Convolution & Correlation
Compute the discrete linear convolution of two real-valued sequences, plus cross-correlation and autocorrelation. Convolution combines two series into one of length m + n − 1: (a ∗ b)[k] = Σⱼ a[j]·b[k−j] — the same operation as multiplying two polynomials, so (1,2,3) ∗ (1,1) = (1,3,5,3) (i.e. (1+2x+3x²)(1+x)). Cross-correlation measures sliding similarity; autocorrelation correlates a series with itself at every lag. Runs locally in your browser.
Series a
Series b
Result
Convolution (a ∗ b)[k] = Σⱼ a[j]·b[k−j] over all valid j, producing m + n − 1 values; it is commutative and identical to polynomial multiplication (treat each series as coefficients). Cross-correlation (a ⋆ b)[k] = Σⱼ a[j]·b[j+k] — the sliding dot product, unnormalized; it equals convolution of a with the reversed b. Autocorrelation is cross-correlation of a with itself: r[k] = Σⱼ a[j]·a[j+k], peak at lag 0. Values are real numbers parsed from comma/space/newline-separated input. Pairs with the Moving Average and Statistics tools. Everything runs locally — nothing leaves your browser.