Karplus-Strong algorithm
The Karplus-Strong algorithm is a method of sound synthesis which is particularly suitable for simulating the sound of stringed instruments . The algorithm was presented in the Computer Music Journal in 1983 by Kevin Karplus and Alex Strong. A US patent was granted in 1987. The algorithm is based on a circuit in which sound samples circulate and pass through a filter . A random noise is initially fed into this cycle, which is modified and output by the filter once in each cycle.
functionality
First, p samples with random noises are introduced into the circuit, which fill a memory ( FIFO ) that can hold p samples. Then the input is terminated and the first sample leaves the memory, is output, runs through the filter and is now filled into the memory in its modified version. The whole thing happens at a rate of R samples per second, which leave the memory and go through the circuit.
Due to a psychoacoustic phenomenon, the "periodicity pitch" (periodic pitch), one perceives a pitch of R / p Hz. The timbre is determined by the selected input noise. In order to simulate the decay characteristics of a plucked string, a low-pass filter is used. As a result, high-frequency components of the noise lose energy more quickly than the low-frequency ones.
From the point of view of technical signal processing, there is a convolution of the signal with itself, in which a dedicated section, namely the resulting duration, becomes the period of the reproduced signal. As a result of the damping, the signal gradually approximates a sine wave. The harmonic content initially contained in the noise pattern decays, similar to the behavior of a deflected string.
Remarks
Noises with a dense spectrum are particularly suitable as input samples, such as B. a white noise . If you want to simulate different strengths when striking the strings, let the samples circulate a few times before the first output without outputting them. This creates a more realistic effect than simply adjusting the volume before outputting.
Web links
- Derivation of the algorithm and implementation in LabView (English)