band limited noise

band_limited_noise

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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


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)


from scipy.io import wavfile
# parameters: lower freq limit, upper freq limit, number of samples =samplerate*duration(seconds), sample rate)
x = band_limited_noise(200, 3000, 4410000, 44100)
x = np.int16(x * (2**15 - 1))
wavfile.write("test.wav", 44100, x)


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spectral bandwidth of generated mono wav file can be examined using soundspec