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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 theprocess 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 x t
  • Sampling frequency F s
  • Sampling interval T s (Note that: F s 1 T s )
  • Sampled signal x s n . (Note that x s n x n T s )
  • Real angular frequency
  • Digital angular frequency . (Note that: T s )

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 theoriginal signal from the sampled version.

Finished? Have at look at:

  • Proof
  • Illustrations
  • Matlab Example
  • Aliasing applet
  • Hold operation
  • System view
  • Exercises

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Source:  OpenStax, Fundamentals of signal processing. OpenStax CNX. Nov 26, 2012 Download for free at http://cnx.org/content/col10360/1.4
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