Multiplication of Signals
Signal multiplication is also a basic signal operation. The multiplication of two or more signals involves multiplying their amplitudes, which creates a new signal. This basic operation is very useful in the process of modulation, filtering etc.
Mathematical representation of multiplication of two signals:
Let X1(t) and X2(t) are two signals which are multiplied to create a new signal Y(t)
Then, Y(t) = X1(t) . X2(t)
Example: X1(t) and X2(t) are two signals shown below. Find Y(t) = X1(t) . X2(t) ?
X1(t) = 3 ; [Tex]-1 \leq t \leq 3[/Tex]
0 ; otherwise
X2(t) = 2 ; [Tex]0 \leq t \leq2[/Tex]
0 ; otherwise
then Y(t) = X1(t) . X2(t)
Y(t) = 6 ; [Tex]0 \leq t \leq 2[/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