TABLE OF CONTENTS The single most important concept when simulating communication systems on a computer is that there is no such concept as continuous. All variables such as time, amplitude, and frequency are stored as numbers in the computer with some sort of quantization. To see why this is true and necessary, consider the following question: How many points are there on a time line segment in the range 0 ? t ?1 seconds? The answer, of course, is infinite. One of the strange things in mathematics is that the number of points in the range 0 ? t ?2 seconds is the same as for the range 0 ? t ?1 seconds!
Given that we must quantize all variables, let us start with time. Time is the independent variable that drives all system simulations. The fundamental question is: What is the smallest time step T that is needed? Usually one specifies sample rate f s = 1/ T in samples/second. If we choose f s too large, the number of time steps needed to complete the simulation will be very long, slowing the execution time. If we take f s too small, then the effects of aliasing (to be described below) will seriously affect the simulation output. The answer to this question is the Nyquist Sampling Theorem. The reader is strongly urged to understand this theorem before embarking on a simulation.
Consider any continuous time function r(t). The...
