Whitening waveform from known PSD

[francois-rozet]

Hi 👋, I am new to PyCBC and I'm trying to simulate and process waveforms in the frequency domain.
Unfortunately, I am unable to whiten the waveforms in the frequency domain even though I have the PSD used to generate the noise.

In practice, I have a waveform s in the frequency domain (FrequencySeries) projected on the H1 detector. I add noise to s with

cutoff_freq = 20.
psd = aLIGOZeroDetHighPower(len(s), s.delta_f, cutoff_freq)
noise = frequency_noise_from_psd(psd)
s = s + noise

Is there a way to perform whitening on s without transforming it to the time domain (TimeSeries), since I already have the psd of the noise ?

[francois-rozet]

I've done some research and looked at the source code. The solution I found is to normalize the signal with respect to the PSD.

In my example,

idx = int(psd.duration * cutoff_freq)
norm = np.sqrt(psd / psd.delta_f)
norm[:idx] = norm[idx]
norm[-1:] = norm[-2]

s = s / norm

norm[:idx] = norm[idx] and norm[-1:] = norm[-2] prevent divisions by zero for frequencies that are out-of-range.