Discrete Convolution Calculator
Calculate full linear or zero-padded circular convolution of two numeric sequences, with every output index shown.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Accumulate pairwise products at summed indices; for circular mode fold the full linear result modulo the entered period.
Linear c[k]=Σa[i]b[k−i]; circular indices are taken modulo N
Worked example
Linear convolution of [1,2,3] and [1,1] is [1,3,5,3]. At circular period 3 the last value wraps into index zero, giving [4,3,5].
Assumptions and input details
Each input has 1–128 real values. Circular period is an integer at least as long as each input and at most 256; shorter inputs are zero-padded. Full linear output has N+M−1 values. No sample-interval factor, cropping, correlation reversal, audio upload or signal processing outside the stated finite sums is applied.
References: SciPy: full discrete linear convolution and output size
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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