Next  |  Prev  |  Top  |  REALSIMPLE Top

Adding A Lowpass Filter

There is one final weakness of the digital waveguide model that we have developed so far. Energy at higher frequencies in vibrating strings tends to decay more quickly than at lower frequencies. This is true of physical systems in general because any mass vibrating at an infinitely-large frequency would have infinite energy. However, the current model does not implement this decay phenomenon. The simplest way to ensure that high-frequency energy decays quickly is to insert what is called a lowpass filter into the loop. Lowpass filters pass more energy at lower frequencies than they do at higher frequencies. In a loose sense, this is equivalent to assigning smaller $g$'s to higher frequencies than to lower frequencies. Figure 7 depicts the finalized basic digital waveguide model that incorporates a lowpass filter.

Figure 7: Digital waveguide model with lowpass filter
\includegraphics{figures/fullwaveguide2.eps}

Sharp edges (or transients) in signals are characterized by energy at high frequencies. Since lowpass filters remove high-frequency energy, they tend to smooth out sharp edges in signals. This is precisely what the lowpass filter in the digital waveguide model does. For instance, if the waveguide is initialized with a rectangular pluck, the rectangular signal not only becomes slightly smaller due to $g$, but the sharp edges become smoothed out more and more after each trip around the waveguide. The result is visualized in Figure 8 with one animation frame taken every period of $N$ samples.

Figure 8: Visualization of a damped vibrating string simulation with lowpass filter (one animation frame per period of $N$ samples in time) where the string is initialized according to a rectangular pluck
Image digital-gain-LPF

This improved digital waveguide physical model more accurately captures the behavior of a vibrating string, and so, as you will experience in the following section, it also produces much more realistic simulated string sounds. Much more information is available on digital waveguide modeling [1].


Next  |  Prev  |  Top  |  REALSIMPLE Top

Download waveguideintro.pdf

``Plucked String Digital Waveguide Model'', by Edgar J. Berdahl, and Julius O. Smith III,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2008-06-05 under the Creative Commons License (Attribution 2.5), by Edgar J. Berdahl, and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA