Introduction 1.29 2003/07/01 19:00:00 GMT-5 2004/01/09 01:42:30.978 US/Central Anders Gjendemsjo gjendems@NO-SPAM.tele.ntnu.no Anders Gjendemsjo gjendems@NO-SPAM.tele.ntnu.no Sampling Overview Introduction to sampling Contents of Sampling chapter Introduction(Current module) Proof Illustrations Matlab Example Hold operation System view Aliasing applet Exercises Table of formulas

Why sample? This section introduces sampling. Sampling is the necessary fundament for all digital signal processing and communication. Sampling can be defined as the process of measuring an analog signal at distinct points. Digital representation of analog signals offers advantages in terms of robustness towards noise, meaning we can send more bits/s use of flexible processing equipment, in particular the computer more reliable processing equipment easier to adapt complex algorithms

Claude E. Shannon

Claude Elwood Shannon (1916-2001)

Claude Shannon has been called the father of information theory, mainly due to his landmark papers on the "Mathematical theory of communication". Harry Nyquist was the first to state the sampling theorem in 1928, but it was not proven until Shannon proved it 21 years later in the paper "Communications in the presence of noise".

Notation In this chapter we will be using the following notation Original analog signal xt Sampling frequency Fs Sampling interval Ts (Note that: Fs 1 Ts ) Sampled signal xs n . (Note that xs n x n Ts ) Real angular frequency Ω Digital angular frequency ω. (Note that: ω Ω Ts )

The Sampling Theorem When sampling an analog signal the sampling frequency must be greater than twice the highest frequency component of the analog signal to be able to reconstruct the original signal from the sampled version.

Finished? Have at look at: Proof Illustrations Matlab Example Aliasing applet Hold operation System view Exercises