This paper highlights the extraction of micro-Doppler (m-D) features from radar signal returns of helicopter and human targets using the wavelet transform method incorporated with time-frequency analysis. In order for the extraction of m-D features to be realized, the time domain radar signal is decomposed into a set of components that are represented at different wavelet scales. The components are then reconstructed by applying the inverse wavelet transform. After the separation of m-D features from the target's original radar return, time-frequency analysis is then used to estimate the target's motion parameters. The autocorrelation of the time sequence data is also used to measure motion parameters such as the vibration/rotation rate. The findings show that the results have higher precision after the m-D extraction rather than before it, since only the vibrational/rotational components are employed. This proposed method of m-D extraction has been successfully applied to helicopter and human data.
-Fractional Fourier transform (FRFT) is a generalization of the Fourier transform, rediscovered many times over the past hundred years. In this paper, we provide an overview of recent contributions pertaining to the FRFT. Specifically, the paper is geared toward signal processing practitioners by emphasizing the practical digital realizations and applications of the FRFT. It discusses three major topics. First, the manuscripts relates the FRFT to other mathematical transforms. Second, it discusses various approaches for practical realizations of the FRFT. Third, we overview the practical applications of the FRFT. From these discussions, we can clearly state the FRFT is closely related to other mathematical transforms, such as time-frequency and linear canonical transforms. Nevertheless, we still feel that major contributions are expected in the field of the its digital realizations and applications, especially, since many digital realizations of the FRFT still lack properties of the continuous FRFT. Overall, the FRFT is a valuable signal processing tool. Its practical applications are expected to grow significantly in years to come, given that the FRFT offers many advantages over the traditional Fourier analysis. I. IIn very simple terms, the fractional Fourier transform (FRFT) is a generalization of the ordinary Fourier transform [1]. Specifically, the FRFT implements the so-called order parameter α which acts on the ordinary Fourier transform operator. In other words, the αth order fractional Fourier transform represents the αth power of the ordinary Fourier transform operator. When α = π/2, we obtain the Fourier transform, while for α = 0, we obtain the signal itself. Any intermediate value of α (0 < α < π/2) produces a signal representation that can be considered as a rotated time-frequency representation of the signal [2], Signal Processing, Vol. 91 No. 6, June, 2011 [3].Interestingly enough, the idea of the fractional powers of the Fourier operator has been "discovered" several times in the literature. Initially, the idea appeared in the mathematical literature between the two world wars (e.g., [4], [5]). More publications relating to this idea appeared after the second world war, however they were sporadic (e.g. [6]). The idea of fractional Fourier operator re-gains a momentum in 1980's with publications by Namias (e.g. [7]). Following Namias' contributions, a large number of papers appeared in the literature during 1990's tying the concept of the fractional Fourier operators to many other fields (e.g., time-frequency analysis as described in [2]). We have also witnessed a number of recent contributions attempting to understand the practical applications of the FRFT beyond optics.The main goal of this publication is to provide an overview of recent developments regarding the FRFT and its applications. Although a number of publications reviewing the FRFT has also appeared in recent years (e.g., [1], [8], [9]), some of these publications are geared towards explaining the mathematical eloquence b...
Estimation of the instantaneous frequency (IF) of a harmonic complex-valued signal with an additive noise using the Wigner distribution is considered. If the IF is a nonlinear function of time, the bias of the estimate depends on the window length. The optimal choice of the window length, based on the asymptotic formulae for the variance and bias, can be used in order to resolve the bias-variance tradeoff. However, the practical value of this solution is not significant because the optimal window length depends on the unknown smoothness of the IF. The goal of this paper is to develop an adaptive IF estimator with a time-varying and data-driven window length, which is able to provide quality close to what could be achieved if the smoothness of the IF were known in advance. The algorithm uses the asymptotic formula for the variance of the estimator only. Its value may be easily obtained in the case of white noise and relatively high sampling rate. Simulation shows good accuracy for the proposed adaptive algorithm.
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