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The 18 pages that link to Discrete Fourier transform, each with the reason it gives.

• Fourier transformBroader topic: It is the computational counterpart used when data are available as finite samples.

• Fourier analysisBroader topic: It makes frequency analysis possible for sampled, finite data.

• Digital signal processingRelated: It converts sampled data into a frequency representation useful for analysis and filtering.

• OrthogonalityBroader topic: Its frequency vectors are orthogonal, enabling exact coefficient recovery.

• Frequency responseRelated: It estimates frequency-domain behavior from sampled measurements, with finite-resolution limitations.

• Root of unityRelated: Its kernel uses powers of a primitive root of unity to encode periodic frequencies.

• Orthonormal basisRelated: It computes coordinates in a finite Fourier basis for sampled data.

• Fast Fourier transformNarrower topic: The FFT computes this transform without evaluating every input-output pair directly.

• Orthogonal frequency-division multiplexingRelated: It efficiently maps OFDM symbols between frequency-domain subcarriers and time-domain samples.

• Fourier coefficientRelated: Its outputs are finite-data counterparts of Fourier coefficients.

• Digital signal processorRelated: Frequency analysis is a standard DSP task, often computed with an efficient algorithm.

• Fourier analysis on finite groupsCompared with: It is the familiar cyclic-group case of the broader finite-group theory.

• Summation by partsRelated: Summation by parts can bound transforms when oscillation interacts with changing weights.

• Parseval's identityBroader topic: For finite sequences, the corresponding identity equates sample energy and appropriately normalized transform energy.

• Parseval's theoremBroader topic: Its finite-dimensional version yields an exact sum-of-squares identity.

• Pontryagin dualityBroader topic: For finite abelian groups, its frequency labels are precisely the group characters.

• Numerical relayRelated: Relays use it to estimate fundamental-frequency phasors from sampled waveforms.

• Position and momentum spacesCompared with: It is a finite-data analogue, whereas quantum position and momentum representations often use continuous transforms.