Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications

1.3 STATISTICAL SIGNAL PROCESSING WITH MATLAB®

Although continuous-time random processes and discrete-time random sequences are covered in this book, all simulation examples generated using MATLAB®1 are necessarily discrete-time sequences. In this section, we provide an overview of methods for generating random sequences, and of filters for modifying their properties and frequency-domain characteristics.

1.3.1 Random Number Generation

The random number generators in MATLAB provide a means for realizing a pseudorandom sequence where the samples across time instants are independent and thus uncorrelated. There are two basic random number generators:

1. randn(N,1). Generates an vector of numbers on from the standard Gaussian distribution with zero mean and unit variance.

2. rand(N,1). Generates an vector of numbers from the continuous uniform distribution on .

Example histograms with samples for the two random number generators are shown in Figure 1.31, where n is the number of samples ...