4. Winer denoise audio filter

import matplotlib.pyplot as plt
import torch

from cutcutcodec.core.filter.audio.add import FilterAudioAdd
from cutcutcodec.core.filter.audio.cat import FilterAudioCat
from cutcutcodec.core.filter.audio.equation import FilterAudioEquation
from cutcutcodec.core.filter.audio.subclip import FilterAudioSubclip
from cutcutcodec.core.filter.audio.wiener import FilterAudioWiener
from cutcutcodec.core.generation.audio.equation import GeneratorAudioEquation
from cutcutcodec.core.generation.audio.noise import GeneratorAudioNoise

4.1. Create a syntetic noise

In a winer filter, the noise has to be ergodic.

# simulate a wite noise plus a 50Hz sector electrical noise
(noise,) = FilterAudioEquation(
    GeneratorAudioNoise(0).out_streams,
    "0.3*fl_0 + 0.2*sin(2*pi*100*t) + 0.1*sin(2*pi*200*t) + 0.1*sin(2*pi*400*t) + 0.05*sin(2*pi*800*t)",
    "0.3*fr_0 + 0.2*cos(2*pi*100*t) + 0.1*cos(2*pi*200*t) + 0.1*cos(2*pi*400*t) + 0.05*cos(2*pi*800*t)",
).out_streams

4.2. Create a syntetic perfect signal

# make a stereo musical note A
(perfect,) = GeneratorAudioEquation(
    "0.6*sin(2*pi*440*t) + 0.2*sin(2*pi*880*t)",
    "0.6*cos(2*pi*440*t) + 0.2*cos(2*pi*880*t)",
).out_streams
# add 10 seconds of silence at the beginning
(perfect,) = FilterAudioCat(
    [FilterAudioSubclip(GeneratorAudioEquation("0", "0").out_streams, 0, 10).out_streams[0], perfect]
).out_streams

4.3. Add the two signals to make realisic noisy signal

(noisy,) = FilterAudioAdd([perfect, noise]).out_streams

4.4. Use Winer filter to denoised the signal

(noise_sample,) = FilterAudioSubclip([noisy], 0, 5).out_streams  # select 5 second of noise
(denoised,) = FilterAudioWiener(
    [noise_sample, noisy], level=1.0
).out_streams

rate = 8000
noise_frame = noise.snapshot(0, rate, 20*rate)
perfect_frame = perfect.snapshot(0, rate, 20*rate)
noisy_frame = noisy.snapshot(0, rate, 20*rate)
denoised_frame = denoised.snapshot(0, rate, 20*rate)

4.5. Visualise the signal

# display noisy frame
plt.title("Spectogram of the noisy signal")
plt.xlabel("time (s)")
plt.ylabel("frequency (Hz)")
plt.specgram(noisy_frame[0], Fs=noisy_frame.rate, NFFT=1024)
plt.show()

# display denoised frame
plt.title("Spectogram of the denoised signal")
plt.xlabel("time (s)")
plt.ylabel("frequency (Hz)")
plt.specgram(denoised_frame[0], Fs=denoised_frame.rate, NFFT=1024)
plt.show()

# signal in temporal domains
plt.title("Winer filtering in temporal domain.")
plt.plot(torch.arange(noisy_frame.shape[1]) / noisy_frame.rate, noisy_frame[0], label="noisy signal")
plt.plot(torch.arange(denoised_frame.shape[1]) / denoised_frame.rate, denoised_frame[0], label="denoised signal")
plt.legend()
plt.show()