How to generate noise in frequency range with numpy?

Question

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?

Answer 1

Here 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)