lagrange_delay()

MAYAFLUX_API std::vector< double > MayaFlux::Kinesis::Discrete::lagrange_delay	(	double	delay,
		size_t	order
	)

Lagrange fractional-delay FIR coefficients.

Interpolates between samples at a non-integer offset by fitting a polynomial through order + 1 consecutive points. Order 1 is linear interpolation; order 3 at a fractional position reproduces the Catmull-Rom weights held as a matrix in Kinesis::BasisMatrices, generalised to any order.

Accuracy is highest when delay falls near the centre of the tap span, so callers wanting a delay of D samples with order N typically use an integer delay line of D - N/2 followed by this kernel for the remainder.

Parameters

delay	Delay in samples, need not be integral; clamped to [0, order]
order	Polynomial order; produces order + 1 taps

Returns

Coefficient vector of length order + 1

Definition at line 253 of file Coefficients.cpp.

{
    const size_t taps = order + 1;
    const double d = std::clamp(delay, 0.0, static_cast<double>(order));
 
    std::vector<double> h(taps, 1.0);
    for (size_t k = 0; k < taps; ++k) {
        for (size_t j = 0; j < taps; ++j) {
            if (j == k)
                continue;
            h[k] *= (d - static_cast<double>(j))
                / (static_cast<double>(k) - static_cast<double>(j));
        }
    }
    return h;
}

References delay(), h, and k.

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