(BQ) Part 2 book "Signals and systems using MATLAB" has contents: Sampling theory, Discrete-Time signals and systems, The Z-Transform, fourier analysis of discrete time signals and systems, introduction to the design of discrete filters, applications of discrete time signals and systems | 3 PART Theory and Application of Discrete-Time Signals and Systems This page intentionally left blank CHAPTER 7 Sampling Theory The pure and simple truth is rarely pure and never simple. Oscar Wilde (1854–1900) Irish writer and poet INTRODUCTION Since many of the signals found in applications such as communications and control are analog, if we wish to process these signals with a computer it is necessary to sample, quantize, and code them to obtain digital signals. Once the analog signal is sampled in time, the amplitude of the obtained discrete-time signal is quantized and coded to give a binary sequence that can be either stored or processed with a computer. The main issues considered in this chapter are: I How to sample—As we will see, it is the inverse relation between time and frequency that provides the solution to the problem of preserving the information of an analog signal when it is sampled. When sampling an analog signal one could choose an extremely small value for the sampling period so that there is no significant difference between the analog and the discrete signals— visually as well as from the information content point of view. Such a representation would, however, give redundant values that could be spared without losing the information provided by the analog signal. If, on the other hand, we choose a large value for the sampling period, we achieve data compression but at the risk of losing some of the information provided by the analog signal. So how do we choose an appropriate value for the sampling period? The answer is not clear in the time domain. It does become clear when considering the effects of sampling in the frequency domain: The sampling period depends on the maximum frequency present in the analog signal. Furthermore, when using the correct sampling period the information in the analog signal will remain in the discrete signal after sampling, thus allowing the reconstruction of the original signal from the samples. .
