Integration of Signals
In the same manner as differentiation, integration of signals can only be applied to continuous-time signals. It is the definite integration of the signal over the interval from negative infinity to present time t. This operation is used to find the area under the curve of the signal.
Mathematical representation of integration of signal
X(t) is a continuous-time signal and Y(t) represents integration of X(t)
then, [Tex]Y(t) = \displaystyle \int_{-\infty}^{t} X(t)dt[/Tex]
Integration of sin wave produces cosine wave and integration of cosine wave generates sin wave.
Example: We we integrate a square wave signal, triangular wave signal produces.
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