# Signals and systems

In signal processing, we are mainly interested in signals and em systems. A typical signal might be a sound, a bit of music, a photographic image, a seismic vibration, or just about any physical phenomena that can be measured over time and/or space. Usually, we represent a signal by a function , where is time, and is the value measured at time . For an image, we would have a function of two variables , where represents the intensity of the image at position in the plane, say.

A system takes one signal in, and outputs another signal. It could be a physical system: an earthquake in India starts a signal (vibrations) on one side of the earth, the earth transmits the vibrations to the other side (the system), and a new signal is felt in Calgary (the received vibrations). It could be an electrical system: a sound is picked up by a microphone (the input signal), the signal is passed to a stereo amplifier (the system), and the resulting amplified signal is output to the speakers (the output signal). It could be a computational system: a string of numbers is input to a computer, the computer churns away on the numbers (adding, subtracting, multiplying, etc -- the system), and a string of numbers is output by the computer. It could be a combination of such systems: a digital camera captures a real image through its lens, the intensities are converted to a function , and then the computer mucks around with the values of the function to compute a sharper image, represented by a new function . Here, the input is the real image, the system is the camera/computer, the output is the function .

The point is: signals are functions, and systems operate on signals.