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 ...

As supported by the LAW OF SUPERPOSITION, sine tones of varying amplitudes will combine to form a complex harmonic SPECTRUM. If every period of sound has been subjected to Fourier analysis by a ...

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… ...

With the new algorithm, called the sparse Fourier transform (SFT), streams of data can be processed 10 to 100 times faster than was possible with the FFT.

In this paper we offer a method for constructing functions with many gaps in their supports and in the supports of their Fourier transform. As a result we answer a question of Benedicks [Ben1] and we ...

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 ...

Fourier analysis may be performed mathematically if the expression f (t) describing the waveform or COMPLEX TONE is known, or else by converting the sound to digital form by a computer which then ...