基于中國余數(shù)定理及全相位理論的高精度頻率估計算法研究
發(fā)布時間：2019-03-08 09:03
【摘要】：高頻信號的頻率估計與檢測是雷達(dá)通信、聲吶、地震監(jiān)測、故障診斷乃至醫(yī)學(xué)醫(yī)療等領(lǐng)域信號處理中至關(guān)重要的問題。但是根據(jù)奈奎斯特定律,若要精確估計實(shí)信號頻率,至少要求一個信號周期內(nèi)采樣到2個以上樣點(diǎn),這必然要求采樣速率大于等于兩倍的待測高頻信號的頻率,因此耗費(fèi)的硬件成本高。本文旨在解決在多路欠采樣條件下(令信號頻率為f0,要求采樣速率fs2f0)高頻信號頻率的精確估計問題。為此,本文將古老的中國余數(shù)定理(Chinese Remainder Theorem,CRT)引入該領(lǐng)域中�；谥袊鄶�(shù)定理的信號頻率估計是近年來信號處理、電磁學(xué)以及光學(xué)等領(lǐng)域的前沿問題,但目前這些研究僅限于對復(fù)指數(shù)信號做粗略頻率估計。因而首先需完成復(fù)信號精確頻率估計工作,為此本論文引入原創(chuàng)的全相位FFT譜分析理論,借助apFFT/FFT相位差頻譜校正法獲得的精確頻率余數(shù),結(jié)合中國余數(shù)定理,實(shí)現(xiàn)了對復(fù)指數(shù)信號做精確頻率估計,并將其成功應(yīng)用于多普勒偏移估計中。為進(jìn)一步將欠采樣頻率估計從復(fù)指數(shù)信號拓展到實(shí)余弦信號領(lǐng)域,本文提出兩種基于不同頻譜校正措施的余數(shù)篩選方法,精準(zhǔn)地提取出余數(shù)定理所需的余數(shù)信息,實(shí)現(xiàn)了欠采樣實(shí)余弦信號精細(xì)頻率估計。其估計過程如下:(1)對高頻余弦波形進(jìn)行過零點(diǎn)檢測,確定信號的相位信息;(2)對各路欠采樣信號做快速傅里葉變換(或者全相位快速傅里葉變換),并借助Candan估計器(或者全相位比值譜校正)對各路譜峰值做頻率校正以獲取高精度余數(shù)估計,基于此算出頻偏值以做相位校正;(3)用提出的基于相位特征分類方法對校正得到的余數(shù)做篩選;(4)將篩選出的頻率余數(shù)代入閉合形式的中國余數(shù)定理得到原信號頻率的高精度估計。此外,本文還推導(dǎo)出了頻率估計方差的理論表達(dá)式。數(shù)據(jù)模擬實(shí)驗(yàn)不但驗(yàn)證了該表達(dá)式的正確性,還反映了論文提出的方案具有高精度和高抗噪性能。
[Abstract]:Frequency estimation and detection of high frequency signals is an important problem in radar communication, sonar, seismic monitoring, fault diagnosis and even medical treatment. But according to Nyquist's law, in order to accurately estimate the real signal frequency, it is necessary to sample more than two samples in at least one signal cycle, which necessarily requires the frequency of the high frequency signal to be measured at a sampling rate greater than or equal to two times. As a result, the cost of hardware is high. The aim of this paper is to solve the problem of accurate estimation of the high frequency signal frequency under the condition of multi-channel undersampling (let the signal frequency be f _ 0, which requires the sampling rate fs2f0). In this paper, the ancient Chinese remainder theorem (Chinese Remainder Theorem,CRT) is introduced into this field. The estimation of signal frequency based on Chinese remainder theorem is a frontier problem in the fields of signal processing, electromagnetism and optics in recent years, but at present these studies are limited to rough frequency estimation of complex exponential signals. Therefore, it is necessary to complete the accurate frequency estimation of complex signals at first. Therefore, this paper introduces the original all-phase FFT spectrum analysis theory, with the help of the apFFT/FFT phase difference spectrum correction method to obtain the accurate frequency remainder, combined with the Chinese remainder theorem. The accurate frequency estimation of complex exponential signal is realized, and it is successfully applied to Doppler migration estimation. In order to extend the undersampling frequency estimation from the complex exponential signal to the real cosine signal, two methods of residual selection based on different spectral correction measures are proposed in this paper, which can accurately extract the remainder information required by the remainder theorem. The precision frequency estimation of undersampled real cosine signal is realized. The estimation process is as follows: (1) Zero-crossing detection of the high-frequency cosine waveform is carried out to determine the phase information of the signal; (2) Fast Fourier transform (or all-phase Fast Fourier transform) is performed for each undersampled signal, and frequency correction is performed for each spectral peak value by means of Candan estimator (or all-phase ratio spectrum correction) to obtain high-precision residual estimation. Based on this, the frequency offset is calculated for phase correction. (3) using the proposed phase feature classification method to select the corrected remainder, (4) to substitute the filtered frequency remainder into the closed form of Chinese remainder theorem to obtain the high-precision estimation of the original signal frequency. In addition, the theoretical expression of the variance of frequency estimation is also derived in this paper. The data simulation experiment not only verifies the correctness of the expression, but also reflects the high precision and anti-noise performance of the proposed scheme.
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TN911.23
本文編號：2436649
[Abstract]:Frequency estimation and detection of high frequency signals is an important problem in radar communication, sonar, seismic monitoring, fault diagnosis and even medical treatment. But according to Nyquist's law, in order to accurately estimate the real signal frequency, it is necessary to sample more than two samples in at least one signal cycle, which necessarily requires the frequency of the high frequency signal to be measured at a sampling rate greater than or equal to two times. As a result, the cost of hardware is high. The aim of this paper is to solve the problem of accurate estimation of the high frequency signal frequency under the condition of multi-channel undersampling (let the signal frequency be f _ 0, which requires the sampling rate fs2f0). In this paper, the ancient Chinese remainder theorem (Chinese Remainder Theorem,CRT) is introduced into this field. The estimation of signal frequency based on Chinese remainder theorem is a frontier problem in the fields of signal processing, electromagnetism and optics in recent years, but at present these studies are limited to rough frequency estimation of complex exponential signals. Therefore, it is necessary to complete the accurate frequency estimation of complex signals at first. Therefore, this paper introduces the original all-phase FFT spectrum analysis theory, with the help of the apFFT/FFT phase difference spectrum correction method to obtain the accurate frequency remainder, combined with the Chinese remainder theorem. The accurate frequency estimation of complex exponential signal is realized, and it is successfully applied to Doppler migration estimation. In order to extend the undersampling frequency estimation from the complex exponential signal to the real cosine signal, two methods of residual selection based on different spectral correction measures are proposed in this paper, which can accurately extract the remainder information required by the remainder theorem. The precision frequency estimation of undersampled real cosine signal is realized. The estimation process is as follows: (1) Zero-crossing detection of the high-frequency cosine waveform is carried out to determine the phase information of the signal; (2) Fast Fourier transform (or all-phase Fast Fourier transform) is performed for each undersampled signal, and frequency correction is performed for each spectral peak value by means of Candan estimator (or all-phase ratio spectrum correction) to obtain high-precision residual estimation. Based on this, the frequency offset is calculated for phase correction. (3) using the proposed phase feature classification method to select the corrected remainder, (4) to substitute the filtered frequency remainder into the closed form of Chinese remainder theorem to obtain the high-precision estimation of the original signal frequency. In addition, the theoretical expression of the variance of frequency estimation is also derived in this paper. The data simulation experiment not only verifies the correctness of the expression, but also reflects the high precision and anti-noise performance of the proposed scheme.
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TN911.23
【引證文獻(xiàn)】
相關(guān)碩士學(xué)位論文 前1條
1 黃勵勤;電機(jī)轉(zhuǎn)子全自動動平衡機(jī)的研制與開發(fā)[D];華南理工大學(xué);2016年
，本文編號：2436649
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