RE: resolution in the fft

[dastew]

---

From: address@hidden
To: address@hidden; address@hidden; address@hidden
Subject: RE: resolution in the fft
Date: Wed, 10 Jun 2009 12:26:28 +0000



> From: address@hidden
> To: address@hidden; address@hidden
> Subject: RE: resolution in the fft
> Date: Wed, 10 Jun 2009 10:02:22 +0200
>
>
>
> > -----Original Message-----
> > From: Matthias Brennwald [mailto:address@hidden Behalf Of
> > Matthias Brennwald
> > Sent: Wednesday, June 10, 2009 7:59 AM
> > To: address@hidden
> > Subject: Re: resolution in the fft
> >
>
> ...
>
> >
> > Dear Markus
> >
> > 1. The short answer is: you can't increase the resolution of
> > the fft,
> > because the resolution is given by the number of samples in
> > your signal.
> > 2. The somewhat longer answer is: you can increase the resolution of
> > the fft by adding more samples to your signal. You can do
> > this either
> > by using a higher sampling rate (I'd recommend to do this if
> > possible)
>
> Be careful here! You will get a longer output vector for a longer input
> vector, but as long as the time represented in the input vector remains
> constant, the frequency resolution will remain constant. The extra output
> will represent higher frequencies, i.e. an increase in bandwidth.

I don't agree with this.
If Fs (sample frequency) is the same then Fs/2 ( highest frequency that FFT produces) will be the same.
If you do a window (sample) that is 8 samples long then you have a resolution of 4 bins from DC to Fs/2.
And If you do a widow (sample) that is 1000 samples long then you have a resolution of 500 bins from DC to Fs/2.

HTH

 Doug Stewart



Now I see that I misread what was said and  now I agree with with "Rolf.Schirmacher".

If you change both the samplr rate (Fs) and the window size (sample size) ten you can get the situation where the window represents the same amount of time and thus no more resolution in frequency space.

My apologies to "Rolf.Schirmacher"

Doug Stewart


>
> > or by padding zeroes at the end of the signal (I'd classify this as
> > cheating, though).
>
> Exactly. The FFT you compute is mathematically correct, of course, but the
> time domain signal does no longer represent the physical process you have in
> mind ;-)
>
>
> So, as the physical response is calculated here according to a model, the
> best way to increase the frequency resolution is calculate the model
> response for a longer time and analyse this longer input vector. This should
> also reduce the DC component (which however will always remain as your
> signal will be positive >0 for this simple loading / unloading process for
> all times, even it is cheasing exponentially ...).
>
> Rolf
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