# Why I get negative values on using periodogram after Fourier analysis?

sorry for bothering you with this question today. I am trying to analyze wave data that was produced using a wave tank. The period used for the waves is 1.7s, the waves encountered an obstacle at some point and then reflections are expected.

I plotted one of the sensors that are a wave gauge system. And I obtained the next plot: The x is the time in seconds and the y the wave height in mm. After this I use the code:

ListLinePlot[Abs[Fourier[datcy]], PlotRange -> All]


And then I get the Fourier transform and I also plot just the data:

I know the plot is reflected and that is why I have a double one, but what I don't get in wolfram or maybe on signal analysis is how I get a power spectrum that is negative after this:

Periodogram[datcy[[All, 2]], Frame -> True,


GridLinesStyle -> Directive[Red, Dashed], PlotRange -> All] It's on DB?, if that is true then technically there are no negative values and I should interpret as a -150 DB?. I am a bit lost here. Also, have a bit of doubt about why the amplitude of the Fourier plot doest not relate to the amplitude of my wave?.

## 1 Answer

The periodogram plots the magnitude of the Fourier transform. The default magnitude scaling is decibels, defined in this function as $$10\cdot\rm{log}_{10}|y|^2$$. We can clearly see that your Fourier transform is less than 1 for a big part of the x-axis. A number that is less than 1 has a logarithm that is negative, hence the negative values.

• Thank you very much! now I can relate to the stuff I am plotting. – mrvladivostok Aug 16 '19 at 17:03