Stanford Computer Music Theory Package

SCMTheory

The main body of Mathematica functions are contained in this package. Emphasis is on spectral transformation and display of sound signals.

Function Examples -- demonstrations of particular functions and use of options with those functions.

SeqPlot -- a function for plotting periodic sequences. Allows for periodic extension, bandlimited interpolation; many display options.

DFTAnalyze -- a function to plot a complex signal and its spectrum. Can plot either as real/imaginary or magnitude/phase.

EvenOddPlot a function which will plot the even, odd, and combined forms of a function.

EvenOddSinusoidPlot -- a specialized version of EvenOddPlot which will plot the even and odd parts of real sinusoid with arbitrary phase.

Example notebooks

Modulo Sequences -- demonstration of various sequence manipulators, including: flip, repeat, shift, stretch, decimate, interpolate, convolution, correlation and zero padding.

Spectral Plots -- Plotting complex sequences in 2 and 3 dimensions.

Generalized Complex Sinusoid -- Presents the four component mathematica parts of a complex sinusoid: amplitude, phase, frequency and decay.

Parabolic Peak Interpolation -- Demonstrates the technique of parabolic peak interpolation to detect frequency components in spectra.

Spectrum by Similarity -- Demonstrates the basic principle of measuring a spectrum and compares measuring spectra with real and complex sinusoids.

Windowing

Windows

Implementation of various windows described in the following paper:
Harris, Frederic J. "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform," Proceedings of the IEEE, Vol.66, No.1 (January 1978) pp. 51-84.
Includes continuous and discrete forms of the windows, and also functions to display the fourier transform of the windows.

Time Domain Alias Cancellation

TDAC

A small package to demonstrate an audio compression technique of converting a time signal into a critically sampled frequency signal with no increase in data rate.

Using sound files

SoundFile

Demonstrates how to read a soundfile into Mathematica. Not extensively developed because Mathematica is slow at large numeric processing. Works only on NeXT/Sun sound files, but is designed to extend to other formats easily.

FM synthesis spectral plots

FMPlot

This package contains functions for plotting and manipulating frequency spectra of carrier/frequency/index combinations used in simple FM synthesis. In addition, additive-synthesis spectral plots can be created and manipulated with this package.