dhat

constexpr std::vector<Complex> dhat(const std::vector<Complex> &X, int type = 2) noexcept: Calculates the discrete Hartley transform [1] of a complex sequence.

Parameters

const std::vector<Complex> &X

A complex sequence.

Returns

template<>
type std::vector<Complex>

A complex sequence.

The discrete Hartley transform may be calculated by multiplying the result of an FFT on the input by \(1 + 1i\).

Example

std::vector<Complex> X = {1 + 2_j, 2 + 3_j, 3, 4, 5};
std::vector<Complex> Y = dhat(X);

for(int i = 0; i < Y.size(); i++){
    std::cout << Y[i] << "\n";
}

Output:

15 + 5j
-5.94095 + 5.78022j
-3.3123 + 1.3363j
-1.6877 - 2.19041j
0.940955 + 0.0738814j

References