HBWT_AnaSynth

Python implementation of the Harmonic Band Wavelet Transform (HBWT).
N.B.: Only mono WAV format files are supported!

Please cite these works and software if you use HBWT_AnaSynth in your research:
[1] A. A. Díaz Salazar, R. S. Mendes, "Analysis/Synthesis Of The Andean Quena Via Harmonic Band Wavelet Transform", In: Proceedings of the 18th International Conference on Digital Audio Effects (DAFx-15), 2015, pp. 1–4. Online.
[2] A. A. Díaz Salazar, "HBWT_AnaSynth", Campinas, Brazil, 2015. Online.
[3] A. A. Díaz Salazar, “Analysis of musical instruments via the Harmonic Band Hurst Exponent: Comparative study of the Quena and other wind instruments” (in Portuguese), University of Campinas, 2015. Online.

Example

Run ex_hbwt_pr.py for an example of HBWT perfect reconstruction of a sound signal.
Open ex_hbwt_pr_notebook.py for the notebook version.

import lib.libhbwt as HBWT_Ana # HBWT Analysis
import lib.libihbwt as HBWT_Synth # HBWT Synthesis
from scipy.signal import daub, qmf # Daubechies wavelets
from scipy.io import wavfile # WAV files
from lib.stereo2mono import * # stereo to mono conversion
from lib.float32 import * # 'float32' input data type normalization
from lib.estimatef0 import * # fundamental frequency estimation

# Load input signal
filename = 'quena'
fs, x = wavfile.read('./input/'+filename+'.wav') # input signal 'x'
if x.ndim == 2: x = stereo2mono(x) # mono audio conversion
xn, data_type = float32(x) # data type normalization
# Model parameters
h     = daub(11) # Daubechies-11 low pass filter coefficients
g     = qmf(h) # Daubechies-11 high pass filter coefficients
f0, P = estimatef0(xn, fs) # f0: fundamental frequency (Hz), P: signal period (in number of samples)
N     = 5 # levels of wavelet decomposition
# Analysis step
a, b, w = HBWT_Ana.hbwt(xn, h, g, P, N) # HBWT decomposition 'a' and 'b' and CMFB filter bank 'w'
# Synthesis step
yn = HBWT_Synth.ihbwt(a, b, h, g) # reconstructed signal 'xn'
# Write ouput signal
yn = yn[:len(x)] # prune ending zeros
y  = ifloat32(yn, data_type) # data type back normalization
wavfile.write('./output/'+filename+'_synth.wav', fs, y) # write WAV output file

References

[1] A. A. Díaz Salazar, R. S. Mendes, "Analysis/Synthesis Of The Andean Quena Via Harmonic Band Wavelet Transform", In: Proceedings of the 18th International Conference on Digital Audio Effects (DAFx-15), 2015, pp. 1–4. Online.
[2] A. A. Díaz Salazar, "HBWT_AnaSynth", Campinas, Brazil, 2015. Online.
[3] A. A. Díaz Salazar, “Analysis of musical instruments via the Harmonic Band Hurst Exponent: Comparative study of the Quena and other wind instruments” (in Portuguese), University of Campinas, 2015. Online.
[4] P. Polotti, G. Evangelista, "Fractal Additive Synthesis via Harmonic-Band Wavelets", In: Computer Music Journal, vol. 25, no. 3, pp. 22–37, Mar. 2001. DOI: 10.1162/014892601753189510.