pwtools.signal.lorentz¶
- pwtools.signal.lorentz(M, std=1.0, sym=True)[source]¶
Lorentz window (same as Cauchy function). Function skeleton stolen from scipy.signal.windows.gaussian().
The Lorentz function is
\[L(x) = \frac{\Gamma}{(x-x_0)^2 + \Gamma^2}\]Here \(x_0 = 0\) and std = \(\Gamma\). Some definitions use \(1/2\,\Gamma\) instead of \(\Gamma\), but without 1/2 we get comparable peak width to Gaussians when using this window in convolutions, thus
scipy.signal.gaussian(M, std=5)
is similar tolorentz(M, std=5)
.- Parameters:
M (int) – number of points
std (float) – spread parameter \(\Gamma\)
sym (bool)
- Returns:
w
- Return type:
(M,)