in this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the fourier transform. as a consequence, we extend the fundamental theorems of abelian fourier transform to non-abelian case.

This paper is concerned with the approach to teaching an introductory course on Fourier theory for engineers. Commonly called Signals and Systems (or some variation), this course generally introduces four transforms: the Fourier Transform, the Fourier Series, the Discrete-Time Fourier Transform (DTFT), and the Discrete Fourier Transform (DFT). Our concern is that the method and order of topic p...

An efficient algorithm for computing the one-dimensional partial fast Fourier transform fj = ∑c(j) k=0 e Fk is presented. Naive computation of the partial fast Fourier transform requires O(N) arithmetic operations for input data of length N . Unlike the standard fast Fourier transform, the partial fast Fourier transform imposes on the frequency variable k a cutoff function c(j) that depends on ...

In 1965 J. Cooley and J. Tukey published an article detailing an efficient algorithm to compute the Discrete Fourier Transform, necessary for processing the newly available reams of digital time series produced by recently invented analog-to-digital converters. Since then, the Cooley– Tukey Fast Fourier Transform and its variants has been a staple of digital signal processing. Among the many ca...

A novel technique of analysis of an arbitrary primary time series into a set of secondary, timelimited, local, constituent time series, the TT-transform, is presented. The time–time representation is derived from the S-transform, a method of representation of a real time series as a set of complex, time-localized spectra. When integrated over time, the S-transform becomes the Fourier transform ...

In this paper, the satellite intermodulation is evaluated in frequency domain, for N-carrier input. Fourier transform is applied to avoid large equations where the number of carriers is quite low. The algorithm is probed with well-known series for particular cases with two input carriers. Additionally, it is also possible to evaluate AM-AM conversion in a large set of input carriers. Key-Words:...