Differentiation of Signals
The operation of differentiation of signal is only applicable to continuous–time signals as differentiation is not defined for discontinuous signals. It represents instantaneous slope or the rate of change of the continuous signal with respect to time.
Mathematical representation of differentiation of signal:
Let x(t) is a continuous-time signal and y(t) represents differentiation of x(t)
then, [Tex]y(t) = \frac{d x(t)}{dt}[/Tex]
y(t) is the derivative of the signal x(t), which represents the instantaneous rate of change of x(t) at every instant of time.
Differentiation of sin wave produces cosine wave and differentiation of cosine wave generates sin wave.
Example: When we differentiate triangular wave, square wave is generated.
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