Exploring Signals and Systems: Core Concepts of Sampling Theory
Sampling theory links continuous and discrete-time signals and systems. For example, you can get a discrete-time signal from a continuous-time signal by taking samples every T seconds. This article points out some useful relationships associated with sampling theory. Key concepts include the low-pass sampling theorem, the frequency spectrum of a sampled continuous-time signal, reconstruction using an ideal lowpass filter, and the calculation of alias frequencies.
The table of properties begins with a block diagram of a discrete-time processing subsystem that produces continuous-time output y(t) from continuous-time input x(t). This block diagram motivates the sampling theory properties in the remainder of the table.
The process of converting continuous-time signal x(t) to discrete-time signal x[n] requires sampling, which is implemented by the analog-to-digital converter (ADC) block. The block with frequency response
represents a linear time invariant system with input x[n] and output y[n]. The discrete-time signal y[n] is returned to the continuous-time domain via a digital-to-analog converter and a reconstruction filter.