Re: [Discuss-gnuradio] Signal processing question : FFT frequency resolution

[Tomaž Šolc]

Dear Steve,

in general you cannot have 1 Hz resolution by analyzing only 100 ms 
worth of signal. A simple way of looking at it is that you are only 
fitting one tenth of a 1 Hz waveform in your window. So by only looking 
at the waveform through your narrow window you cannot know whether the 
waveform repeats, say, every 1 s or every 200 ms.

If you want to have a FFT with 1 Hz resolution every 100 ms what you can 
do is to have 1 s long sliding window (e.g. first FFT is 0.0 - 1.0 s, 
second FFT is 0.1 - 1.1 s, etc.) This obviously requires changing the 
FFT size (and 1 M sample FFT is quite large).

I think the correlation approach you propose is similar to doing FFT on 
a 100 ms window that has been zero-padded to 1 s. Indeed you get 1 Hz 
frequency bins, but their content is effectively only an interpolation 
between 10 Hz bins. You gain no new information.

However, if you can make some assumptions about the signal you are 
analyzing (for example, you know that there is only a single tone 
between 1 and 10 Hz), then some kind of correlation or curve-fitting 
approach might work better than FFT.

Best regards
Tomaž

On 06. 11. 2017 16:42, Steve Gough wrote:
> Hi all,
>
> Could you please help answer a quick signal processing question ? I 
> apologize if this is the wrong mailing list.
>
> I have a sampling rate of 1M samples/second, and I perform an FFT every 
> 100ms. This gives me a frequency resolution of 10Hz (i.e. each bin size 
> is 10Hz). Is there any way I can increase my frequency resolution (say 
> from 10Hz to 1Hz) without changing the FFT size ?
>
> If I "manually" correlate different frequency sinusoids (1Hz sinusoid, 
> 2Hz sinusoid etc) with the samples acquired in the 100ms duration, can 
> this give me a higher frequency resolution (1Hz in the above case) ?
>
> Thanks in advance!
> Steve
>
>
>
>
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