Karplusyhtälö

The Karplus-Strong algorithm, often referred to as the Karplusyhtälö in Finnish, is a digital waveguide synthesis method used for generating realistic and natural-sounding plucked or struck string instrument sounds. Developed by Kevin Karplus and Alex Strong in the 1980s, it simulates the vibration of a string and the resulting sound produced by its interaction with a resonating body.

At its core, the Karplus-Strong algorithm uses a delay line and a feedback loop. An initial excitation signal, representing the plucking or striking action, is fed into a finite impulse response (FIR) filter. The output of this filter is then fed back into the input of the delay line. The delay line's length determines the fundamental frequency of the note, while the feedback loop sustains the sound. The signal within the delay line gradually decays over time due to a damping factor applied in the feedback path, mimicking the natural attenuation of a real string.

The characteristic timbre of different instruments is achieved by applying further filtering to the output signal. This filtering can simulate the body resonance of instruments like guitars or pianos, shaping the harmonic content and adding richness to the synthesized sound. The simplicity and efficiency of the Karplus-Strong algorithm make it a popular choice in real-time audio synthesis applications and for creating a wide range of percussive and string-like textures.