**NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW
VERSION:** "Mathematics of the Discrete
Fourier Transform (DFT), with Audio Applications --- Second
Edition", by Julius
O. Smith III, W3K
Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright ©
*2017-09-28* by Julius O. Smith III -
Center for Computer Research
in Music and Acoustics (CCRMA), Stanford University

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Mathematica for Selected PlotsThe Mathematica code for producing Fig. 5.1 (minus the annotations which were done using NeXT Draw and EquationBuilder from Lighthouse Design) is

Plot[10 Sin[2 Pi 2.5 t + Pi/4],{t,0,1}, PlotLabel->“10 Sin[2 Pi 2.5 t + Pi/4]“, PlotPoints->500, AxesLabel->{” Sec”, “Amp.”}];The Mathematica code for Fig. 5.2 is

Show[ Plot[Sin[2 Pi 2.5 t],{t,-0.1,1.1}, PlotPoints->500, AxesLabel->{” Time (Sec)“, “Amplitude”}], Plot[Cos[2 Pi 2.5 t],{t,-0.1,1.1}, PlotPoints->500, PlotStyle->Dashing[{0.01,0.01}] ];For the complex sinusoid plots (Fig. 5.7 and Fig. 5.9), see the Mathematica notebook

ComplexSinusoid.nbon Craig Sapp’s web pageof Mathematica notebooks. (The packageSCMTheory.mis required.)