The signal of interest to me is the ocean wave height as a function of time at a particular location. Its power or variance spectrum is estimated by buoys at regular time intervals.
Specifically, the spectral data is discrete in both time and frequency. The spectral data spans 0.02 and 0.485 Hz, in approximately 0.02 Hz intervals. This spectrum is reported every hour (3600 seconds).
I would like to estimate the spectrum at finer time intervals (every 10 minutes, say). If have the spectrum at 1 am, 2 am, ... 11 am, what is the best way to estimate the spectrum at 5:30 am? I'm considering a linear interpolator, or a conventional decimator, but I'm wondering if there is an optimal way to do this.