pwtools.signal.cauchy

pwtools.signal.cauchy(M, std=1.0, sym=True)

Lorentz window (same as Cauchy function). Function skeleton stolen from scipy.signal.windows.gaussian().

The Lorentz function is

$$L(x)=\frac{\mathrm{\Gamma }}{(x-x_0{)}^2+{\mathrm{\Gamma }}^2}$$

Here $x_0=0$ and std = $\mathrm{\Gamma }$. Some definitions use $1/2\mathrm{\Gamma }$ instead of $\mathrm{\Gamma }$, 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 to lorentz(M, std=5).

Parameters:

• M (int) – number of points

• std (float) – spread parameter $\mathrm{\Gamma }$

• sym (bool)

Returns:

w

Return type:

(M,)