Signals and Systems Basics: Signal Operations
We often need to perform different signal operations such as time-shifting, compression, expansion, and reversing. Examples for each of these basic signal operations are provided, as well as a discussion on how to decompose a signal into its even and odd components.
Signal Operations Example #1
Running Time: 4:35
Basic signal operations include time shifting, scaling, and reversal. In this video, a continuous-time signal x(t) is sketched and then 4 different signal operation examples are demonstrated. Time shifting, compression, expansion, and reversal are all considered individually.
More complicated combined signal operations are considered in the subsequent videos.
Signal Operations Example #2
Running Time: 6:12
The previous video considered signal operations such as time shifting and time compression performed individually. In this video, a combined operation consisting of both a time shift and compression are considered. The original signal is sketched, and then the time-shifted time-compressed signal is derived and sketched.
Signal Operations Example #3
Running Time: 5:32
In this video, a combined operation consisting of both a time shift, scaling, and reversal are considered. The original signal is sketched, and then the time-shifted time-expanded and time-reversed signal is derived and sketched.
Even and Odd Decomposition of a Signal
Running Time: 5:23
We know that any continuous-time signal can always be decomposed into a sum of even and odd components, e.g. it can always be written as x(t) = xe(t) + xo(t) where xe(t) is an even signal and xo(t) is an odd signal.
A specific continuous-time signal x(t) is sketched in this video example, and then the equations for xe(t) and xo(t) are used to find the even and odd signal components of the signal.