The fractional Fourier transform is a time–frequency distribution and an extension of the classical Fourier transform. There are several known applications of the fractional Fourier transform in the areas of signal processing, especially in signal restoration and noise removal. This paper provides an introduction to the fractional Fourier transform and its applications. These applications deman...

This paper is part 6 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on correlation. The correlation is performed in the time domain (slow correlation) and in the frequency domain using a Short-Time Fourier Transform (STFT). When the Fourier transform is an FFT, the correlation is said to be a " fast ...

Very broadly speaking, the Fourier transform is a systematic way to decompose “generic” functions into a superposition of “symmetric” functions. These symmetric functions are usually quite explicit (such as a trigonometric function sin(nx) or cos(nx)), and are often associated with physical concepts such as frequency or energy. What “symmetric” means here will be left vague, but it will usually...

Image compression is a crucial step in image processing area. Image Fourier transforms is the classical algorithm which can convert image from spatial domain to frequency domain. Because of its good concentrative property with transform energy, Fourier transform has been widely applied in image coding, image segmentation, image reconstruction. This paper adopts Radix-4 Fast Fourier transform (R...

A new signal-adaptive joint time-frequency distribution for the analysis of nonstationary signals is proposed. It is based on a fractionalFourier-domain realization of the weighted Wigner distribution producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms. Improvement over the standard time-frequency representations is achieved when the principal ...

Wavelet analysis is a new mathematical technique and in the recent years enormous interest in application of engineering has been observed. This new technique is particularly suitable for non-stationary processes as in contrast to the Fourier transform (FT). The wavelet transform (WT) allows exceptional localization, both in time and frequency domains. The application of the WT to earthquake en...