Digitization and Discrete Systems: Sampling and Quantization

Abstract

Digitization of signals allows us to use digital computers for analyzing them. Digitization is the process of converting continuous-time signals into a sequence of numbers. This is a two-stage process involving sampling in time and quantizing for representation of the samples by a finite number of digits or bits. The sampling theorem specifies the minimum rate of sampling a signal for digitization and also prescribes how to completely reconstruct the original signal from the samples. Analog data in principle has infinite resolution, which means that it can be amplified to any extent to see finer details. Digital data on the other hand must be quantized into a finite number of bits. Since the values between the quantized levels are unknown, quantization of data introduces apparent noise into the measurement. Discrete-time signals can be processed by discrete systems which behave similar to analog systems in many ways. The convolution sum is the discrete-time form of the continuous-time convolution integral. This defines the basic input-output relation of discrete-time systems.

The purpose of computation is insight, not numbers.

– Richard Hamming