What Is a Signal? The Foundation of DSP

The Ubiquitous Nature of Signals

Signals are everywhere. From the electrical impulses firing in your neurons as you read this, to the Wi-Fi packets carrying this article through the air, to seismic waves traveling through Earth’s crust—every physical phenomenon that varies with time, space, or any independent variable is a signal.

In engineering terms, a signal is any physical quantity that varies with respect to one or more independent variables (time, space, distance, temperature) and carries information. Mathematically, it’s expressed as a function of one or more independent variables.

Examples:

• $s_1(t) = 5t$ — a signal varying with time $t$
• $s_2(x) = 2x^2$ — a signal varying with spatial coordinate $x$
• $f(x, y) = 2x^2 + 3y$ — a multivariable signal depending on two spatial coordinates

---