https://jasper-aa64.github.io/tags/convolution/Recent content in Convolution on JasperHugoen-usTue, 28 Apr 2026 00:00:00 +0800https://jasper-aa64.github.io/posts/number-theory-0-common-formulae/Tue, 28 Apr 2026 00:00:00 +0800https://jasper-aa64.github.io/posts/number-theory-0-common-formulae/Legendre’s formula, divisor and multiple convolutions in O(n log n), offline-difference batch processing for H(n)=Σf(d)g(⌊n/d⌋).https://jasper-aa64.github.io/posts/combinatorics-2-ex1-difference-convolution/Sat, 25 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-2-ex1-difference-convolution/Cross-correlation via ordinary convolution: reverse-A and reverse-B extraction methods, derivation, and Ring Trick II (cyclic shift score maximisation via difference convolution).https://jasper-aa64.github.io/posts/combinatorics-2-ex2-cyclic-convolution/Sat, 25 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-2-ex2-cyclic-convolution/Cyclic convolution definition, FFT/NTT implementation for n=2^k, zero-padding, why n must be a power of two, and the fold-back technique for arbitrary n.https://jasper-aa64.github.io/posts/combinatorics-2-1-fft-lagrange-interpolation/Sat, 25 Apr 2026 00:00:00 +0000https://jasper-aa64.github.io/posts/combinatorics-2-1-fft-lagrange-interpolation/Polynomial representations, FFT/DFT over complex numbers, Triple Sums, Fuzzy Search (difference convolution), FFT template, Lagrange interpolation (O(n²) and O(n) equidistant), sum of k-th powers, Assigning Prizes polynomial DP.