FPGA Central

Hi NG,

I would like to have someone confirm (or not), that I have understood
the following correctly:

I have a signal which is sampled at .125 Hz. In this signal, a pulse
lasting for 130 samples (i.e. 1040 s) is present. I would like to
analyze this pulse and see the frequency content of it. I therefore
window it with some window (Hanning or something like it) and calculate
the FFT. In my spectrum I can now resolve frequencies up to .125/2
(Nyquist), and I will have 130/2 frequency bins in my spectrum which
will govern the frequency resolution. I can therefore resolve 65
different frequencies between 0 Hz and 0.0625 Hz.

So, by shortening the window I am looking at, I decrease the number of
frequency bins (i.e. resolution), but I do not change the limits of the
frequencies I can resolve?

Is this correct? And if not, can somebody set me straight? Should be
simple..

Thanks very much in advance!

Best,

M.L.

M.L. wrote:
> Hi NG,
>
> I would like to have someone confirm (or not), that I have understood
> the following correctly:
>
> I have a signal which is sampled at .125 Hz. In this signal, a pulse
> lasting for 130 samples (i.e. 1040 s) is present. I would like to
> analyze this pulse and see the frequency content of it. I therefore
> window it with some window (Hanning or something like it) and calculate
> the FFT. In my spectrum I can now resolve frequencies up to .125/2
> (Nyquist), and I will have 130/2 frequency bins in my spectrum which
> will govern the frequency resolution. I can therefore resolve 65
> different frequencies between 0 Hz and 0.0625 Hz.
>
> So, by shortening the window I am looking at, I decrease the number of
> frequency bins (i.e. resolution), but I do not change the limits of the
> frequencies I can resolve?
>
> Is this correct? And if not, can somebody set me straight? Should be
> simple..
>
> Thanks very much in advance!
>
> Best,
>
> M.L.
>
Shorter windows lead to less resolution, but upper frequency remains
Nyquist, yes.

If all you care about is the detail of the interior of the pulse then
you are using the right method. If, however, you want to understand the
frequency content of _the whole pulse_ as it rises from zero, does it's
thing, then falls back to zero you'd be much better served to do a FFT
that includes the whole pulse with a generous helping of zeros outside
of it. If this is indeed what you want to know I suggest you take an
array that's at least 1024 samples long, if not longer. You can put the
pulse in the middle or at either end -- your magnitudes won't change,
only your phases.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

Ok - Thanks Tim! I appreciate it..

Best,

M.L.

M.L. wrote:
> Hi NG,
>
> I would like to have someone confirm (or not), that I have understood
> the following correctly:
>
> I have a signal which is sampled at .125 Hz. In this signal, a pulse
> lasting for 130 samples (i.e. 1040 s) is present. I would like to
> analyze this pulse and see the frequency content of it. I therefore
> window it with some window (Hanning or something like it) and calculate
> the FFT. In my spectrum I can now resolve frequencies up to .125/2
> (Nyquist), and I will have 130/2 frequency bins in my spectrum which
> will govern the frequency resolution. I can therefore resolve 65
> different frequencies between 0 Hz and 0.0625 Hz.
>
> So, by shortening the window I am looking at, I decrease the number of
> frequency bins (i.e. resolution), but I do not change the limits of the
> frequencies I can resolve?
>
> Is this correct? And if not, can somebody set me straight? Should be
> simple..

Yes, if.... Is it possible for the signal you sampled to have component
frequencies higher than 1/16 second? If there are any, they will
contaminate the components you're looking for. As an example, it would
be impossible after sampling to distinguish a component at .070 Hz from
one at .055.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Hello Jerry,

I am not sure what you mean.. Why will the effect that you describe be
introduced?

Thanks!

Best,

M.L.

M.L. wrote:
> Hello Jerry,
>
> I am not sure what you mean.. Why will the effect that you describe be
> introduced?

It's called "aliasing". see
http://www.dsptutor.freeuk.com/alias...asingDemo.html

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯