Mathematica for signal processing

By Nasser Abbasi, updated 1/21/2008

I started using Mathematica package called “signals and systems” version 1.2.1, which I bought around 2005 from WRI web site.

These are documentation from that package

Introduction chapter PDF

Analyzing signals chapter PDF

Filter design chapter PDF

Transforms chapter PDF

Representing signals and systems chanpter PDF

In addition, I collected all the commands in that package below

Options specific to the analysis function.

Options specific to MagnitudePhasePlot.

Options for PoleZeroPlot.

Representing analog filters.

Objects for specifying the magnitude response of a filter.

Allowed types of filters for analog filter design.

Option to DesignAnalogFilter.

Frequency transformations of an analog filter object.

Some common mappings for use with AnalogFilterTransformation.

Finding the DC gain.

Representing an analog tapped delay line.

Representing a digital IIR filter.

Methods for converting an analog prototype filter into a digital filter.

Representing a digital FIR filter.

Functions for assisting in the design of two-dimensional decimation systems.

Options for DesignDecimationSystem2D.

The Laplace transform and its inverse.

Options for LaplaceTransform.

Option specific to the inverse Laplace transform.

The Fourier transform and its inverse.

The Z transform and its inverse.

Options for ZTransform.

Options for inverse Z transform.

The discrete-time Fourier transform and its inverse.

The discrete Fourier transform and its inverse.

Options for DiscreteFourierTransform and InverseDiscreteFourierTransform.

Special syntax for transforming a numeric vector.

Determining stability from a transform object.

Assumptions made by transforms during a computation.

Functions for extracting parts of transform objects.

Data objects resulting from forward transforms.

The transform-based equation solvers.

Options for the solving functions.

Functions to perform convolution.

Options for convolution.

Functions for animating convolution by the "flip-and-slide" technique.

Functions for autocorrelation.

Functions to perform cross-correlation.

Functions for working with intervals.

Functions generating particular polynomials.

Functions for manipulating polynomials and rational polynomials.

General matrix operations.

Functions to determine information about resampling matrices.

Functions for finding common multiples and divisors of resampling matrices.

Operations on resampling matrices.

Function for computing various Smith form matrices.

Options for Smith form decomposition.

Decomposing a matrix based on a precomputed Smith form.

The option for ConstrainedSmithFormDecomposition.

Computations with polygons.

Options for WritePtolemySimulation.

A signal simplification function

Options to SimplifySignal.

This is an example using it To find discrete fourier transform

assume we have signal {3,2,1,0,1,2}, period N=6, then write

t=DiscreteFourierTransform[SampledData[{3,2,1,0,1,2},1,n],6,n,k]

The result is correct but need to divide by N

To extract the stuff I am interested in do: