Frequency-Response Matching Using

Digital Filter Design Methods

Given force inputs and velocity outputs, the *frequency response*
of an ideal mass was given in Eq.
(7.1.2) as

and the frequency response for a spring was given by Eq. (7.1.3) as

Thus, an ideal mass is an

where we assume . Similarly, point-to-point ``trans-admittances'' can be defined as the velocity Laplace transform at one point on the physical object divided by the driving-force Laplace transform at some other point. There is also of course no requirement to always use driving force and observed velocity as the physical variables; velocity-to-force, force-to-force, velocity-to-velocity, force-to-acceleration, etc., can all be used to define transfer functions from one point to another in the system. For simplicity, however, we will prefer admittance transfer functions here.

- Ideal Differentiator (Spring Admittance)
- Digital Filter Design Overview
- Digital Differentiator Design
- Fitting Filters to
Measured Amplitude Responses
- Measured Amplitude Response
- Desired Impulse Response
- Converting the Desired Amplitude Response to Minimum Phase

- Further Reading on Digital Filter Design

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University