Convolution Integral Calculator

Analyze sampled signal overlap with clear numerical output. Compare sequences, inspect buildup, and export polished results for deeper learning today.

Calculator Inputs

Use commas or spaces. These are sampled values of the first signal.
Use the response samples in the order they occur.
The calculator multiplies each overlap sum by Δt.

Example Data Table

Signal Start Index Samples Sampling Interval Meaning
x[n] 0 1, 2, 3 1 Input sequence
h[n] 0 1, 0.5, 0.25 1 Impulse response
y[n] 0 1, 2.5, 4.25, 2, 0.75 1 Convolution result

Formula Used

Continuous form:

\[ y(t)=\int_{-\infty}^{\infty} x(\tau)\,h(t-\tau)\,d\tau \]

Sampled numerical form used here:

\[ y[n]\approx \sum_{k=0}^{N-1} x[k]\cdot h[n-k]\cdot \Delta t \]

The tool evaluates overlapping products of the sampled signals, sums them for each output position, and scales the sum by the chosen sampling interval.

How to Use This Calculator

  1. Enter sampled values for the first signal and impulse response.
  2. Set the starting index of each sequence if they do not begin at zero.
  3. Provide the sampling interval to scale the numerical approximation correctly.
  4. Optionally normalize signals or enable term-by-term steps.
  5. Press Compute Convolution to show the result above the form.
  6. Review the output table, graph, peak value, and energy summary.
  7. Use the CSV or PDF buttons to export the computed results.

Frequently Asked Questions

1. What does this calculator compute?

It computes the numerical convolution of two sampled signals. The output shows how one sequence shapes the other across all valid overlaps.

2. Why is there a sampling interval input?

The continuous convolution integral becomes a weighted sum after sampling. The interval Δt scales each product term and improves the approximation.

3. Can I enter decimals and negative values?

Yes. The parser accepts integers, decimals, and negative values. Separate numbers with commas or spaces.

4. What do the start indices control?

They align sequences on the correct sample positions. This matters when signals begin before or after zero and affects the output index range.

5. What does normalization do?

Normalization divides each sequence by the sum of its absolute values. It helps compare signal shapes when raw amplitudes differ greatly.

6. Why is my output longer than the inputs?

Convolution length equals input length plus response length minus one. Each shift creates a new overlap, extending the result.

7. What does the graph show?

The chart plots both input sequences and the convolution result. It helps you inspect overlap behavior, output growth, and decay patterns visually.

8. Is this exact continuous convolution?

It is a sampled numerical approximation. Accuracy depends on your sampling interval and how well the samples represent the original continuous signals.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.