This is documentation for Mathematica 9, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Signal Processing

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.


Importing & Exporting Signals

Import, Export import and export data in standard formats

"SND" ▪ "WAV" ▪ "AIFF" ▪ "MAT" ▪ "EDF" ▪ ...

BinaryReadList ▪ BinaryWrite ▪ ...


Sound ▪ SampledSoundList ▪ SampledSoundFunction

ListPlay ▪ Play ▪ EmitSound

Filtering »

ListConvolve convolve a signal with any kernel (apply FIR filter)

RecurrenceFilter compute the response of an IIR filter

LowpassFilter ▪ HighpassFilter ▪ ...

GaussianFilter ▪ MeanFilter ▪ MeanShiftFilter ▪ ...

Digital Filter Design

LeastSquaresFilterKernel FIR filter designed by a least-squares method

FrequencySamplingFilterKernel ▪ EquirippleFilterKernel

ToDiscreteTimeModel generate an IIR filter model from an analog prototype

Analog Filter Design

ButterworthFilterModel ▪ Chebyshev1FilterModel ▪ Chebyshev2FilterModel ▪ EllipticFilterModel ▪ BesselFilterModel

TransferFunctionModel object representing a transfer-function model

TransferFunctionTransform convert between different types of analog filters

Window Functions »

KaiserWindow ▪ DirichletWindow ▪ HannWindow ▪ HammingWindow ▪ BlackmanWindow ▪ ...

Discrete Transforms

ListZTransform compute the Z transform of a list

ListFourierSequenceTransform ▪ DiscreteChirpZTransform ▪ DiscreteHadamardTransform

FourierMatrix create a Fourier matrix

FourierDCTMatrix ▪ FourierDSTMatrix ▪ HadamardMatrix

Visualization and Analysis

ListPlot ▪ ListLinePlot ▪ DiscretePlot


Spectrogram ▪ SpectrogramArray ▪ Periodogram ▪ PeriodogramArray ▪ ImagePeriodogram

Utility Functions

Upsample, Downsample insert zeros or remove elements from a list

Take ▪ Reverse ▪ Clip ▪ Chop ▪ Rescale