WolframSignal ProcessingA CORE PART OF
WOLFRAM LANGUAGE

Signal Processing & Analysis.

Comprehensive signal processing capabilities, tightly bundled with powerful calculus, statistics and machine learning, for students and professionals in engineering, finance, medicine and more.

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Rich Access to Data

Access technical, medical, financial and other data by importing from standard file formats (CSV, EDF, MP3, ...), read data by connecting to devices (microphones, ...) or access data through data feeds (stock prices, exchange rates, ...).

Spectral & Time-Frequency Analysis

Perform time-domain and spectral analysis and visualization. Use various techniques including convolution, Fourier, cosine and wavelet transforms to extract signal measurements and higher-level features for classification, recognition and more.

Filtering & Filter Design

Filter signals to perform enhancement, frequency selection, change detection and more. Immediately access a large collection of highly optimized filters. Design and use custom FIR, IIR and analog filters (Butterworth, Chebyshev, elliptic, ...).

Filter Deployment

Automatically generate and deploy filters to microcontrollers such as Arduino to rapidly build prototypes of real-life signal processing systems. Exchange filters as Functional Mockup Units (FMUs) with 100+ other FMI-compatible tools.

Machine Learning for Signals

Use highly optimized machine learning and neural networks for tasks such as signal classification, anomaly detection and speech recognition. Immediately use various pre-trained models or build your own.

Audio & Speech Signal Processing

Analyze and process speech, music or other audio signals. Use classical signal processing or modern machine learning to perform event detection, identification, classification and recognition.

Time Series Signal Processing

Compute descriptive statistics, apply filters and visualize time series data to extract information or make predictions. Work with data from any field including econometrics, finance, meteorology, physiology and more.

Guide to Time Series Processing

Wolfram Signal Processing Documentation

Wolfram Signal Processing is an integrated part of Wolfram Language. The full system contains over 6,000 built-in functions covering all areas of computation—all carefully integrated so they work perfectly together.

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Time Series Processing

ListConvolve ▪ ListDeconvolve ▪ RecurrenceFilter ▪ LowpassFilter ▪ HighpassFilter ▪ BandpassFilter ▪ BandstopFilter ▪ DifferentiatorFilter ▪ HilbertFilter ▪ Fourier ▪ FourierSeries ▪ FourierTransform ▪ FourierSequenceTransform ▪ ShortTimeFourierTransform ▪ LaplaceTransform ▪ ZTransform ▪ ListZTransform ▪ Spectrogram ▪ Periodogram ▪ Cepstrogram ▪ ButterworthFilterModel ▪ EllipticFilterModel ▪ KaiserWindow ▪ HammingWindow ▪ BlackmanWindow ▪ Sum ▪ DSolve ▪ RSolve ▪ TransferFunctionModel ▪ TransferFunctionPoles ▪ BodePlot ▪ Plot ▪ EvaluationMonitor ▪ Exclusions ▪ ExclusionsStyle ▪ FeedbackType ▪ Filling ▪ FillingStyle ▪ LabelingSize ▪ MaxRecursion ▪ MeshFunctions ▪ MeshShading ▪ PhaseRange ▪ PlotHighlighting ▪ PlotLabels ▪ PlotLayout ▪ PlotPoints ▪ PlotStyle ▪ RegionFunction ▪ StabilityMargins ▪ StabilityMarginsStyle ▪ MachinePrecision ▪ NyquistPlot ▪ NicholsPlot ▪ SingularValuePlot ▪ GainPhaseMargins ▪ AbsArgPlot ▪ Eigenvalues ▪ StateFeedbackGains ▪ SystemsModelDelay ▪ SamplingPeriod ▪ SystemsModelLabels ▪ TransferFunctionFactor ▪ TransferFunctionCancel ▪ Unevaluated ▪ StateSpaceModel ▪ TransferFunctionZeros ▪ ToContinuousTimeModel ▪ Function ▪ AffineStateSpaceModel ▪ NonlinearStateSpaceModel ▪ CreateSystemModel ▪ Module ▪ Sin ▪ RSolveValue ▪ AsymptoticRSolveValue ▪ DifferenceRoot ▪ FindSequenceFunction ▪ FindGeneratingFunction ▪ FindLinearRecurrence ▪ Derivative ▪ DirichletCondition ▪ Vectors ▪ Matrices ▪ RegionQ ▪ ParametricNDSolve ▪ DiscreteVariables ▪ WeierstrassP ▪ Erf ▪ C ▪ IncludeSingularSolutions ▪ ParametricPlot ▪ Inactive ▪ FinancialDerivative ▪ Activate ▪ NDSolve ▪ AsymptoticDSolveValue ▪ WhenEvent ▪ DEigensystem ▪ DEigenvalues ▪ NDEigensystem ▪ NDEigenvalues ▪ GreenFunction ▪ CompleteIntegral ▪ Solve ▪ DifferentialRoot ▪ StreamPlot ▪ ItoProcess ▪ SystemModelSimulate ▪ TruncateSum ▪ Block ▪ Infinity ▪ GeneratedParameters ▪ StandardForm ▪ Parallelize ▪ Refine ▪ Fibonacci ▪ LucasL ▪ ArcTan ▪ ArcCot ▪ QPolyGamma ▪ LerchPhi ▪ HypergeometricPFQ ▪ PolyGamma ▪ Zeta ▪ HarmonicNumber ▪ GammaRegularized ▪ BetaRegularized ▪ ChebyshevU ▪ ChebyshevT ▪ StirlingS1 ▪ StirlingS2 ▪ Binomial ▪ CatalanNumber ▪ DifferenceDelta ▪ SeriesCoefficient ▪ PrimeQ ▪ Primes ▪ EllipticTheta ▪ Total ▪ Product ▪ NSum ▪ AsymptoticSum ▪ SumConvergence ▪ CDF ▪ RootSum ▪ DivisorSum ▪ ParallelSum ▪ ArrayReduce ▪ Table ▪ ExactBlackmanWindow ▪ BlackmanHarrisWindow ▪ BlackmanNuttallWindow ▪ Array ▪ TukeyWindow ▪ BartlettWindow ▪ HannWindow ▪ Arg ▪ Graphics ▪ PaddingSize ▪ Tiny ▪ Small ▪ Medium ▪ Large ▪ Full ▪ ScalingFunctions ▪ ArrayPlot ▪ AlignmentPoint ▪ Center ▪ AspectRatio ▪ Axes ▪ AxesLabel ▪ AxesOrigin ▪ AxesStyle ▪ Background ▪ BaselinePosition ▪ BaseStyle ▪ ClippingStyle ▪ ColorFunctionScaling ▪ ColorFunction ▪ ColorRules ▪ ContentSelectable ▪ CoordinatesToolOptions ▪ DataRange ▪ DataReversed ▪ Epilog ▪ FormatType ▪ Frame ▪ FrameLabel ▪ FrameStyle ▪ FrameTicks ▪ FrameTicksStyle ▪ GridLines ▪ GridLinesStyle ▪ ImageMargins ▪ ImagePadding ▪ ImageSize ▪ LabelStyle ▪ MaxPlotPoints ▪ Mesh ▪ MeshStyle ▪ GrayLevel ▪ GoldenRatio ▪ PlotLabel ▪ PlotLegends ▪ PlotRangeClipping ▪ PlotRangePadding ▪ PlotRegion ▪ PlotTheme ▪ $PlotTheme ▪ PreserveImageOptions ▪ Prolog ▪ RotateLabel ▪ TargetUnits ▪ Ticks ▪ TicksStyle ▪ All ▪ PlotRange ▪ Plot3D ▪ ContourPlot ▪ DensityPlot ▪ ParametricPlot3D ▪ DiscreteRatio ▪ VerifyConvergence ▪ ExponentialGeneratingFunction ▪ InverseZTransform ▪ GeneratingFunction ▪ AccuracyGoal ▪ PerformanceGoal ▪ $PerformanceGoal ▪ PrecisionGoal ▪ UnitStep ▪ Floor ▪ SquareWave ▪ TriangleWave ▪ SawtoothWave ▪ HeavisideTheta ▪ DiracDelta ▪ HeavisideLambda ▪ HeavisidePi ▪ ComplexPlot ▪ MittagLefflerE ▪ PrincipalValue ▪ WorkingPrecision ▪ DSolveValue ▪ Regularization ▪ NIntegrate ▪ MeijerG ▪ InverseLaplaceTransform ▪ UnilateralConvolve ▪ MellinTransform ▪ FractionalD ▪ CaputoD ▪ InverseFourierSequenceTransform ▪ BilateralZTransform ▪ TraditionalForm ▪ BesselJ ▪ True ▪ OrnsteinUhlenbeckProcess ▪ FourierCosTransform ▪ InverseFourierTransform ▪ Convolve ▪ BilateralLaplaceTransform ▪ HankelTransform ▪ RadonTransform ▪ Piecewise ▪ CharacteristicFunction ▪ Asymptotic ▪ Assumptions ▪ $Assumptions ▪ GenerateConditions ▪ False ▪ Pi ▪ FourierCoefficient ▪ FourierSinSeries ▪ FourierCosSeries ▪ Series ▪ Integrate ▪ Extract ▪ SparseArray ▪ Sinc ▪ MatrixExp ▪ FourierParameters ▪ InverseFourier ▪ FourierDCT ▪ FourierDST ▪ FourierSinTransform ▪ FindRepeat ▪ FindTransientRepeat ▪ Fit ▪ FindPeaks ▪ DerivativeFilter ▪ Image ▪ Image3D ▪ Automatic ▪ SampleRate ▪ SampledSoundList ▪ SampledSoundFunction ▪ Sound ▪ SoundNote ▪ None ▪ Map ▪ OutputResponse ▪ RecurrenceTable ▪ Method ▪ Padding ▪ MaxIterations ▪ N ▪ ImageDeconvolve ▪ Length ▪ ListCorrelate ▪ ImageConvolve ▪ LinearRecurrence ▪ BlockMap ▪ Partition ▪ Accumulate ▪ Inner ▪ CellularAutomaton ▪ ArrayFilter ▪ PadLeft ▪ DiscreteConvolve ▪ ToeplitzMatrix ▪ DiskMatrix ▪ GaussianMatrix ▪ TimeSeriesModelFit ▪ MAProcess ▪ ARProcess ▪ ARMAProcess ▪ SARIMAProcess ▪ ARIMAProcess ▪ SARMAProcess ▪ FARIMAProcess ▪ ARCHProcess ▪ GARCHProcess ▪ RandomFunction ▪ EstimatedProcess ▪ TimeSeriesForecast ▪ KalmanFilter ▪ TemporalData ▪ FindProcessParameters ▪ AdjustTimeSeriesForecast ▪ CovarianceFunction ▪ CorrelationFunction ▪ AbsoluteCorrelationFunction ▪ PartialCorrelationFunction ▪ PowerSpectralDensity ▪ WeakStationarity ▪ TimeSeriesInvertibility ▪ ToInvertibleTimeSeries ▪ UnitRootTest ▪ AutocorrelationTest ▪ Differences ▪ MovingAverage ▪ AudioCapture ▪ SpeechSynthesize ▪ WebAudioSearch ▪ ExampleData ▪ AudioPlay ▪ AudioPause ▪ AudioStop ▪ AudioStream ▪ AudioData ▪ Duration ▪ AudioSampleRate ▪ AudioChannels ▪ Plus ▪ Times ▪ Power ▪ Abs ▪ Log ▪ Mean ▪ Variance ▪ Median ▪ Quantile ▪ AudioPlot ▪ AudioResample ▪ AudioTrim ▪ AudioPad ▪ AudioReverse ▪ AudioDelete ▪ AudioInsert ▪ AudioReplace ▪ AudioPartition ▪ AudioSplit ▪ AudioPan ▪ AudioChannelMix ▪ AudioNormalize ▪ AudioAmplify ▪ ConformAudio ▪ AudioJoin ▪ AudioOverlay ▪ AudioChannelSeparate ▪ AudioChannelCombine ▪ AudioReverb ▪ AudioFade ▪ AudioDelay ▪ AudioTimeStretch ▪ AudioFrequencyShift ▪ AudioSpectralMap ▪ AudioSpectralTransformation ▪ AudioIntervals ▪ AudioMeasurements ▪ AudioAnnotate ▪ WienerFilter ▪ TotalVariationFilter ▪ AudioIdentify ▪ PitchRecognize ▪ AudioInstanceQ ▪ SpeechRecognize ▪ SpeechCases ▪ SpeechInterpreter ▪ Classify ▪ Predict ▪ Nearest ▪ FeatureNearest ▪ FeatureSpacePlot ▪ FindClusters ▪ NetEncoder ▪ NetChain ▪ NetGraph ▪ Import ▪ Export ▪ BinaryReadList ▪ BinaryWrite ▪ Audio ▪ AudioGenerator ▪ AudioPitchShift ▪ AudioLocalMeasurements ▪ TimeSeries ▪ EventSeries ▪ MovingMap ▪ TimeSeriesAggregate ▪ TimeSeriesResample ▪ GaussianFilter ▪ MeanFilter ▪ MeanShiftFilter ▪ ArrayResample ▪ Interpolation ▪ ListInterpolation ▪ Downsample ▪ Upsample ▪ LeastSquaresFilterKernel ▪ FrequencySamplingFilterKernel ▪ EquirippleFilterKernel ▪ ToDiscreteTimeModel ▪ BiquadraticFilterModel ▪ Chebyshev1FilterModel ▪ Chebyshev2FilterModel ▪ BesselFilterModel ▪ TransferFunctionTransform ▪ DirichletWindow ▪ ListFourierSequenceTransform ▪ DiscreteChirpZTransform ▪ DiscreteHadamardTransform ▪ DiscreteWaveletTransform ▪ InverseWaveletTransform ▪ FourierMatrix ▪ FourierDCTMatrix ▪ FourierDSTMatrix ▪ HadamardMatrix ▪ KalmanEstimator ▪ FindHiddenMarkovStates ▪ ListPlot ▪ ListLinePlot ▪ ListStepPlot ▪ DiscretePlot ▪ SpectrogramArray ▪ PeriodogramArray ▪ ImagePeriodogram ▪ CepstrumArray ▪ CepstrogramArray ▪ ShortTimeFourier ▪ InverseShortTimeFourier ▪ ShortTimeFourierData ▪ InverseSpectrogram ▪ WaveletScalogram ▪ WaveletListPlot ▪