Extended Karplus-Strong Algorithm

The Extended Karplus-Strong (EKS) algorithm [213] extends the KS digitar in a number of ways that will be introduced one-by-one and then brought together in the complete program listing shown in Figures D.10 and D.11. The EKS extensions were motivated by the demands of a musical composition^D.5and the interpretation of the KS algorithm as a transfer-function model of a simplified physical string [437, pp. 158-198] (see also §). They illustrate how several small digital filters can achieve various desired musical effects. We will see that the EKS can be regarded as a blend of spectral and physical (transfer-function) modeling techniques.

Figure D.4 illustrates where the various filters may be located in the patch. The filters in series outside the feedback loop can of course be implemented in any order, and the filters within the feedback loop can be arbitrarily reordered. (The series order of linear, time-invariant filters may matter in fixed-point, but generally not in floating-point.)

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Subsections

• Pick-Direction Lowpass Filter
• Pick-Position Comb Filter
• One-Zero String Damping Filter
• Two-Zero String Damping Filter
• Dynamic Level Lowpass Filter
  • Design 1: Impulse Invariant Method
  • Design 2: Bilinear Transform Method
  • Faust Implementation
  
  
• Tuning the EKS String
  • Tuning by Linear Interpolation
  • Tuning by Allpass Interpolation
  • Tuning by Lagrange Interpolation
  
  
• Adding String Stiffness
• EKS Faust Listing
• MIDI Control of an EKS Patch in PD
• Generality of the EKS Algorithm

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Order a Hardcopy of Physical Audio Signal Processing

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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.