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Delay-Free Loops

Backward-Euler numerical integrator:

$\displaystyle v_n \;=\;v_{n-1} + T\,\hat{\dot v}_n
$

Corresponding BE digital mass model:

$\displaystyle \hat{v}_n \;=\;\hat{v}_{n-1} + \frac{T}{m} f_n
$

where $\hat{v}_n$ is the $n$th sample of the estimated velocity, $f_n$ is the driving force at sample $n$, $m$ is the mass, and $T$ is the sampling interval


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Download DigitizingNewton.pdf
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``Introduction to Physical Signal Models'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2020-01-22 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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