Fourier transforms make it possible for our electronics to handle visual and audio signals in a sophisticated way. They underlie our ability to process this data efficiently, and teach computers ...

Schönlieb gives an example of how Fourier transforms are used in her own area of mathematics, a field called inverse problems. She explains how images generated using magnetic resonance tomography are ...

That's why the Fourier transform is useful for compression. An eight-by-eight block of pixels can be thought of as a 64-sample signal, and thus as the sum of 64 different frequencies.

The Fourier series is the basis for much of digital signal processing, allowing you to build a signal from the sum of many sinusoids. You can also go in reverse and break a signal up into its ...

An interesting aspect of time-varying waveforms is that by using a trick called a Fourier Transform (FT), they can be represented as the sum of their underlying frequencies. This mathematical insig… ...

For example, in photonics, the Fourier transform links an optical pulse's temporal and spectral characteristics, makes it possible to analyse an image in terms of a distribution of spatial ...

The finite Fourier transform for periodic distributions is generalized in such a way that for every distribution f and every open interval (-a, a) there exists a Fourier series which agrees with f on ...

Synchrotron-based Fourier transform infrared (FTIR) spectro-microtomography is a nondestructive, label-free imaging technique that allows chemical fingerprinting of intact, three-dimensional ...

A group of MIT researchers believe they’ve found a way to speed up audio, video, and image compression by improving on the Fourier transform. If you’re not familiar with the method, it ...

Absorption-Mode: The Next Generation of Fourier Transform Mass Spectra. Analytical Chemistry, 2012; 84 (6): 2923 DOI: 10.1021/ac3000122 ...