1.2 Analog signals

The signals signals and relations presented in this module are quite similar to those in the Discrete time signals module. So do compare and find similarities and differences!

Manipulating signals

Mathematical operations on analog signals are unambiguous. We require that the signals are defined over the same timeinterval when using operations such as addition, multiplication, division and so on.

Elementary signals&Relations

The (dirac) delta function

The delta function is a peculiar function that has zero duration, infinite height, but still unit area!Mathematically we have the following two properties

(We assume that $x(t)$ is "well behaved" at $t=$ , that is continuous and finite.)

The unit step function

The unit step function is equal to zero when its argument is negative and equal to one for non-negative arguments, see for plots.

Trigonometric functions

The trigonometric functions are central to signal processing and telecommunications. They are defined as follows, where $$ is the angular frequency. $=2\pi F_0$ , where $F_0$ is the frequency of the signal.

The complex exponential function

The complex exponential function is central to signal processing and some call it the most important signal. $i=\sqrt{-1}$ is the imaginary unit.

Euler's relations

The complex exponential function can be written as a sum of its real and imaginary part.

Matlab file

unit_step_analog.m

Take a look at

• Introduction
• Discrete time signals
• Discrete vs Analog signals
• Frequency definitions and periodicity
• Energy&Power
• Exercises