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fixed scaling in susceptibilities()

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Jan Benda 2025-05-23 19:37:40 +02:00
parent 94ea6d1313
commit 153269117a
1 changed files with 22 additions and 12 deletions
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34
spectral.py
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@ -170,17 +170,27 @@ def susceptibilities(stimulus, spikes, dt=0.0005, nfft=2**9):
```
The gain of the transfer function is the absolute value of the
transfer function:
transfer function and has the unit Hz/[s]:
```
gain = np.abs(prs)/pss
```
The second-order susceptibility can be computed like this:
The second-order susceptibility has the unit [r]/[ss] and
can be computed like this:
```
chi2 = prss*0.5/(pss.reshape(1, -1)*pss.reshape(-1, 1))
```
The variance of the stimulus is the integral over the power spectrum:
```
chi2 = prss*0.5/np.sqrt(pss.reshape(1, -1)*pss.reshape(-1, 1))
deltaf = freqs[1] - freqs[0] # same as 1/(dt*nfft)
vars = np.sum(pss)*deltaf
```
Likewise for the response.
The response spectral density prr approaches the firing rate for large frequencies.
Parameters
----------
@ -198,19 +208,18 @@ def susceptibilities(stimulus, spikes, dt=0.0005, nfft=2**9):
freqs: ndarray of float
The frequencies corresponding to the spectra.
pss: ndarray of float
Power spectrum of the stimulus.
Power spectral density of the stimulus in unit [s]^2/Hz.
prr: ndarray of float
Power spectrum of the response averaged over segments.
Power spectral density of the response averaged over segments in unit Hz^2/Hz = Hz.
prs: ndarray of complex
Cross spectrum between stimulus and response averaged over segments.
Cross spectrum between stimulus and response averaged over segments in unit Hz[s]/Hz = [s].
prss: ndarray of complex
Cross bispectrum between stimulus and response averaged over segments.
n: int
Number of segments.
"""
freqs = np.fft.fftfreq(nfft, dt)
idx = np.argmin(freqs)
freqs = np.roll(freqs, -idx)
freqs = np.fft.fftshift(freqs)
f0 = np.argmin(np.abs(freqs)) # index of zero frequency
fidx = np.arange(len(freqs))
fsum_idx = fidx.reshape(-1, 1) + fidx.reshape(1, -1) - f0
@ -219,16 +228,17 @@ def susceptibilities(stimulus, spikes, dt=0.0005, nfft=2**9):
f0 = len(freqs)//4
f1 = 3*len(freqs)//4
segments = range(0, len(stimulus) - nfft, nfft)
scale = dt/nfft/n
# stimulus:
p_ss = np.zeros(len(freqs))
fourier_s = np.zeros((len(segments), len(freqs)), complex)
n = 0
for j, k in enumerate(segments):
fourier_s[j] = np.fft.fft(stimulus[k:k + nfft], n=nfft)
fourier_s[j] = np.roll(fourier_s[j], -idx)
fourier_s[j] = np.fft.fftshift(fourier_s[j])
p_ss += np.abs(fourier_s[j]*np.conj(fourier_s[j]))
n += 1
p_ss /= n
p_ss *= scale
# response spectra:
time = np.arange(len(stimulus))*dt
p_rr = np.zeros(len(freqs))
@ -245,12 +255,12 @@ def susceptibilities(stimulus, spikes, dt=0.0005, nfft=2**9):
fourier_s12 = np.conj(fourier_s1)*np.conj(fourier_s2)
# response:
fourier_r = np.fft.fft(b[k:k + nfft] - np.mean(b), n=nfft)
fourier_r = np.roll(fourier_r, -idx)
fourier_r = np.fft.fftshift(fourier_r)
p_rr += np.abs(fourier_r*np.conj(fourier_r))
p_rs += np.conj(fourier_s[j])*fourier_r
p_rss += fourier_s12*fourier_r[fsum_idx]
n += 1
return freqs[f0:f1], p_ss[f0:f1], p_rr[f0:f1]/n, p_rs[f0:f1]/n, p_rss[f0:f1, f0:f1]/n, n
return freqs[f0:f1], p_ss[f0:f1], p_rr[f0:f1]*scale, p_rs[f0:f1]*scale, p_rss[f0:f1, f0:f1]*dt*scale, n
def diag_projection(freqs, chi2, fmax):