I have a main signal, for example sinus with period of 200 samples.
I would like to add a noise to this signal. The periods of "noise signal parts" should be in range for example 5-30 samples.
I thought that will be enough to generate multiple sinuses in this range with different randomly chosen amplitudes:
noise = np.sin(np.array(range(N))/0.7)*np.random.random(1) + np.sin(np.array(range(N))/1.1)*np.random.random(1) + np.sin(np.array(range(N))/1.5)*np.random.random(1)
But this solution is still too much "deterministic" for my purpose.
How could I generate noise with randomly changing amplitude and period?
In MathWorks' File Exchange: fftnoise - generate noise with a specified power spectrum you find matlab code from Aslak Grinsted, creating noise with a specified power spectrum. It can easily be ported to python:
def fftnoise(f):
f = np.array(f, dtype='complex')
Np = (len(f) - 1) // 2
phases = np.random.rand(Np) * 2 * np.pi
phases = np.cos(phases) + 1j * np.sin(phases)
f[1:Np+1] *= phases
f[-1:-1-Np:-1] = np.conj(f[1:Np+1])
return np.fft.ifft(f).real
You can use it for your case like this:
def band_limited_noise(min_freq, max_freq, samples=1024, samplerate=1):
freqs = np.abs(np.fft.fftfreq(samples, 1/samplerate))
f = np.zeros(samples)
idx = np.where(np.logical_and(freqs>=min_freq, freqs<=max_freq))[0]
f[idx] = 1
return fftnoise(f)
Seems to work as far as I see. For listening to your freshly created noise:
from scipy.io import wavfile
x = band_limited_noise(200, 2000, 44100, 44100)
x = np.int16(x * (2**15 - 1))
wavfile.write("test.wav", 44100, x)