" - a compact $f(x)$ will have a broad spectrum.\n", " - a broad $f(x)$ will have a compact spectrum" "The $rext_B(x)$ function is a rectangle centered at $x=0$ with ...

Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.

Abstract: In this paper, an algorithm of time-distributed fast Fourier transform and inverse fast Fourier transform (TD-FFT/TD-IFFT) is proposed. This work is motivated by the needs to implement ...

Abstract: The purpose of the study is to the develop new discrete Fourier transform, by generalizing the classical discrete Fourier transform (DFT) in the form of a parametric discrete Fourier ...

The inverse Fourier transform (inverse FFT or iFFT) reverses the operation of the Fourier transform and derives a time-domain representation from a frequency-domain dataset. Figure 1. The inverse ...