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Understanding the 'Phasing Method' of Single Sideband Demodulation

Complex Digital Signal Processing in Telecommunications

Introduction to Sound Processing

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FFT Spectral Analysis Software

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Physical Audio Signal Processing
    Lumped Models

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The elementary impedance element in mechanics is the dashpot which may be approximated mechanically by a plunger in a cylinder of air or liquid, analogous to a shock absorber for a car. A constant impedance means that the velocity produced is always linearly proportional to the force applied, or $ f(t) = \mu v(t)$, where $ \mu $ is the dashpot impedance, $ f(t)$ is the applied force at time $ t$, and $ v(t)$ is the velocity. A diagram is shown in Fig. 7.1.

Figure 7.1: The ideal dashpot characterized by a constant impedance $ \mu $. For all applied forces $ f(t)$, the resulting velocity $ v(t)$ obeys $ f(t) = \mu v(t)$.

In circuit theory, the element analogous to the dashpot is the resistor $ R$, characterized by $ v(t) = R i(t)$, where $ v$ is voltage and $ i$ is current. In an analog equivalent circuit, a dashpot can be represented using a resistor $ R = \mu$.

Over a specific velocity range, friction force can also be characterized by the relation $ f(t) = \mu v(t)$. However, friction is very complicated in general [419], and as the velocity goes to zero, the coefficient of friction $ \mu $ may become much larger. The simple model often presented is to use a static coefficient of friction when starting at rest ($ v(t)=0$) and a dynamic coefficient of friction when in motion ( $ v(t)\neq 0$). However, these models are too simplified for many practical situations in musical acoustics, e.g., the frictional force between the bow and string of a violin [308,549], or the internal friction losses in a vibrating string [73].

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See for details.


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