Path: utzoo!utgpu!news-server.csri.toronto.edu!bonnie.concordia.ca!thunder.mcrcim.mcgill.edu!snorkelwacker.mit.edu!apple!usc!sdd.hp.com!hp-pcd!hplsla!bobc
From: bobc@hplsla.HP.COM (Bob Cutler)
Newsgroups: comp.dsp
Subject: Re: Help on FFT frequency resolution
Message-ID: <9360017@hplsla.HP.COM>
Date: 10 Jan 91 21:25:08 GMT
References: <8156.278a8f4d@jetson.uh.edu>
Organization: HP Lake Stevens, WA
Lines: 38



>This seems to increase the DFFT frequency resolution.  But I remember I read
>from a text book somewhere that says it isn't so (I forget which book that is);
>the padding is just a way of interpolation.  Is it true?
>

In a sense, it is.  The best way to think about this problem is to imagine
that you had all 1024 samples to begin with and then applied a rectangular
window 512 points wide.  This multiplication in the frequency domain 
corresponds to a convolution in the frequency domain.  To understand how
the windowing is going to affect your data, you need to consider the
window shape (in the frequency domain).  For example, a rectangular window
has a sin(x)/x type of response.  Narrow windows (in the time domain) are
generally fat in the frequency domain.  So, in the frequency domain, a
512 point rectangular window would be twice as wide (i.e. cover twice
as many bins) as a 1024 point window.  In this example the nulls in the 
sinc(x) function would be two bins apart instead of one bin apart..

>If the padding is just an interpolation, is it acceptable to use the values
>to calculate the amplitudes of the harmonics (not PSD) at 1 Hz, 3 Hz, etc.?
>
>If it is not acceptable mathematically, is there a way to find what I want at
>those frequencies?
>

It sounds as though you're more interested in amplitude accuracy that
frequency resoltion.  If this is the case, then you don't even really need
to go to a double width FFT.  Just select a window function that emphasises
amplitude accuracy.  With the appropriate window, it won't matter if the
spectral line does not land on a frequency bin.   Don't forget to apply
a gain correction for the selected window if you're interested in the
absolute levels of each harmonic.

					Bob Cutler
					KE7ZJ
					Hewlett-Packard
					Lake Stevens Instrument Division