num::spectral::dst1

Defined in header <spectral/dst.hpp>

vec<real> dst1(const vec<real> &x);

Unnormalised DST-I of an N-point vector via complex FFT.

X[k] = sum_{j=1}^{N} x[j] * sin(jkpi/(N+1)), k = 1..N (stored 0-indexed). Odd-extension y = [0, x, 0, -rev(x)] has length M = 2(N+1). FFT(y)[k] = -2i * sum sin(...) => DST(x)[k-1] = -Im(FFT(y)[k]) / 2.