Addition of Signals
The addition operation of two or more signals consists of adding amplitude of all the signal at every instant of time or space, resulting in new signals that have the characteristics of all signals combined together.
Mathematical representation of addition of signals
Let X1(t) , X2(t) , …………….. Xn(t) are n signals which are added to produce a new signal Y(t).
Then, Y(t) = X1(t) + X2(t) + X3(t)+ …………….. + Xn(t)
Example: Let X1(t) , X2(t) are two signals on which we have applied addition operation of signals that results y(t) then find the signal y(t)?
Solution:
X1(t) = 1 ; [Tex]-1 \leq t \leq 3[/Tex]
0 ; otherwise
X2(t) = 2 ; [Tex]0 \leq t \leq 2[/Tex]
0 ; otherwise
then y(t) = X1(t) + X2(t)
y(t) = 1 ; [Tex]-1 \leq t \leq 0[/Tex]
2 ; [Tex]0 \leq t \leq 2[/Tex]
1 ; [Tex]2 \leq t \leq3[/Tex]
0 ; otherwise
Graphically,
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