inv_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::inv_fft ( const V &  y )

inline

Return the inverse discrete Fourier transform of the specified complex vector.

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

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

• The adjoint computation is given by

  adjoint(y) += (1 / length(x)) * fft(adjoint(x))

If the input is of size zero, the result is a size zero vector. The only difference between the discrete DFT and its inverse is the sign of the exponent.

Template Parameters

V	type of complex vector argument

Parameters

[in]

y

vector to inverse transform

Returns

inverse discrete Fourier transform of y

Definition at line 86 of file fft.hpp.