Signal Classifications and Properties

There are two types of signals one is discrete and other is continuous-signal.

Contentious time signal use time sampling to convert in to discrete time signal. The discrete time signal use reconstruction to convert continuous time signal.

Continuous time signals properties:
X(t) is the function and the t is continuous with all real values between negative infinity and infinity.

There is also piece wise continuous function. A continuous time signal x(t) is continuous at all t except at a finite or countably infinite collection of points t.

Discrete time signal properties:
It is only represent only at discrete values of time where n =1,2 ,3 ,4

There is different between discrete data are 0, undefined.

Symmetry and decomposition
Even symmetry is said to have even signal. x(-t)=x(t) This mean time reversal still equal to original signal.(Top one is even)

Odd symmetry is when -x(t)=-x(t) BUT x(t=0) = 0 (bot is odd)

Decomposition happen when even and odd function are added together.

Periodic and aperiodic
A signal x(t) can be periodic if x(t)=x(t+T) for all t and the T has to greater than 0.

Fundamental period is T initial is the minimum positive none zero value of T.

Fundamental frequency is calculate by 2pi over T initial.

(Anything does not meet above condition is aperiodic)

Practice Problems
Practice problem

Solutions

Extra Resources
From MIT - Part 1 and Part 2