Time-Reversal of Signals
The time reversal of a signal is the folding of the signal about the vertical axis, or the line t = 0. It is simply taking a mirror image of the signal about the vertical axis. Time reversal and time shifting are both very useful in finding the convolution of signals.
The time reversal of a continuous time signal x(t) can be represented as x(-t)
Note
- Even symmetric signals are not affected by time reversal.
- Whereas time reversal affects odd or asymmetric signals.
Example: x(t) be a signal shown below. find x(-t)?
x(t) = 1 ; [Tex] -2 \leq t \leq 2[/Tex]
0 ; otherwise
put t = -t then we get x(-t )
x(-t) = 1 ; [Tex] -2 \leq -t \leq 2 \space or -2 \leq t \leq 2[/Tex]
0 ; otherwise
both x(t) and x(-t) are same because x(t) is an Even signal.
graphically,
Example : let x(t) be a signal shown below find x(-t)?
graphically, we can find out x(-t) by taking mirror image of x(t) about vertical axis.
Basic Signal Operations
Basic signal operations are nothing but signal manipulation or modification tools that are used in signal processing and analysis. It helps to understand the signals in different situations. These operations allow the modification and enhancement of signals for specific applications.
In this article, we will discuss the basic signal operations and understand different operations related to the time and amplitude of the signal. In time transformations, we will cover time scaling, time shifting, and time reversal, and in amplitude transformations amplitude scaling of signals, amplitude reversal of signals, addition of signals, multiplication of signals, differentiation of signals and integration of signals. We also cover various advantages, disadvantages and applications of time and amplitude transformations.
Table of Content
- What are Basic Signal Operations?
- Classification
- Basic Signal Operations on Independent Variable Time
- Basic Signal Operations on Dependent Variable Amplitude
- Addition
- Multiplication
- Differentiation
- Integration