Bridge Transmittance

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Index: Physical Audio Signal Processing

Physical Audio Signal Processing

Bridge Modeling

Bridge Reflectance

Digitizing Bridge Reflectance

Bass tones are generally low in pitch and contain a lot of low-frequency content. Low-pass filters emphasize low frequencies. For example, turning up the bass knob on a stereo controls a low-pass filter that increases the amount of low-frequency content you hear. — Click for http://ccrma.stanford.edu/~jos/filters/Simplest_Lowpass_Filter_I.html

A transverse wave causes a disturbance in the medium perpendicular to the direction in which the wave moves. — Click for http://en.wikipedia.org/wiki/Transverse

A resonator is a recursive filter that boosts signal amplitude at a particular frequency. The simplest resonator is made using a two-pole filter. The impulse response of the two-pole resonator is an exponentially decaying sinusoidal oscillation, where the zero-crossing rate is (twice) the resonance frequency. — Click for https://ccrma.stanford.edu/~jos/filters/Two_Pole.html

The velocity of an object is the time derivative of the object's displacement. Velocity is a commonly chosen wave variable in physical modeling. — Click for http://ccrma.stanford.edu/~jos/Mohonk05/Ideal_Struck_String_Velocity.html

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A filter in the audio signal processing context is any operation that accepts a signal as an input and produces a signal as an output. Most practical audio filters are linear and time invariant, in which case they can be characterized by their impulse response or their frequency response. — Click for https://ccrma.stanford.edu/~jos/filters/What_Filter.html

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Physical Audio Signal Processing

Bridge Modeling

Bridge Reflectance

Digitizing Bridge Reflectance

Bridge Transmittance

The bridge transmittance is the filter needed for the signal path from the vibrating string to the resonant acoustic body.

Since the bridge velocity equals the string endpoint velocity (a ``series'' connection), the velocity transmittance is simply

$\displaystyle \hat{\tau}_b(s) \eqsp \frac{V_b(s)}{V^{+}(s)} \eqsp \frac{V^{+}(s)+V^{-}(s)}{V^{+}(s)} \eqsp 1-\hat{\rho}_b(s).$

If the bridge is rigid, then its motion becomes a velocity input to the acoustic resonator. In principle, there are three such velocity inputs for each point along the bridge. However, it is typical in stringed instrument models to consider only the vertical transverse velocity on the string as significant, which results in one (vertical) driving velocity at the base of the bridge. In violin models (§9.6), the use of a ``sound post'' on one side of the bridge and ``bass bar'' on the other strongly suggests supporting a rocking motion along the bridge.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Bridge Transmittance

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4 Copyright © 2024-06-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University