idcht

constexpr std::vector<Complex> idcht(const std::vector<Complex> &X, int type = 2) noexcept: Calculates the inverse discrete Chebyshev 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 Chebyshev transform may be calculated by scaling the input sequence by a factor of \(\sqrt{N/2}\) and the first element by \(\sqrt{2}\) and applying an IDCT type 2 to the result.

Example

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

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

Output:

27.129 + 11.2586j
-22.9178 + 7.81229j
7.44259 + 2.23607j
-6.2927 - 3.34015j
0.229061 - 6.78645j

References