Sign in

Not a member? | Forgot your Password?

Search Online Books

Search tips

Free Online Books

Free PDF Downloads

A Quadrature Signals Tutorial: Complex, But Not Complicated

Understanding the 'Phasing Method' of Single Sideband Demodulation

Complex Digital Signal Processing in Telecommunications

Introduction to Sound Processing

C++ Tutorial

Introduction of C Programming for DSP Applications

Fixed-Point Arithmetic: An Introduction

Cascaded Integrator-Comb (CIC) Filter Introduction


FFT Spectral Analysis Software

See Also

Embedded SystemsFPGA
Chapter Contents:

Search Physical Audio Signal Processing


Book Index | Global Index

Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?


Digital Waveguide Bowed-String

A more detailed diagram of the digital waveguide implementation of the bowed-string instrument model is shown in Fig.9.52. The right delay-line pair carries left-going and right-going velocity waves samples $ v_{sr}^{+}$ and $ v_{sr}^{-}$, respectively, which sample the traveling-wave components within the string to the right of the bow, and similarly for the section of string to the left of the bow. The `$ +$' superscript refers to waves traveling into the bow.

Figure 9.52: Waveguide model for a bowed string instrument, such as a violin.

String velocity at any point is obtained by adding a left-going velocity sample to the right-going velocity sample immediately opposite in the other delay line, as indicated in Fig.9.52 at the bowing point. The reflection filter at the right implements the losses at the bridge, bow, nut or finger-terminations (when stopped), and the round-trip attenuation/dispersion from traveling back and forth on the string. To a very good degree of approximation, the nut reflects incoming velocity waves (with a sign inversion) at all audio wavelengths. The bridge behaves similarly to a first order, but there are additional (complex) losses due to the finite bridge driving-point impedance (necessary for transducing sound from the string into the resonating body). According to [95, page 27], the bridge of a violin can be modeled up to about $ 5$ kHz, for purposes of computing string loss, as a single spring in parallel with a frequency-independent resistance (``dashpot''). Bridge-filter modeling is discussed further in §9.2.1.

Figure 9.52 is drawn for the case of the lowest note. For higher notes the delay lines between the bow and nut are shortened according to the distance between the bow and the finger termination. The bow-string interface is controlled by differential velocity $ v_{\Delta}^{+}$ which is defined as the bow velocity minus the total incoming string velocity. Other controls include bow force and angle which are changed by modifying the reflection-coefficient $ \rho(v_{\Delta}^{+})$. Bow position is changed by taking samples from one delay-line pair and appending them to the other delay-line pair. Delay-line interpolation can be used to provide continuous change of bow position [267].

Previous: Bowed Strings
Next: The Bow-String Scattering Junction

Order a Hardcopy of Physical Audio Signal Processing

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.


No comments yet for this page

Add a Comment
You need to login before you can post a comment (best way to prevent spam). ( Not a member? )