Free Convolution Calculator
Calculate discrete convolution for two sequences, inspect each overlap, and see the full output sequence with correct indexing. Useful for digital filters, moving averages, impulse responses, and probability sequences.
0: 1 1: 2 2: 3
Each output point is a dot product of overlapping samples. That makes the calculator useful for signal processing, digital filters, moving averages, and discrete probability distributions.
How Discrete Convolution Works
Convolution is the algebra of overlap. For each output index, the calculator multiplies the samples that line up, then adds those products together. That makes convolution the core operation behind FIR filters, smoothing windows, and many sequence-based math problems.
Signal processing
Use convolution to model how a system responds when an input signal passes through a filter.
Probability
Convolving two discrete distributions gives the distribution of their sum.
Index-aware output
Start indices keep the output aligned when a sequence begins before or after zero.
Continuous Convolution, in Brief
Continuous convolution uses an integral instead of a sum: one function is flipped and shifted across the other, and the overlap is integrated over all shifts. This page stays focused on the discrete version, which is the right tool for sampled data and digital systems.
Frequently Asked Questions
What is discrete convolution?
Discrete convolution combines two sequences by sliding one sequence across the other and summing the overlapping products at each output position. It is used in filters, systems analysis, and probability.
Why does the calculator ask for start indices?
Start indices keep the output aligned correctly when your sequences do not begin at zero. That matters in signal-processing and difference-equation problems where the index labels carry meaning.
What is the output length of a convolution?
If the first sequence has length m and the second has length n, the output has m + n - 1 samples.
Is this a continuous convolution calculator?
This page focuses on discrete sequences. Continuous convolution is usually handled with integrals, so this tool is best suited for signal processing, probability mass functions, and other sampled data.
Related Calculators
Simpson's Rule Calculator
Approximate definite integrals from a function or equally spaced table values.
P-Value Calculator
Calculate statistical significance for various tests.
Standard Deviation Calculator
Calculate population and sample standard deviation, variance, and mean.
Significant Figures Calculator
Count sig figs and evaluate math expressions properly.
Share This Calculator
Found this tool helpful?
Help others discover it with one click.
Copy Link
Suggested hashtags: #convolution #calculator #Calculator #FreeTools #AICalculator