In the first case (low-pass filter), the frequency noise level is a constant below a cutoff frequency but zero above this threshold. When , the lineshape is Gaussian and the linewidth increases as . When , the lineshape becomes Lorentzian and the linewidth is independent of .

In the second case (high-pass filter) the frequency noise level is a constant above a cutoff frequency but zero below this threshold. When , the lineshape is Lorentzian and the linewidth is given by . When increases and approaches , a sharp peak appears at the center of the lineshape, and the other spectral components are repelled from the center, forming sidebands beyond . When , the sidebands are strongly suppressed and the lineshape is reduced to the central peak whose linewidth is limited by the sampling rate of the discrete Fourier transform.

These observations lead us to separate the frequency noise spectrum into two regions where the effect of noise on the lineshape is radically different: 1) the slow modulation area (left side of the red line), where the noise contributes to the laser linewidth, with a Gaussian shape, and 2) the fast modulation area (right side of the red line), where the noise contributes only to the wings of the line (sidebands) and not to the linewidth, thus transforming the lineshape from Gaussian to Lorentzian.