black formatter

1 files changed, 43 insertions, 9 deletions

diff --git a/qolab/math/spectral_utils.py b/qolab/math/spectral_utils.py
index 797267e..dea7840 100644
--- a/qolab/math/spectral_utils.py
+++ b/qolab/math/spectral_utils.py
@@ -4,9 +4,17 @@ from scipy.fft import rfft, rfftfreq
 
 def spectrum(t, y):
     """
-    Calculate spectrum of real value signal with stripped away zero frequency component.
-    Preserves amplitude of a coherent signal (Asin(f*t)) independent of sampling
-    rate and time interval.
+    Calculate amplitude spectrum of real value signal.
+
+    Unlike ``scipy.fft.rfft()``, preserves amplitude (A) of a coherent signal
+    ``A*sin(f*t)`` independent of sampling rate and time interval.
+    I.e. at frequency 'f' we will get 'A'.
+
+    It also strips away zero frequency component.
+
+    Returns
+    -------
+    array of frequencies and corresponding amplitudes
     """
     N = t.size
     dt = np.mean(np.diff(t))
@@ -19,9 +27,17 @@ def spectrum(t, y):
 
 def noise_density_spectrum(t, y):
     """
-    Calculate noise amplitude spectral density (ASD), the end results has unitis of y/sqrt(Hz)
-    i.e. it does sqrt(PSD) where PSD is powerd spectrum density.
+    Calculate noise amplitude spectral density (ASD) spectrum.
+
+    The end results has units of [units of y]/sqrt(Hz).
+    I.e. it calculates sqrt(PSD) where PSD is power spectrum density.
     Preserves the density independent of sampling rate and time interval.
+
+    It also strips away zero frequency component, since it uses ``spectrum``
+
+    Returns
+    -------
+    reduced array of frequencies and corresponding ASDs
     """
     freq, yf = spectrum(t, y)
     yf = yf * np.sqrt(t[-1] - t[0])  # scales with 1/sqrt(RBW)
@@ -30,11 +46,29 @@ def noise_density_spectrum(t, y):
 
 def noise_spectrum_smooth(fr, Ampl, Nbins=100):
     """
-    Smooth amplitude spectrum, especially at high frequency end.
-    Could be thought as logarithmic spacing running average.
-    Since we assume the spectrum of the nose, we do power average (rmsq on amplitudes)
-    Assumes that set of frequencies is positive and equidistant set.
+    Smooth amplitude spectral density (ASD) spectrum.
+
+    Could be thought as a running average with logarithmic spacing, so high
+    frequency components average  bins with more "hits" and thus smoothed the most.
+
+    Since we assume the input spectrum of the nose (ASD),
+    we do power average (rmsq on amplitudes).
+
+    Assumes that the input frequencies are in positive and equidistant set.
     Also assumes that frequencies do not contain 0.
+
+    Parametes
+    ---------
+    fr : list or array
+        array of frequencies
+    Ampl : list or array
+        array of corresponding noise amplitudes ASD
+    Nbin : integer
+        number of the bins (default is 100) in which frequencies are split
+
+    Returns
+    -------
+    reduced array of frequencies and corresponding ASDs
     """
 
     frEdges = np.logspace(np.log10(fr[0]), np.log10(fr[-1]), Nbins)