Related Forms

We see from the preceding example that a filtered-delay loop (a feedback comb-filter using filtered feedback, with delay-line length in the above example) simulates a vibrating string in a manner that is independent of where the excitation is applied. To simulate the effect of a particular excitation point, a feedforward comb-filter may be placed in series with the filtered delay loop. Such a ``pluck position'' illusion may be applied to any basic string synthesis algorithm, such as the EKS [437,213].

By an exactly analogous derivation, a single feedforward comb filter can be used to simulate a magnetic pick-up location on a simulated electric guitar string. A pick-up is formally the transpose of an excitation. For a discussion of filter transposition (using Mason's gain theorem [304,305]), see, e.g., [340,460].^5.8

The comb filtering can of course also be implemented after the filtered delay loop, again by commutativity. This may be desirable in situations in which comb filtering is one of many options provided for in the ``effects section'' of a synthesizer. Post-processing comb filters are often used in reverberator design and in virtual pick-up simulation.

The comb-filtering can also be conveniently implemented using a second tap from the appropriate delay element in the filtered delay loop simulation of the string, as depicted in Fig.4.19. The new tap output is simply summed (or differenced, depending on loop implementation) with the filtered delay loop output. Note that making the new tap a moving, interpolating tap (e.g., using linear interpolation), a flanging effect is available. The tap-gain can be brought out as a musically useful timbre control that goes beyond precise physical simulation (e.g., it can be made negative). Adding more moving taps and summing/differencing their outputs, with optional scale factors, provides an economical chorus or Leslie effect. These extra delay effects cost no extra memory since they utilize the memory that's already needed for the string simulation. While such effects are not traditionally applied to piano sounds, they are applied to electric piano sounds which can also be simulated using the same basic technique.

---

Order a Hardcopy of Physical Audio Signal Processing

Previous: Algebraic derivation
Next: Summary

---

written by 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 Associate Professor (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 http://ccrma.stanford.edu/~jos/ for details.