RE: resolution in the fft

[dastew]

> 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



>
> > 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 time domain signal does no longer represent the physical process you have in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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