fft() [2/2]

template<typename V , require_eigen_vector_vt< is_complex, V > * = nullptr, require_var_t< base_type_t< value_type_t< V > > > * = nullptr>

plain_type_t< V > stan::math::fft ( const V &  x )

inline

Return the discrete Fourier transform of the specified complex vector.

Given an input complex vector x[0:N-1] of size N, the discrete Fourier transform computes entries of the resulting complex vector y[0:N-1] by

y[n] = SUM_{i < N} x[i] * exp(-n * i * 2 * pi * sqrt(-1) / N)

The adjoint computation is given by

adjoint(x) += length(y) * inv_fft(adjoint(y))

If the input is of size zero, the result is a size zero vector.

Template Parameters

V	type of complex vector argument

Parameters

[in]

x

vector to transform

Returns

discrete Fourier transform of x

Definition at line 41 of file fft.hpp.