Sound synthesis using an allpass filter chain

with audio-rate coefficient modulation

Jari Kleimola, Jussi Pekonen, Henri Penttinen, Vesa Välimäki

Dept. of Signal Processing and Acoustics

Helsinki University of Technology, TKK

Jonathan S. Abel

CCRMA, Dept. of Music

Stanford University

The example sounds from the paper can be found below. There are also some additional sounds which did not make it into the paper, but might be of interest otherwise. All sounds are 44.1 kHz 16-bit mono WAVs, normalized to -3 dB. The spectrograms at the top of this page were taken from the first two wavs, the rest of the sounds are in the order of appearance.

The software implementation with source code can be downloaded here. The zip file contains two Pure Data (PD) externals (ap~ is the chain, ksap~ is the string model, both compiled against PD v0.40.3-extended), C source, and a couple of example patches from the paper.

Spectrogram sounds

left figure: cascade - Two chains in a cascade, with dedicated modulators
right figure: string - Simple physical string model, augmented with an allpass chain inside the model

Theory

fig. 2a: single allpass stage - fx=1000 Hz, fm=100 Hz, N=1, M=0->0.99
fig. 2b: chain of 70 allpass stages - fx=1000 Hz, fm=100 Hz, N=70, M=0->0.99
fig. 4: the shape of the FM modulator - fx=2000 Hz, fm=1 Hz, N=200, M=0.99
fig. 7: comparison of AM, FM and CM - a) AM b) FM c) CM

Synth sounds

fig. 9: pseudo analog classics fx = 100 Hz, fx = 200 Hz - a) sawtooth c) square c) triangle
fig. 10: cascade 1 - N1=73, N2=100, fx=200, fm1=299, fm2=33, M1=0->0.5, M2=0->0.99
synth A: cascade 2 - N1=73, N2=1, fx=200, fm1=99, fm2=50, M1=0->0.99, M2=0.99
synth B: frequency sweep - sweeping the modulator frequency
synth C: 2-operator FM source - complex carrier, fm and M changed manually

Augmented physical models and effects

string A: no modulation - simple string model, f0=65 Hz, stretch=0.22, damp=0.98
string B: chain inside the model - N=2, fm=66, M=0.77
string C: chain outside the model - N=12, fm=66, M=0.77
fig. 11: beating - f0=1000 Hz, fm=1010 Hz
bell A: no modulation - inharmonic bell sound from a dispersive 1D waveguide
bell B: chain outside the model (wallchime) - as above, post-processed with CM

all sounds zipped - 12.5 MB