# Understanding spectral leakage in a pink noise dominated signal

I've been reading about power spectral density estimation based on the DFT, about spectral leakage, windowing functions and the Welch method. I've recorded a signal that's supposed to be pretty much pink noise, but of course, there's always something superimposed, am I'm struck by the effect it has on the result of the estimation.

The blue line shows the estimation using a rectangular window of size N with no overlap, whereas the orange line uses a Hann window with 2/3 overlap (this is supposed to give best amplitude and power flatness). N=10000 is such that I get a bin size of 1mHz and around 200 adjacent windows in the case of the boxcar window.

So I understand that there's two effects that need to be traded off when choosing a windowing function: The -3db frequency (or width of the main lobe) and the decay of the side lobe amplitude. I looked at the response of both windows.

With this knowledge I however still fail to understand whether the hann window underestimates the overall power compared to the boxcar window or if the side lobes of the boxcar window raise the overall level compared to the Hann window curve. I also don't know if the side ripples seen in the Hann window curve are "real" or just leakage from the noise upwards of 3Hz and whether this is an effect of the main lobe width or from the side lobes.

• If you want to see if something is actually pink, it's best to plot it on a log-log scale. Pink is then a straight line with a -10dB/decade slope. Its also good practice to label your axis with actual units. Commented Mar 2, 2022 at 9:59
• @Hilmar I decided in this case for the linear frequency scale as to not skew the (perceived) symmetry of the lobes in the orange curve. Units are usually good practice, I agree, but in some cases (I'd argue this is one), "Hz" or "rad" is irrelevant and just distracts from the shape. Commented Mar 2, 2022 at 10:03