**NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW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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## A Basic Tutorial on Sampling Theory

A basic tutorial on sampling theory is presented. Aliasing due to sampling of continuous-time signals is characterized mathematically.Shannon’s sampling theorem is proved. A pictorial representation of continuous-time signal reconstruction from discrete-time samples is given.

Subsections