Signal Processing

The Wolfram Language 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.

ReferenceReference

Importing & Exporting Signals

Import, Export import and export data in standard formats

"WAV"  ▪  "AIFF"  ▪  "MP3"  ▪  "MIDI"  ▪  "SND"  ▪  "FLAC"  ▪  "OggVorbis"  ▪  ...

BinaryReadList  ▪  BinaryWrite  ▪  ...

Sound »

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

GaussianFilter  ▪  MeanFilter  ▪  MeanShiftFilter  ▪  LowpassFilter  ▪  ...

Resampling & Interpolation

ArrayResample resample an array of data

Interpolation  ▪  ListInterpolation  ▪  Downsample  ▪  Upsample

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  ▪  HammingWindow  ▪  BlackmanWindow  ▪  ...

Discrete Transforms

ListZTransform compute the Z transform of a list

ListFourierSequenceTransform  ▪  DiscreteChirpZTransform  ▪  DiscreteHadamardTransform

DiscreteWaveletTransform  ▪  InverseWaveletTransform  ▪  ...

FourierMatrix create a Fourier matrix

FourierDCTMatrix  ▪  FourierDSTMatrix  ▪  HadamardMatrix

Signal Decoding

KalmanEstimator use an optimal estimator to find internal states

FindHiddenMarkovStates use Viterbi and other decoding to find internal states

Visualization and Analysis

BodePlot magnitude and phase plots of the frequency response of a filter

ListPlot  ▪  ListLinePlot  ▪  DiscretePlot

Spectrogram  ▪  SpectrogramArray  ▪  Periodogram  ▪  PeriodogramArray  ▪  ImagePeriodogram

WaveletScalogram  ▪  WaveletListPlot  ▪  ...