of respective sampling rates of M1-ML within an observation interval T time to obtain a plurality of sampling sequences, wherein each sampling sequence xi(n) corresponds to the number of sampling points of TMi, i is greater than or equal to 1 and is less than or equal to L, and the value of T is a positive real number less than 1; for the ith undersampled path,implementing TMi point DFT on the sampling sequence xi (n) to obtain a spectrum peak Xi(k) corresponding to the sampling sequence xi(n), and then obtaining a spectrum peak position kp, i; for the ithundersampled path, correcting the spectrum peak position kp, i by using a spectrum corrector to obtain a frequency offset estimated value (the formula is described in the specification), and calculating a remainder estimated value of the ith path according to the spectrum peak position kp, i and the frequency offset estimated value (the formula is described in the specification); and using the sampling rates M1-ML as module values, and substituting the module values into the closed robust Chinese remainder theorem together with the remainder estimated value to calculate a final frequency estimated value (the formula is described in the specification). The estimator comprises: an ADC sampler, a DSP device and an output display device. By adoption of the short interval frequency estimationmethod disclosed by the invention, the computational complexity of obtaining the remainder is reduced, and the robustness of frequency estimation is improved.

Description

technical field [0001] The invention relates to the technical field of array signal analysis and processing, in particular to the Chinese remainder theorem, spectrum correction, and small-size DFT (discrete Fourier transform). Through the combination of these techniques, an improved Chinese remainder theorem (Chinese remainder Theorem, CRT) frequency estimation method and estimator based on spectrum correction is proposed, which can effectively improve the estimation efficiency and noise resistance robustness. Background technique [0002] Frequency estimation of high-frequency waveforms plays an important role in a wide range of applications such as wireless communication and radar ranging [1] . However, solving this problem in a direct and discrete manner is trickier. This is because limited by the Nyquist theorem, sampling high-frequency signals requires a higher-speed analog-to-digital (A / D) converter, which consumes a lot of power consumption and high hardware costs. ...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H04L7/027H04L27/00
CPCH04L27/0014H04L7/027H04L2027/0026
Inventor 黄翔东杨孟凯李长滨
Owner TIANJIN UNIV
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