based on an earlier version of the Wolfram Language.
Mathematica has powerful signal processing capabilities, including digital and analog filter design, filtering, and signal analysis using the state-of-the-art algebraic and numerical methods that can be applied to audio, image, or other data.
ListConvolve — convolve a signal with any kernel (apply FIR filter)
RecurrenceFilter — compute the response of an IIR filter
LeastSquaresFilterKernel — FIR filter designed by a least-squares method
ToDiscreteTimeModel — generate an IIR filter model from an analog prototype
TransferFunctionModel — object representing a transfer-function model
TransferFunctionTransform — convert between different types of analog filters
ListZTransform — compute the Z transform of a list
FourierMatrix — create a Fourier matrix