KarplusStrong

Karplus-Strong is a digital synthesis technique for creating plucked-string sounds. It is a simple form of physical modeling and digital waveguide synthesis that uses a short delay line and a feedback loop to sustain a resonant waveform. The initial excitation is provided by a short burst of noise, simulating the pluck.

Operation involves a delay line (a ring buffer) that is seeded with white noise. At each time step, the sample entering the delay is the average of the two samples at the output end, typically scaled by a decay factor. The common implementation uses a two-point averaging filter, effectively a low-pass, to model energy loss and string stiffness. The sample taken from the front of the delay line provides the output, while the averaged value is fed back into the end of the delay line. The delay length N determines the pitch, with the fundamental frequency approximately f0 ≈ fs / N, where fs is the sample rate.

Variations and extensions include using more complex loop filters to alter timbre, allowing glissandos by changing delay length over time, or injecting different excitation signals. These adjustments enable a range of plucked-string textures beyond the simplest tone.

History and impact: The algorithm was introduced in 1983 by Kevin Karplus and Alex Strong as a lightweight, efficient method for digital string synthesis. It has become a classic example in digital signal processing and physical modeling, used in education, research, and practical sound design for its simplicity and musical usefulness.