Adam Panagos / Engineer / Lecturer

###### 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 on Dependent Variables

1/14/2023

Running Time: 8:15

This collection of videos looks at various signal operations. This first video starts with operations on dependent variables, i.e. operations on the amplitude of the signal. These operations include amplitude scaling, signal addition, signal multiplication, differentiation, and integration.

#### Signal Operations: Time Scaling

1/14/2023

Running Time: 8:07

Consider the signal x(t). A time-scaled version of the signal is x(at) where the time variable t has been replaced by at. Depending on the value of "a", this will cause x(t) to be compressed or expanded. For values of a greater than 1, time is expanded, for values a less than 1, time compression occurs.

#### Signal Operations: Time Reversal

1/14/2023

Running Time: 6:14

Consider the signal x(t). A time-reversed version of the signal is x(-t) where the time variable t has been replaced by -t. Time-reversing a signal "flips" the signal around the origin of the horizontal time axis. Several examples of time-reversal are provided.

#### Signal Operations: Time Shifting

1/14/2023

Running Time: 5:56

This video reviews the definition of time shifting a signal and provides several worked examples.

Consider the signal x(t). A time-shifted version of the signal is x(t-T) where the time variable t has been replaced by t-T. Depending on the value of "T", this will cause x(t) to be shifted to the left or right. For values of T greater than 0, this is a shift to the right. For values of T less than 0, this is a shift to the left.

#### Signal Operations: Combined Operations

1/14/2023

Running Time: 6:03

The previous videos investigated the individual signal operations of time scaling, time reversal, and time shifting. This video provides examples of combining these operations to convert the signal x(t) into the signal x(at-b). While the signal x(at-b) can be obtained using any order of operations, care must be taken, as the specific values used when shifting and scaling will change based on the order of operations.

#### Signal Operations Example #1

1/12/2016

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

1/12/2016

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

1/12/2016

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

1/12/2016

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.