Convolution Demo Online — Interactive Signal Convolution Visualizer
Watch convolution happen step by step. See the kernel flip, slide across the input signal, and accumulate each output sample — animated in real time, entirely in your browser.
Input Signal f[n]
Kernel h[n]
Output (f ∗ h)[n]
How Convolution Works
Discrete linear convolution computes each output sample as a weighted sum of input samples, with the weights given by a flipped kernel:
$$y[n] = \sum_{k} f[k] \cdot h[n - k]$$
The procedure is often called flip-and-slide:
- Flip — reverse the kernel h to get h[−k].
- Slide — shift the flipped kernel by n positions to get h[n−k].
- Multiply — at each position, multiply the overlapping samples of f and the shifted kernel pointwise.
- Sum — add up all the products to get y[n].
- Repeat — increment n and repeat until all output samples are computed.
Output Length
If the input signal has N samples and the kernel has M samples, the linear convolution output has N + M − 1 samples. This is because the kernel starts hanging off the left edge and finishes hanging off the right edge.
Convolution as Filtering
In signal processing, convolution with a kernel is equivalent to filtering. A box blur (moving average) smooths the signal, an edge-detect kernel highlights rapid changes, and a Gaussian kernel provides smooth low-pass filtering with less ringing than a box.
Convolution FAQ
What is convolution?
Convolution is a mathematical operation that combines two signals to produce a third. In discrete form, the output y[n] equals the sum of f[k] times h[n−k] for all k. It measures how the shape of one signal is modified by the other. Convolution is the foundation of linear time-invariant (LTI) system analysis, filtering, and many signal processing operations.
What is the difference between convolution and correlation?
Convolution flips (time-reverses) one of the signals before sliding and multiplying, while cross-correlation does not flip. Mathematically, correlation of f and h equals convolution of f with the time-reversed h. Correlation measures similarity between signals; convolution describes the output of an LTI system.
Why do we flip the kernel in convolution?
Flipping arises naturally from the definition of an LTI system response. When an input passes through a system with impulse response h[n], the output at time n depends on past input values weighted by h in reverse order — h[0] weights the current input, h[1] weights the previous input, and so on. This reversal is the "flip" in the flip-and-slide procedure.
What is the difference between linear and circular convolution?
Linear convolution produces an output of length N+M−1 where N and M are the input lengths. Circular (cyclic) convolution wraps the signals around and produces an output of length max(N,M). The DFT computes circular convolution; to get linear convolution via FFT, you must zero-pad both signals to at least N+M−1 before transforming.
What are practical applications of convolution?
Convolution is used everywhere: image blurring and sharpening (2-D convolution with kernels), audio reverb (convolving a dry signal with an impulse response), low-pass/high-pass filtering, edge detection in computer vision, probability (the PDF of a sum of random variables is the convolution of their individual PDFs), and polynomial multiplication.
Cite This Tool
APA
Fourier Tools. (2026). Convolution Demo Online — Interactive Signal Convolution Visualizer. Retrieved February 17, 2026, from https://fourier.tools/tools/convolution
BibTeX
@misc{fouriertools2026conv,
title = {Convolution Demo Online — Interactive Signal Convolution Visualizer},
author = {Fourier Tools},
year = {2026},
url = {https://fourier.tools/tools/convolution},
note = {Accessed: 2026-02-17}
}