Interference Suppression in the Wigner Distribution Using Fractional Fourier Transformation and Signal Synthesis

Abstract

A novel method for the suppression of cross terms in the timefrequency domain is introduced. First, interference is identified using a fractional Fourier transform-based technique. Then, auto-terms are detected, synthesized, and subtracted from the original signal. The process is repeated until all signal components are extracted. Finally, the Wigner distributions of pure auto-terms are superimposed to yield a high readability representation.Index Terms-Fractional Fourier transform, reduced interference distributions, Wigner distribution (WD).

Robust multicomponent LFM signals synthesis algorithm based on masked ambiguity function

“…The analysis above is based on the assumption that the crossterms are removed completely, otherwise (14) would not hold any more. In this section, a MAF algorithm is presented to suppress the cross-terms.…”

“…e.g. STFT [10], Smoothed pseudo-WD (SPWD) [11], linear/nonlinear filters [12], fractional Fourier transform (FrFT) [13][14][15], etc. The masked WD (MWD) algorithms utilizing these techniques can eliminate the cross-terms while preserving the quality of the WD of individual components.…”

A New Form of Gabor Wigner Transform by Adaptive Thresholding in Gabor Transform and Wigner Distribution and the Power of Signal Synthesis Techniques to Enhance the Strengths of GWT

“…The time-frequency resolution is improved by using quadratic TFRs. However significant efforts are made to define algorithms for cross-terms suppression, which appear due to the quadratic nature of these distributions [5][6][7]. In our earlier contribution [7], we have discussed in detail merits and demerits of time representation of a signal, frequency representation of a signal, and the basic goal of a time frequency representation (TFR), linear time frequency representations (TFRs), quadratic TFRs and most widely used cross-term suppression techniques.…”

“…In our earlier contribution [7], we have discussed in detail merits and demerits of time representation of a signal, frequency representation of a signal, and the basic goal of a time frequency representation (TFR), linear time frequency representations (TFRs), quadratic TFRs and most widely used cross-term suppression techniques. This contribution [7] also includes a brief discussion on already proposed combination of GWT [8,9] and exploits the strength of fractional Fourier transform [4][5][6][7][8] to study GWT.…”

An Efficient FPGA-based Implementation of Fractional Fourier Transform Algorithm

“…Thus we can extract the signal easily in an appropriate fractional Fourier domain when it is not possible to separate the signal and noise in spatial or frequency domain [5]. The extra degree of freedom introduced by the choice of the fractional order of transformation (angle of rotation) gives the FrFT a potential improvement in any application where the ordinary Fourier transform (FT) is used [22][23][24][25]. The FrFT has been found many applications in the areas of signal processing such as multirate signal processing, signal and image recovery, restoration and enhancement, pattern recognition, beam forming, perspective projections, system synthesis, mutual intensity synthesis, radar, and system decomposition [6-18, 26, 27].…”