# 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.