Fourier transform on finite groups information

the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform...

In physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function...

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of...

In mathematics, the discrete Fourier transform over a ring generalizes the discrete Fourier transform (DFT), of a function whose values are commonly complex...

itself is called a Fourier transformation. Its output, the Fourier transform, is often given a more specific name, which depends on the domain and other...

the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum...

Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an...

A Fast Fourier Transform (FFT) is an algorithm that computes the Discrete Fourier Transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis...

of Fourier series List of Fourier-related transforms Fourier transform on finite groups Fractional Fourier transform Continuous Fourier transform Fourier...

fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to...

compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative group of complex numbers...

nonabelian groups. However, there is a straightforward generalization to Locally Compact Abelian (LCA) groups. This generalizes the Fourier transform to L 1...

The precursor of the transforms were the Fourier series to express functions in finite intervals. Later the Fourier transform was developed to remove...

The cyclotomic fast Fourier transform is a type of fast Fourier transform algorithm over finite fields. This algorithm first decomposes a DFT into several...

related to Fourier transform on finite groups. For a more general field K, whenever the characteristic of K does not divide the order of the group G, then...

more dimensions. One of the more popular multidimensional transforms is the Fourier transform, which converts a signal from a time/space domain representation...

sign of the shift depending on the sign of the frequency (see § Relationship with the Fourier transform). The Hilbert transform is important in signal processing...

waveform, and the two versions are mathematically related by the Fourier transform. The spectrum is of particular interest when pulses are subject to...

domains with a pair of mathematical operators called transforms. An example is the Fourier transform, which converts a time function into a complex valued...

A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies...

The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the sinusoidal frequency...