Convolution Calculator
Calculate discrete convolution of two sequences with step-by-step calculations. Perfect for signal processing, image processing, probability theory, and mathematical analysis.
Discrete Convolution Calculator
Common Convolution Examples
Click on these links to see instant calculations with common sequences:
Convolution Calculations
Convolution is a mathematical operation that combines two sequences to produce a third sequence. It's fundamental in signal processing, image processing, and probability theory.
Discrete Convolution Formula
Where: f and g are input sequences, * denotes convolution
Output length = length(f) + length(g) - 1
Example: [1,2] * [3,4] = [3, 10, 8]
Common Convolution Examples
| Sequence 1 | Sequence 2 | Convolution Result | Application |
|---|---|---|---|
| [1,2,3] | [1,1,1] | [1,3,6,5,3] | Moving average |
| [1,0,1] | [1,2,1] | [1,2,3,2,1] | Impulse response |
| [1,2,1] | [1,-1] | [1,1,-1,-1] | Difference filter |
| [1,1,1,1] | [0.25,0.25,0.25,0.25] | [0.25,0.5,0.75,1,0.75,0.5,0.25] | Smoothing filter |
| [1,0,0,1] | [1,1,1] | [1,1,1,1,1,1] | Rectangular pulse |
- Signal Processing: Filter design, system analysis, and signal modification
- Image Processing: Blurring, sharpening, edge detection, and feature extraction
- Probability Theory: Combining probability distributions and random variables
- Machine Learning: Convolutional neural networks and feature detection
- Mathematics: Solving differential equations and transform analysis
Frequently Asked Questions
What is convolution in mathematics?
Convolution is a mathematical operation that combines two sequences to produce a third sequence. For discrete sequences, (f * g)[n] = Σ f[m] × g[n-m] for all valid m.
How do you calculate discrete convolution?
To calculate discrete convolution: 1) Reverse one sequence, 2) Shift it by n positions, 3) Multiply corresponding elements, 4) Sum the products. Repeat for each output position n.
What are the applications of convolution?
Convolution is used in signal processing for filtering, image processing for effects like blurring, probability for combining distributions, and machine learning in convolutional neural networks.