TABLE OF CONTENTS Signals with known characteristics are often needed to test signal processing procedures or to simulate signals with specific properties. This section will introduce methods to generate random signals with different first order probability characteristics and to further exemplify the probability concepts for describing signals.
Random number generators can be used to generate random number sequences that can be used to simulate signals by simply assuming that successive numbers are also successive time samples. Almost all higher-level languages and environments have random number function calls in the system library. One of the most used algorithms is the linear congruential generator, and it will be described briefly. It has the recurrence relationship
| (4.84) |  |
where I( n), a, and c are integers, b is the computer's wordlength, and m = 2 b. Therefore, the integers range in value from 0 to m - 1 inclusive. The sequence is initiated with a seed number, I(0), and the recursion relationship is used to generate subsequent numbers. All system functions return a floating point number, y( n) = I( n) /m; that is, y( n) has a magnitude range 0 ? y( n) < 1 and is uniformly distributed. Thus for these types of algorithms, m y = 0.5 and 
= 0.0833.
The goal is to produce a series of random numbers that...
