The key to the existence of a generalized formalism and transform is based on a generalization of the formalism of generalized functions, and the Dirac-delta impulse in particular.

This multipart series will review the discrete Fourier Transform and describe how to avoid common problems when transitioning from the time to frequency domain.

The formalism of the Dirac delta function developed in a previous article allows us to understand the phenomenon of aliasing in a simple and comprehensive way. In a previous article, we established ...

Fourier transforms are one of the most important algorithms in math, and help our electronics handle visual and audio signals in a sophisticated way.

Poisson’s Summation Formula (PSF) has numerous applications, not only in radar imaging. It is the bridge between continuous (infinite integrals) and discrete settings (finite sums) and, hence, links ...

The generalized Fourier transform approach is the extension of the Fourier transform method used for the normal diffusion equation. The feasibility of the approach is validated by comparing the ...

The Fourier transform underpins so much of our technological lives, in most cases probably without our realising it. The ability to mathematically split a waveform into its frequency components and… ...