TABLE OF CONTENTS Digital signal processing is the discipline that studies the rules governing the behavior of discrete signals, as well as the systems used to process them. It also deals with the issues involved in processing continuous signals using digital techniques. Digital signal processing pervades modern life. It has applications in compact disc players, computer tomography, geological processing, mobile phones, electronic toys, and many others.
In analog signal processing, we take a continuous signal, representing a continuously varying physical quantity, and pass it through a system that modifies this signal for a certain purpose. This modification is, in general, continuously variable by nature, that is, it can be described by differential equations.
Alternatively, in digital signal processing, we process sequences of numbers using some sort of digital hardware. We usually call these sequences of numbers digital or discrete-time signals. [1] The power of digital signal processing comes from the fact that, once a sequence of numbers is available to appropriate digital hardware we can carry out any form of numerical processing on them. For example, suppose we need to perform the following operation on a continuous-time signal:
| (1.1) |  |
This would be clearly very difficult to implement using analog hardware. However, if we sample the analog signal x( t) and convert it into a sequence of numbers x( n), it can be input to a digital computer, which can perform the above operation easily and reliably, generating a sequence of numbers y( n). If...
