Digital Signal Processing Tutorial
Operations on Signals
Basic System Properties
Z-Transform
Discrete Fourier Transform
Fast Fourier Transform
Digital Signal Processing Resources
Selected Reading
- 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
Operations Signals - Integration
DSP - Operations on Signals Integration
Integration of any signal means the summation of that signal under particular time domain to get a modified signal. Mathematically, this can be represented as −
$$x(t) ightarrow y(t) = int_{-infty}^{t}x(t)dt$$Here also, in most of the cases we can do mathematical integration and find the resulted signal but direct integration in quick succession is possible for signals which are depicted in rectangular format graphically. Like differentiation, here also, we will refer a table to get the result quickly.
| Original Signal | Integrated Signal |
|---|---|
| 1 | impulse |
| Impulse | step |
| Step | Ramp |
Example
Let us consider a signal $x(t) = u(t)-u(t-3)$. It is shown in Fig-1 below. Clearly, we can see that it is a step signal. Now we will integrate it. Referring to the table, we know that integration of step signal yields ramp signal.
However, we will calculate it mathematically,
$y(t) = int_{-infty}^{t}x(t)dt$
$= int_{-infty}^{t}[u(t)-u(t-3)]dt$
$= int_{-infty}^{t}u(t)dt-int_{-infty}^{t}u(t-3)dt$
$= r(t)-r(t-3)$
The same is plotted as shown in fig-2,
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