A new algorithm performs Fourier transforms using a minimal number of samples. The fast Fourier transform, one of the most important algorithms of the 20th century, revolutionized signal processing.

Harmonic analysis occupies a central position in modern mathematical analysis by providing the tools to express complex functions as superpositions of simpler sinusoidal components via the Fourier ...

Design linear discrete-time systems and filters and analyze their behavior. Represent continuous-time signals and linear systems in discrete time, so that such signals can be recovered in continuous ...

As we listen to a piece of music, our ears perform a calculation. The high-pitched flutter of the flute, the middle tones of the violin, and the low hum of the double bass fill the air with pressure ...

If there's a mathematical idea that applies itself to almost everything in everyday life but is almost unknown outside the scientific world, the Fourier transform has to be the most unsung contender.

Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals. In an increasingly data-driven world, ...

Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform? [Shalma] begins by telling you a little about Joseph Fourier, the French mathematician with an interest in heat propagation ...