[DSP] 1. Analog and Digital Signals

A signal is a function containing information, often of time or space. Examples of signals include music, movies, telegraphs— pretty much any media that conveys information.

Analog signals have continuous domain and range. The sound of a violin is an analog signal, as its volume can have any arbitrary value. But if the music is recorded on a smartphone, it becomes a digital signal. Digital signals have discrete domain and range. To store an analog signal onto a digital device, the signal must be sampled and quantized. Sampling turns the domain into a discrete set and quantization turns the range into a discrete set.

Sampling is represented with the Shah function.

$$ III_T(t)=\sum_{k=-\infty}^{\infty}\delta(t-kT) $$