mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of discrete values. The DTFT is...

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

large numbers. The discrete version of the Fourier transform (see below) can be evaluated quickly on computers using fast Fourier transform (FFT) algorithms...

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

original Fourier transform on R or Rn, notably includes the discrete-time Fourier transform (DTFT, group = Z), the discrete Fourier transform (DFT, group...

The short-time Fourier transform (STFT) is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of...

non-uniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier...

analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key...

continuous-time Fourier transform is evaluated on the s-domain's vertical axis (the imaginary axis), the discrete-time Fourier transform is evaluated...

In mathematics the finite Fourier transform may refer to either another name for discrete-time Fourier transform (DTFT) of a finite-length series.  E.g...

Fourier-transform spectroscopy (FTS) is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source...

maps a function having a discrete time domain into one having a discrete frequency domain. The discrete-time Fourier transform, on the other hand, maps...

of transforms in mathematics. Abel transform Aboodh transform Bateman transform Fourier transform Fourier cosine transform Fourier sine transform Fractional...

Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform converts...

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

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

the Fourier transform the counterpart is the discrete Fourier transform. In addition to spectral analysis of signals, discrete transforms play important...

\end{aligned}}} The Discrete-time Fourier transform (DTFT) of the N + 1 {\displaystyle N+1} length, time-shifted sequence is defined by a Fourier series, which...

a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. The DCTs are generally related to Fourier series...

example, in the context of the discrete-time Fourier transform (DTFT). In particular, the DTFT of the product of two discrete sequences is the periodic convolution...

transform Continuous/periodic–discrete/aperiodic: Fourier series Discrete/aperiodic–continuous/periodic: Discrete-time Fourier transform Continuous/aperiodic–...

Discrete Fourier transform Fast Fourier transform Fejér's theorem Fourier analysis Fourier inversion theorem Fourier sine and cosine series Fourier transform...

Laplace transform, the Z transform is usually used in the context of one-sided signals, i.e. signals that are zero for t<0. The discrete-time Fourier transform...

called Fourier series coefficients. The term Fourier series actually refers to the inverse Fourier transform, which is a sum of sinusoids at discrete frequencies...

a discrete function, u [ n ] , {\displaystyle u[n],} with discrete-time Fourier transform (DTFT), U ( ω ) {\displaystyle U(\omega )} , and discrete Hilbert...

Fourier transform infrared spectroscopy (FTIR) is a technique used to obtain an infrared spectrum of absorption or emission of a solid, liquid, or gas...

}\right)=\sum _{n=0}^{\infty }a_{n}e^{-i\omega n}} is the discrete-time Fourier transform of the sequence a0, a1, .... In calculus, often the growth...

mathematics, the Hartley transform (HT) is an integral transform closely related to the Fourier transform (FT), but which transforms real-valued functions...

The modified discrete cosine transform (MDCT) is a transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being...

n_{2}-k_{2},...,n_{s}-k_{s})} In addition to convolution, the discrete-time Fourier transform (DTFT) is another technique which is often used in system analysis...