chebyshev_series()

MAYAFLUX_API double MayaFlux::Kinesis::Discrete::chebyshev_series ( std::span< const double >  window, std::span< const double >  coefs  )

noexcept

Sum of coefs[k] * T_k(window[0]) over Chebyshev polynomials.

Because T_k(cos t) = cos(kt), a sine of amplitude one passed through this has harmonic k at weight coefs[k]. The input is clamped to [-1, 1] and the sum is evaluated by Clenshaw's recurrence.

Definition at line 156 of file Kernels.cpp.

{
    if (coefs.empty())
        return 0.0;
 
    const double x = std::clamp(window.empty() ? 0.0 : window.front(), -1.0, 1.0);
    double b1 = 0.0;
    double b2 = 0.0;
 
    for (size_t k = coefs.size() - 1; k >= 1; --k) {
        const double b0 = coefs[k] + 2.0 * x * b1 - b2;
        b2 = b1;
        b1 = b0;
    }
    return coefs.front() + x * b1 - b2;
}

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