backward_difference() [2/2]

template<size_t N, typename T >

T MayaFlux::Kinesis::backward_difference ( std::span< const T >  samples, double  dt  )

inlinenoexcept

Convenience overload of backward_difference<N> over a raw span.

Evaluated directly on the span, newest sample first, without building a HistoryBuffer, so it does not allocate and is safe per sample on the audio thread. Samples beyond the end of a span shorter than N + 1 read as zero, the same initial condition a HistoryBuffer starts from.

Definition at line 621 of file Differential.hpp.

{
    static_assert(N >= 1, "backward_difference<N> requires N >= 1; N = 0 is the sample itself");
 
    using S = scalar_t<T>;
 
    const auto at = [samples](size_t k) -> T { return k < samples.size() ? samples[k] : T {}; };
 
    T acc = at(0);
    double binomial = 1.0;
 
    for (size_t k = 1; k <= N; ++k) {
        binomial = binomial * static_cast<double>(N - k + 1) / static_cast<double>(k);
        const double sign = (k % 2 == 0) ? 1.0 : -1.0;
        acc = acc + static_cast<S>(sign * binomial) * at(k);
    }
 
    double denom = 1.0;
    for (size_t i = 0; i < N; ++i)
        denom *= dt;
 
    return acc / static_cast<S>(denom);
}