Re: Maximum resolution in Fourier

On 30 Aug, 09:21, "Marc Kroeks" <i...@xxxxxxxxxxxx> wrote:
Question about maximum resolution in Fourier.

For a project i am asked to make an application measures the EEG with a
samplewindow of about 2 seconds and take a spectrum analysis of that with a
resolution of minimum .1 Hz.

Define "resolution." There are two different meanings:

1) Ho far two close sinusoidals can be before they merge into one
2) Compute a spectrum coefficient at a given frequency

Apparently the resolution is usually given as
1/SampleLength, so in this case .5 Hz.

This is known as either the Heissenberg limit or the time-bandwidth
product which governs the solution to question 1) above. It is a
fundamental property of the DFT that you can not beaten.

Now my sampling device can make
recordings of with up to 2048 Hz sample rate, so I imagined that with a high
enough sample rate, there should be a way to disciminate a 8.5Hz wave from a
8.6Hz wave (we are looking at the peak energy in different ranges from 3 to
7, 7 to 13 and 13 to 20 Hz.

It is solely the duration of the recording that determines
the bin widths. If you double the sampling rate and keep the
duration fixed, the extra spectrum coefficients are spent
filling in the band between the old and the new sampling
frequency. The bin widths remain unaltered.

....
My question, is there a way to take a spectrum with a certain given
resolution (res Hz) when the samplelength is fixed (sl seconds) and the
samplerate (sr Hz) can be adjusted?
The idea is, that the things we are searching for last not so long, maybe a
few seconds, so that taking a longer samplelength would average that thing
out. Are "WaveLets" something that i should study for this purpose?

The only way to separate two close sinusoidals is to
record for at least as long as stated by the Heissenberg
inequality. Wavelets is a different tool to do similar
things as the DFT, but they, too, are governed by the
Heissenberg inequality.

Rune
.

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