Analyze sequence products with accurate padding controls. View indexed outputs, theorem checks, and precision settings. Download clean reports for study, teaching, and signal analysis.
This worked example uses A = [1, 2, 3, 4] and B = [2, -1, 0.5] in full linear mode.
| Sample n | y[n] | Interpretation |
|---|---|---|
| 0 | 2 | First overlap contains only the leading terms. |
| 1 | 3 | Two products contribute to the running total. |
| 2 | 4.5 | All three filter values now overlap the sequence. |
| 3 | 6 | Central overlap usually carries the largest combined weight. |
| 4 | -2.5 | Trailing overlap begins to shrink near the boundary. |
| 5 | 2 | Only the last pair of samples remains active. |
Linear convolution: y[n] = Σ x[k] · h[n - k]. Each output sample sums every valid product between the two sequences at shift n.
Circular convolution: yN[n] = Σ x[k] · h[(n - k) mod N]. The modulo wraps indices onto a period of length N.
Fourier convolution theorem: Y[m] = X[m]H[m], then y[n] = IDFT{Y[m]}. Zero-padding to the full linear length prevents aliasing for linear mode.
Same mode: this page centers the full convolution and returns a result with the same length as Sequence A.
Valid mode: this page returns only the shifts where the shorter sequence fully overlaps the longer one.
It computes discrete convolution between two real-valued sequences. You can evaluate full, same, valid, or circular outputs and inspect indexed results, energy, sums, and Fourier-theorem verification.
The Fourier theorem turns convolution into pointwise multiplication in the frequency domain. That viewpoint is important in signal analysis, filtering, spectral methods, and algorithm design.
Full returns every possible overlap. Same returns a centered result with Sequence A’s length. Valid returns only positions where the shorter sequence overlaps completely.
Use circular convolution for periodic sequences, block processing, and discrete transform applications. Pick a length N that matches the intended period or transform size.
Start indices let you model sequences that begin at nonzero sample numbers. They shift the reported output indices so your result lines up with textbook notation.
A direct DFT check is computationally heavier for long sequences. The page still computes the primary convolution, but it may skip the verification step to keep reporting responsive.
This version focuses on real-valued samples for clean input and output tables. Complex support can be added later by splitting real and imaginary components.
They contain the visible result table with sample index, scaled position, and convolution value. This makes it easy to archive, share, or reuse the computed sequence.
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.