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