- DSP - Miscellaneous Signals
- DSP - Classification of DT Signals
- DSP - Classification of CT Signals
- DSP - Basic DT Signals
- DSP - Basic CT Signals
- DSP - Signals-Definition
- DSP - Home
Operations on Signals
- Operations Signals - Convolution
- Operations Signals - Integration
- Operations Signals - Differentiation
- Operations Signals - Reversal
- Operations Signals - Scaling
- Operations Signals - Shifting
Basic System Properties
- DSP - Solved Examples
- DSP - Unstable Systems
- DSP - Stable Systems
- DSP - Time-Variant Systems
- DSP - Time-Invariant Systems
- DSP - Non-Linear Systems
- DSP - Linear Systems
- DSP - Anti-Causal Systems
- DSP - Non-Causal Systems
- DSP - Causal Systems
- DSP - Dynamic Systems
- DSP - Static Systems
Z-Transform
- Z-Transform - Solved Examples
- Z-Transform - Inverse
- Z-Transform - Existence
- Z-Transform - Properties
- Z-Transform - Introduction
Discrete Fourier Transform
- DFT - Solved Examples
- DFT - Discrete Cosine Transform
- DFT - Sectional Convolution
- DFT - Linear Filtering
- DTF - Circular Convolution
- DFT - Time Frequency Transform
- DFT - Introduction
Fast Fourier Transform
Digital Signal Processing Resources
Selected Reading
- Who is Who
- Computer Glossary
- HR Interview Questions
- Effective Resume Writing
- Questions and Answers
- UPSC IAS Exams Notes
DSP - Operations on Signals Differentiation
Two very important operations performed on the signals are Differentiation and Integration.
Differentiation
Differentiation of any signal x(t) means slope representation of that signal with respect to time. Mathematically, it is represented as;
$$x(t) ightarrow frac{dx(t)}{dt}$$In the case of OPAMP differentiation, this methodology is very helpful. We can easily differentiate a signal graphically rather than using the formula. However, the condition is that the signal must be either rectangular or triangular type, which happens in most cases.
Original Signal | Differentiated Signal |
---|---|
Ramp | Step |
Step | Impulse |
Impulse | 1 |
The above table illustrates the condition of the signal after being differentiated. For example, a ramp signal converts into a step signal after differentiation. Similarly, a unit step signal becomes an impulse signal.
Example
Let the signal given to us be $x(t) = 4[r(t)-r(t-2)]$. When this signal is plotted, it will look pke the one on the left side of the figure given below. Now, our aim is to differentiate the given signal.
To start with, we will start differentiating the given equation. We know that the ramp signal after differentiation gives unit step signal.
![Differentiation Example](/digital_signal_processing/images/differentiation_example.jpg)
So our resulting signal y(t) can be written as;
$y(t) = frac{dx(t)}{dt}$
$= frac{d4[r(t)-r(t-2)]}{dt}$
$= 4[u(t)-u(t-2)]$
Now this signal is plotted finally, which is shown in the right hand side of the above figure.
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