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Index: Physical Audio Signal Processing
Physical Audio Signal Processing
Lagrange Interpolation
Explicit Lagrange Coefficient Formulas
Matlab Code for Lagrange Interpolation
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The impulse response of a system is its output signal in response to the impulse signal. For discrete time (digital) systems, the impulse is a 1 followed by zeros. In continuous time, the impulse is a narrow, unit-area pulse (ideally infinitely narrow). — Click for https://ccrma.stanford.edu/~jos/filters/Impulse_Response_Representation.html
Lagrange interpolation is interpolation based on passing a polynomial through the given sample-points. — Click for https://ccrma.stanford.edu/~jos/pasp/Lagrange_Interpolation.html
As shown in [506, §3.3.3], directly substituting into
Eq.(4.7) derives the following coefficient symmetry
property for the interpolation coefficients (impulse response) of a
Lagrange fractional delay filter:
(5.8)
where
is the order of the interpolator. Thus, the interpolation
coefficients for delay
are the ``flip'' (time reverse) of
the coefficients for delay
.