dcht

constexpr std::vector<Complex> dcht(const std::vector<Complex> &X, int type = 2) noexcept: Calculates the 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 result of a DCT type 2 by a factor of \(\sqrt{2/N}\) and the first element by \(1/\sqrt{2}\).

Example

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

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

Output:

13.4164 + 4.47214j
-6.299 + 4.63649j
1.65398e-15 + 0.874032j
-0.56798 - 2.12201j
-1.86324e-15 - 2.2882

References