fourier_series()

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

noexcept

Fourier series of a phase.

The phase in radians is window[0]. coefs: [a0, a1, b1, a2, b2, ...] and the result is a0 + sum a_k cos(k t) + b_k sin(k t). A final a_k without its b_k is read with b_k = 0. One sine and one cosine are evaluated, the harmonics follow by rotation.

Definition at line 291 of file Kernels.cpp.

{
    if (coefs.empty())
        return 0.0;
 
    const double phase = window.empty() ? 0.0 : window.front();
    const double c1 = std::cos(phase);
    const double s1 = std::sin(phase);
 
    double ck = c1;
    double sk = s1;
    double sum = coefs.front();
 
    for (size_t i = 1; i < coefs.size(); i += 2) {
        sum += coefs[i] * ck;
        if (i + 1 < coefs.size())
            sum += coefs[i + 1] * sk;
 
        const double next_c = ck * c1 - sk * s1;
        sk = sk * c1 + ck * s1;
        ck = next_c;
    }
    return sum;
}

References sum(), and window.

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