idhat

constexpr std::vector<Complex> dhat(const std::vector<Complex> &X, int type = 2) noexcept: Calculates the inverse 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 inverse Hartley transform may be calculated by applying the discrete Hartley transform on the input sequence and scaling the result by \(1/N\).

Example

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

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

Output:

3 + 1j
-1.18819 + 1.15604j
-0.66246 + 0.267261j
-0.33754 - 0.438081j
0.188191 + 0.0147763j

References