Linked from

The 135 pages that link to Fourier transform, each with the reason it gives.

• Fourier seriesCompared with: It is the continuous-frequency counterpart used chiefly for nonperiodic functions.

• Periodic functionCompared with: Unlike Fourier series, it is commonly used for nonperiodic functions on unbounded domains.

• Spherical harmonicsCompared with: It analyzes functions on flat or periodic domains rather than directly on a sphere.

• Laplace transformCompared with: It uses oscillatory kernels, while the Laplace transform also accommodates exponential growth and decay.

• Moment-generating functionCompared with: The characteristic function is a probability-specific Fourier transform and needs no exponential moments.

• Change of variablesCompared with: It changes representation through an integral operation rather than a direct variable substitution.

• WaveletCompared with: Fourier analysis localizes frequency but not position, unlike wavelet analysis.

• Explicit formulaCompared with: The formula’s zero terms behave like oscillatory frequencies, though its analytic setup is Mellin-based.

• Fourier coefficientCompared with: It extends frequency analysis beyond the discrete coefficients of periodic expansions.

• Legendre transformCompared with: It changes representation through oscillatory integration, rather than through convex slope optimization.

• Separation of variablesCompared with: Transforms can reduce differential equations to algebraic or lower-dimensional equations without a product ansatz.

• Mellin transformCompared with: On logarithmic coordinates, the Mellin transform becomes a Fourier transform.

• Wavelet transformCompared with: Its global frequency basis contrasts with wavelets' localization in position and scale.