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Filter Design Approach

We've been talking about the white-box approach in which every first-order element (mass, spring, ...) is explicitly modeled by a first-order finite-difference scheme. This is especially needed for elements that are time varying or pushed into nonlinear regimes of operation.

When a system is linear and time-invariant (LTI), there is no need for such fine-grained modeling, and we can take a a black-box approach, in which we need only model the frequency response from the input(s) to output(s) of the system using a digital filter.

Filter Design Approach to Ideal Integrators and Differentiators

Consider the following simple cases:

The digital filter design formulation typically minimizes frequency-response error with respect to the filter coefficients

Ideal Frequency Responses

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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 © 2020-06-27 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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