The Fourier series is a frequency-domain representation of a continuous-time periodic signal. What about aperiodic signals? The concept of Fourier series can be extended to the Fourier transform, ...

This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier ...

However, aperiodic discrete-time signals require a continuum of complex exponentials to represent them. Thus, the Fourier transform of a discrete-time signal is a continuous function of frequency.

Linear transforms — like a Fourier transform — are a key math tool in engineering and science. A team from UCLA recently published a paper describing how they used deep learning techniques to ...