Modified Constrained Notch Fourier Transform (MCNFT) for Sinusoidal Signals in Noise and Its Performance
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Abstract Estimating the amplitude and phase of a signal accurately even when the frequencies contained in the signal are already known is very important in many areas. The estimation accuracy and the estimation time are important issues in such areas and a method of improving both of these issues by combining the notch characteristics and the band passing characteristics of serially connected notch filters and an adaptive algorithm is presented in this paper. Computer simulations reveal that the performance of the proposed method is superior to previously proposed methods. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 85(2): 65–73, 2002
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For the parameter estimation of linear frequency modulated (LFM) signal, this paper presents an improved arithmetic which is based on fractional Fourier transform (FRFT). Firstly, this paper analyzes the shortcomings of previous methods. Then, according to the characteristics of the LFM signal, a method based on fast Fourier transform (FFT) is used to estimate the coarse chirp rate. Secondly, by analyzing the redundancy of FRFT decomposition, reduced fractional Fourier transform (RFRFT) algorithm is proposed. Then, it develops relationship of signal parameter before and after normalization. Thirdly, it presents a more effective method based on FRFT to implement the parameter estimation of LFM signal. This improved arithmetic enhances the speed of calculation greatly. Finally, simulation results validate the method is able to suppress the noise and cross-terms in lower Signal-to-Noise Ratio (SNR).Comparing with the traditional FRFT, this method has a good performance to match multi-component LFM signals.
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In order to further improve the estimation precision of sinusoid frequency in additive white Gaussian noise background, a new frequency estimation algorithm of sinusoidal signals based on interpolated Fast Fourier Transform(FFT)was proposed. Firstly, zeros of length N were padded to the sinusoid sampled data of length N in the time domain. Next, 2Npoint FFT was performed and the coarse estimation was made by searching the location of the discrete spectrum line with maximum amplitude. Finally, the fine estimation was made by utilizing the spectrum line with maximum amplitude and two sample values of Discrete-Time Fourier Transform(DTFT) of the original signal on the left and right side of the maximum spectrum line. Simulation results show that the root mean square error of the proposed estimator is close to the Cramer-Rao lower bound when the signal frequency locates anywhere between two neighboring FFT discrete spectral lines and the performance is stable. The estimation precision is higher than Candan estimator, Fang estimator, Rational Combination of Three Spectrum Lines(RCTSL) estimator and Aboutanios estimator. The proposed estimator also has lower signal-to-noise ratio threshold than the existing estimators.
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Discrete Fourier Transform (DFT) based frequency estimation is an important topic and an often applied method in measurement science and signal processing in general. This is due to its optimality in terms of frequency estimation error, achieving the best possible performance given by the Cramer Rao lower bound (CRLB) asymptotically and the possibility to implement it computationally efficient via a fast Fourier transform (FFT). Below a certain level of signal-to-noise ratio (SNR), the so called threshold effect occurs, and the performance of the estimator decreases quickly. In this paper, we investigate the effect of windowing the data prior to the frequency estimation process on the threshold.
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Hough Transform
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A novel algorithm for estimating the frequency of a single complex sinusoid in complex white Gaussian noise is proposed. The proposed discrete Fourier transform based algorithm performs a frequency interpolation on the results of an N point complex Fourier transform very well with a novel residue frequency discriminator. Simulation results are included to demonstrate that the estimator is unbiased and approaches the Cramer-Rao bound uniformly over the frequency estimation range. The algorithm has low computational complexity and is well suited for real time applications
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A fast method for parameter estimation of the multi-component linear frequency modulated (multi-LFM) signal is proposed. The signal detector and chirp rate estimator are based on the modulus square of the fractional autocorrelation. By using the estimated chirp rate, an approach based on the fractional Fourier transform (FrFT) is employed for estimation of the amplitude and centre frequency. The proposed algorithm reduces two-dimensional searches, widely used in the time-frequency based method, FrFT and chirp Fourier transform, into two one-dimensional searches. By utilizing the discrete FrFT, along with the fast Fourier transform (FFT) algorithm, the proposed method is a computationally fast alternative for LFM signal detection and parameter estimation. Analysis of the multi-LFM signal is performed using the CLEAN technique as well. Finally, computer simulations are provided to illustrate the performance of the proposed algorithm.
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An accurate frequency estimator of complex sinusoid in additive white noise is proposed. It is based on interpolation of Fast Fourier Transform (FFT) and Discrete-Time Fourier Transform (DTFT). Zero-padding is firstly performed before the FFT of the sinusoid sampled data, and the coarse estimate is obtained by searching the discrete frequency index of the maximum FFT spectrum line. Then the fine estimate is obtained by employing the maximum FFT spectrum line and two DTFT sample values located on the left and right side of the maximum spectrum line. The correlation coefficients between the Fourier Transform of the noises on two arbitrarily spaced spectrum lines are derived, and the MSE calculation formula is derived in additive white noise background based on the correlation coefficients. Simulations results demonstrate that the proposed algorithm has lower MSE than the competing algorithms, and its signal-to-noise ratio (SNR) threshold is lower compared with Candan algorithm, AM algorithm and Djukanovic algorithms.
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The fractional Fourier transform can be considered as the generalization of Fourier transform. After the real cepstrum theory is reviewed, the fractional cepstrum is presented based on fractional Fourier transform. At the same time, how to use the fractional cepstrum is discussed in blind chirp signal processing. A numerical result confirms that the proposed fractional cepstrum does work even at low signal-to-noise ratios.
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