Digital Signals Sampling and Quantization RS （数字信号采样和量化）.pdf

DIGITAL SIGNALS - SAMPLING AND QUANTIZATION Digital Signals - Sampling and Quantization A signal is defined as some variable which changes subject to some other independent variable. We will assume here, that the independent variable is time, denoted by t and the dependent variable could be any physical measurement-variable which changes over time - think for example of a time varying electric voltage. We will denote the generic measurement variable with x or x(t) to make its time-dependence explicit. An elementary example of such a signal is a sinosoid. When we want to represent such a sinosoid in the digital domain, we have to do two things: sampling and quantization which are described in turn. Sampling The first thing we have to do, is to obtain signal values from the continuous signal at regular time-intervals. This process is known as sampling. The sampling interval is denoted as Ts and its reciprocal, the sampling- frequency or sample-rate is denoted as f , where f = 1/T . The result of this process is just a sequence of s s s numbers. We will use n as an index into this sequence and our discrete time signal is denoted as x [n] - it is customary in DSP literature to use parentheses for continuous variables such as the time t and brackets for discrete variables such as our sample index n. Having defined our sampling interval T , sampling just s extracts the signals value at all integer multiples of Ts such that our discrete time sequence becomes: x [n] = x(n · T ) (1)