The Wolfram Language applies its strengths in calculus to the intricacies of integral transforms, with a host of original algorithms that probably now reach almost any closed-form result that can be found, together with full support for symbolic generalized functions.

Laplace Transforms

LaplaceTransform  ▪ InverseLaplaceTransform

BilateralLaplaceTransform  ▪ InverseBilateralLaplaceTransform

Fourier Transforms»

FourierTransform  ▪ InverseFourierTransform

FourierSinTransform  ▪ InverseFourierSinTransform

FourierCosTransform  ▪ InverseFourierCosTransform

FourierCoefficient  ▪ FourierSinCoefficient  ▪ FourierCosCoefficient

FourierSeries  ▪ FourierSinSeries  ▪ FourierCosSeries  ▪ FourierTrigSeries

Mellin Transforms

MellinTransform  ▪ InverseMellinTransform

Hankel Transforms

HankelTransform  ▪ InverseHankelTransform

Hilbert Transforms

HilbertTransform  ▪ InverseHilbertTransform

Radon Transforms

RadonTransform  ▪ InverseRadonTransform

Wavelet Transforms»

ContinuousWaveletTransform  ▪ InverseContinuousWaveletTransform  ▪ ...

Integral Convolutions

Convolve  ▪ MellinConvolve  ▪ UnilateralConvolve

Transform Plots

BodePlot  ▪ NyquistPlot  ▪ NicholsPlot  ▪ SingularValuePlot

Summation Transforms»

Fourier  ▪ ZTransform  ▪ FourierSequenceTransform  ▪ GeneratingFunction  ▪ ...

Related Functions

Integrate  ▪ DSolve

DiracDelta  ▪ DiracComb  ▪ HeavisideTheta  ▪ HeavisidePi  ▪ HeavisideLambda

SquareWave  ▪ TriangleWave  ▪ SawtoothWave

Related Tech Notes

▪
• Integral Transforms and Related Operations
▪
• Discrete Fourier Transforms

Related Guides

▪
• Calculus
▪
• Generalized Functions
▪
• Fourier Analysis
▪
• Data Transforms and Smoothing

Related Links

• Demonstrations related to Integral Transforms (Wolfram Demonstrations Project)
• Wolfram Core Areas: Calculus & Algebra