Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform? [Shalma] begins by telling you a little about ...

Every non-zero complex homomorphism of the almost periodic functions on an abelian group is induced by the Fourier transform. A Plancherel formula for almost periodic functions and a necessary ...

Joseph Fourier, born just 250 years ago, introduced a wonderful idea that revolutionised science and mathematics: any function or signal can be broken down into simple periodic sine-waves. Radio waves ...

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 ...

This is a preview. Log in through your library . Abstract The discrete Fourier-cosine transform (cos-DFT), the discrete Fourier-sine transform (sin-DFT) and the discrete cosine transform (DCT) are ...

THIS article suggests that Walsh functions 1–3 might be used in transform Spectroscopy 4–6 to replace the sinusoidal functions appearing in the Fourier transform. We think this might be the case ...