Convolution Calculator
Calculate convolution of two sequences
Example: 1, 2, 3
Example: 4, 5, 6
How to Use This Calculator
Enter Sequence 1
Input the first sequence as comma-separated numbers. Example: 1, 2, 3
Enter Sequence 2
Input the second sequence as comma-separated numbers. Example: 4, 5, 6
Calculate
Click "Calculate Convolution" to see the convolution of the two sequences.
Formula
(f * g)[n] = Σ(k=0 to n) f[k] × g[n-k]
Where:
- (f * g)[n] = convolution at index n
- f[k] = kth element of first sequence
- g[n-k] = (n-k)th element of second sequence
- Σ = summation over all valid indices
Example: Convolve [1, 2] with [3, 4]
n=0: 1×3 = 3
n=1: 1×4 + 2×3 = 4 + 6 = 10
n=2: 2×4 = 8
Result: [3, 10, 8]
About Convolution Calculator
Convolution is a mathematical operation that combines two sequences to produce a third sequence. It's fundamental in signal processing, probability, and many areas of mathematics and engineering.
Key Applications
- Signal Processing: Filtering, smoothing, and analysis of signals
- Probability: Sum of independent random variables
- Image Processing: Blurring, sharpening, edge detection
- Neural Networks: Convolutional layers in deep learning
Properties
- Commutative: f * g = g * f
- Associative: (f * g) * h = f * (g * h)
- Distributive: f * (g + h) = f * g + f * h
Frequently Asked Questions
What is convolution?
Convolution is a mathematical operation that combines two sequences. It's like "sliding" one sequence over another and computing the sum of products at each position.
Why is convolution important?
Convolution is fundamental in signal processing, probability theory, image processing, and many areas of mathematics and engineering. It describes how systems respond to inputs.
Can I use different length sequences?
Yes! The calculator handles sequences of different lengths. The result length will be (length1 + length2 - 1).
What if I enter invalid numbers?
The calculator will ignore invalid entries and use only valid numbers. Make sure to separate numbers with commas.
Is convolution the same as multiplication?
No, convolution is a more complex operation. While element-wise multiplication is simple, convolution involves summing products across shifted positions.