High resolution line spectra of the V(3,3) signal

The following is a preliminary result of performing higher resolution spectra on the raw EKG data acquired from the 5x5 grid. Below is an image of the 0-32 Hz spectrum (including glitches in the signal) taken from 9 synchronized 4 second records of 1024 pts each, acquired at a sampling rate of 256/sec from the V(3,3) signal of my 5x5 EKG grid (near the standard V4 precordial position). At the top is the average of these 9 spectra.

To produce this image, I did the following:

- Extracted 4 seconds (1024 pts) from each of 10 5 second records of raw data
and synchronized them about the R peak of a waveform, which was placed 1/2 second
into each new record.

- Discarded the last record, as it was the worst and was distorting the average.

The image above is the result from the remaining 9 records. These spectra look like they have peaks at multiples of a base frequency of about 1 Hz. I suspect that this is because my pulse rate was 1/sec for this data. I also suspect that these are actually line spectra, and appear continuous only because of discretization and data windowing (a Blackman window was used here). Although I need to do more work, this does tend to confirm my hypothesis that the EKG signal can actually be represented by a finite Fourier series with a small number of terms, and is not the result of a continuous spectrum.

Below is a 2048 pt spectrum of the average V(3,3) signal, again from 0-32 Hz. To get this I used a "trick" of duplicating the 256 pt signal 8 times, as if it was acquired from 8 seconds of data with absolute periodicity. The resulting line spectrum is very nice. This technique is valid only if one already knows the signal is periodic, since it will make a non-periodic signal so.

I will try doing some signal synthesis using the first few peaks of the spectrum to see how many terms I need before the result looks like an EKG (I will of course need to use the phase information as well). This may give me an estimate of how many independent parameters there are in the underlying dynamics for the entire EKG grid.

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