Chapter 8 - Sampling Theory

Abstract

Processing signals continuous in both time and amplitude with a computer requires one to sample, to quantize, and to code them to obtain digital signals—discrete in both time and amplitude. The uniform sampling Nyquist condition for band-limited signals indicates that the sampling period used depends on the maximum frequency present in the signal. Moreover, by using the correct sampling period, reconstruction of the original signal from the samples is possible by Shannon's sinc interpolation. Practical aspects of the sampling and reconstruction are discussed when considering analog-to-digital (A/D) and digital-to-analog (D/A) converters. Digital communications was initiated with the concept of pulse code modulation (PCM) for the transmission of binary signals. PCM is a practical implementation of sampling, quantization and coding of an analog message into a digital message. Efficient use of the radio spectrum has motivated the development of multiplexing techniques in time and in frequency. In this chapter, we highlight some of the communication techniques that relate to the sampling theory. MATLAB is used to illustrate concepts.