Path: news.mathworks.com!not-for-mail
From: "Chen Sagiv" <chensagivron@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Strange Behavior in Phase Calculation
Date: Wed, 14 May 2008 07:20:17 +0000 (UTC)
Organization: Image Processing &#38; Math More
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NZTideMan <mulgor@gmail.com> wrote in message <5784b2e7-
6422-4da5-bbfa-6f93523e0635@k10g2000prm.googlegroups.com>...
> On May 14, 6:52=A0pm, "Chen Sagiv" 
<chensagiv...@gmail.com> wrote:
> > "Chen Sagiv" <chensagiv...@gmail.com> wrote in message
> >
> > <g0e20u$km...@fred.mathworks.com>...
> >
> >
> >
> >
> >
> > > Dear friends,
> >
> > > I have a strange phenomenon.
> > > I have a cosine wave. I take two instances of it.
> >
> > > I call the first Case 1, where I have 10 cycles of 
this
> > > wave. Case 2 is 10 cycle + one extra point.
> >
> > > Now, when I calculate the FT of both signals, I get a 
non
> > > zero imaginary value for the second case.
> >
> > > If I try to calculate the phase, and use either atan,
> > > atan2, angle and phase commands I get a linear phase.
> >
> > > Isn't it Gibberish ? How does Matlab generate linear
> > phase
> > > when the imaginary part of the FT is practically 
zero ?
> >
> > > I would be happy to get comments on this issue.
> >
> > > Thanks,
> >
> > > Chen
> >
> > Sorry, forgot to attach the code:
> >
> > close all;
> > clear all;
> >
> > % Constants
> > T =3D 10;
> > w0 =3D 2*pi;
> > sigma =3D 1;
> > % Case 1: there are 10 cycles of the cosine function
> > t1 =3D 0:0.01:10-0.01;
> > f1 =3D cos(w0*t1);
> > fw1 =3D fftshift(fft(f1));
> >
> > % Case 2: there are 10 cycles + 1 point
> > t2 =3D 0:0.01:10;
> > f2 =3D cos(w0*t2);
> > fw2 =3D fftshift(fft(f2));
> >
> > figure ;
> > subplot(3,2,1); plot(real(fw1),'.k');
> > title('Case 1: real FT');
> > subplot(3,2,3); plot(imag(fw1),'.k');
> > title('Case 1: imag FT');
> > subplot(3,2,5); plot(atan2(imag(fw1), real(fw1)),'.');
> > title('Case 1: phase of FT');
> > subplot(3,2,2); plot(real(fw2),'.k');
> > title('Case 2: real FT');
> > subplot(3,2,4); plot(imag(fw2),'.k');
> > title('Case 2: imag FT');
> > subplot(3,2,6); plot(atan2(imag(fw2), real(fw2)),'.');
> > title('Case 2: phase of FT');
> >
> > Best,
> >
> > Chen- Hide quoted text -
> >
> > - Show quoted text -
> 
> It's called "leakage".  It's a feature of the FFT, so 
don't for a
> moment think you've discovered something new.
> There's a very good explanation in E Oran Brigham's book 
Fast Fourier
> Transform published in 1973.

Dear NZTideMan,

I am afraid you completely missed my point. 
I am not referring to the leakage (thanks for the reference 
though), but to the linear phase that seems to be 
calculated with no reason.

If you can refer to this point, i will appreciate it. 

Best,

Chen