Signals and Systems - Electrical Engineering

CHAPTER 7 Sampling Theory......................................................................................

The pure and simple truth

is rarely pure and never simple.

Oscar Wilde (1854–1900)

Irish writer and poet

7.1 Introduction

Since many of the signals found in applications such as communications and control are analog, if
we wish to process these signals with a computer it is necessary to sample, quantize, and code them
to obtain digital signals. Once the analog signal is sampled in time, the amplitude of the obtained
discrete-time signal is quantized and coded to give a binary sequence that can be either stored or
processed with a computer.

The main issues considered in this chapter are:

n How to sample—As we will see, it is the inverse relation between time and frequency that provides
the solution to the problem of preserving the information of an analog signal when it is sampled.
When sampling an analog signal one could choose an extremely small value for the sampling
period so that there is no significant difference between the analog and the discrete signals—
visually as well as from the information content point of view. Such a representation would,
however, give redundant values that could be spared without losing the information provided
by the analog signal. If, on the other hand, we choose a large value for the sampling period,
we achieve data compression but at the risk of losing some of the information provided by the
analog signal. So how do we choose an appropriate value for the sampling period? The answer is
not clear in the time domain. It does become clear when considering the effects of sampling in
the frequency domain: The sampling period depends on the maximum frequency present in the
analog signal. Furthermore, when using the correct sampling period the information in the analog
signal will remain in the discrete signal after sampling, thus allowing the reconstruction of the
original signal from the samples. These results, introduced by Nyquist and Shannon, constitute

Signals and Systems Using MATLAB®. DOI: 10.1016/B978-0-12-374716-7.00011-9
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