# “Normalizing” PSD of unequal window lengths

I am acquiring time-varying data with unequal sampling (nature of the source). When building a spectrogram, I have the algorithm choose sample blocks that are are -nearly- the same length -but, they are never equal. Since the peak widths are a function of the sample block length, this means that although two sample blocks, just separated by one sample (sliding window), can have the same underlying frequency content, the total power (if one is to sum the PSD) is different. This is a problem because sometimes, again due to the nature of the data source, adjacent sample blocks can have vastly different lengths, and therefore there is a large variation in the total power.

One possible solution I have thought of is to take an interactive approach to "normalizing" the spectrum. For each spectral component, I can calculate the goodness of fit. Then, choose the best fit sinusoid and subtract it from the data. Doing this iteratively I will eventually reach a noise floor, where no sinusoid fits the data. (one benefit is that it will remove spurious peaks such as aliases). Then, using the list of amplitudes and frequencies, "rebuild" the spectrum assuming that each peak is the sinc shape and width based on the desired sample block length.

I would appreciate any feedback on this approach, or others to try. I am well versed in signal analysis, but with uniform sampling -where these problems don't show up. And after extensive literature search, I have been unable to find a solution.

• Please be more specific about the sampling being unequal. Are the samples equidistant in time within a block of samples? Or does the distant vary from sample to sample? And if that is the case, then do you know the exact sampling time or is that an unknown of the problem? – Jens Feb 2 '15 at 18:30
• I know the sampling time after the fact, and time between samples varies randomly. There are many methods to deal with this (Lomb-Scargle periodogram or other Least Squares Spectral Analysis). The issue is that they are all periodograms, which are noisy (and the data is too sparse to use Welch's, or other averaging methods). I recently learned the general name for what I'm proposing above: matching pursuit. – Adam Jones Feb 2 '15 at 22:25
• I should add, the name for the technique to finding the best fit and removing it iteratively. The idea of adding back in a generalized peak shape is something I can't find anywhere in the literature. – Adam Jones Feb 2 '15 at 22:29