Digital Signal and Image Processing using MATLAB, Volume 1: Fundamentals, 2nd Edition

Chapter 2

Discrete Time Signals and Sampling

Signal processing consists of handling data in order to extract information considered relevant, or to modify them so as to give them useful properties: extracting, for example, information on a plane’s speed or distance from a RADAR signal, making an old and decayed sound recording clearer, synthesizing a sentence on an answering machine, transmitting information through a communication channel, etc.

The processing is called digital if it deals with a discrete sequence of values {x₁, x₂, …}. There are two types of scenarios: either the observation is already a sequence of numbers, as is the case for example for economic data, either the observed phenomenon is “continuous-time”, and the signal’s value x(t) must then be measured at regular intervals.

This second scenario has tremendous practical applications. This is why an entire paragraph of this chapter is devoted to the operation called sampling.

The acquisition chain is described in Figure 2.1.

Figure 2.1 – Digital signal acquisition

The essential part of the acquisition device is usually the analog-to-digital converter, or ADC, which samples the value of the input voltage at regular intervals – every T_s seconds – and provides a coded representation at the output.

To be absolutely correct, this coded value is not exactly equal to the value of x(nT_s). However, in the course of this ...