3.5 Introduction

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 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: $F_s=\frac{1}{T_s}$ )
• Sampled signal $x_s(n)$ . (Note that $x_s(n)=x(n{T}_s)$ )
• Real angular frequency $\Omega$
• Digital angular frequency $\omega$ . (Note that: $\omega =\Omega T_s$ )

The sampling theorem

Finished? Have at look at:

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