NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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.

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Subsections

• Introduction
  • Reconstruction from Samples--Pictorial Version
  • Reconstruction from Samples--The Math
• Aliasing of Sampled Continuous-Time Signals
• Shannon's Sampling Theorem
• Figuring Out Sampling Theory by Playing Around with Complex Sinusoids
  • What frequencies are representable by a geometric sequence?
  • Recovering a Continuous-Time Signal from its Samples
    • Method 1: Additive Synthesis
    • Does it Work?

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