MATLAB Central Newsreader - Need help with Fourier transform

Need help with Fourier transform

Steve Amphlett — Wed, 02 Sep 2009 14:46:04 -0400

<holding head in shame>

If I want to track single frequencies, I can write code like this:

%%%%%%%%%%%%%%%%%code%%%%%%%%%%%%%%

%Time
t=10*(0:32767)'/32768;

% Pass??
n=(1:length(t))';
n=[n n];

% My signal - pure real at 10, a mix at 5
x=3*cos(10*2*pi*t)+7*sin(5*2*pi*t+0.2);

% Dig out the 5 and plot it
re=cos(5*2*pi.*t).*x;
im=sin(5*2*pi.*t).*x;
[sum(re) sum(im)]/length(t)*2

mag=cumsum([re im])./n*2;

subplot(211)
plot(t,mag)

% Dig out the 10 and plot it
re=cos(10*2*pi.*t).*x;
im=sin(10*2*pi.*t).*x;
[sum(re) sum(im)]/length(t)*2

mag=cumsum([re im])./n*2;

subplot(212)
plot(t,mag)

%%%%%%%%%%%%%%%%%code%%%%%%%%%%%%%%

So I can recover the amplitudes of the real and imag components in my fake signal with the summations. But what about the wiggles in the plots?

</holding head in shame>

Re: Need help with Fourier transform

Rune Allnor — Wed, 02 Sep 2009 16:38:32 -0400

On 2 Sep, 16:46, "Steve Amphlett" <Firstname.Lastn...@Where-I-
Work.com> wrote:

> If I want to track single frequencies, I can write code like this:
...
> So I can recover the amplitudes of the real and imag components in my fake signal with the summations. But what about the wiggles in the plots?

...so what you do is to use an integrator to accumulate
the energy of each nominal frequency band...?

One effect that contributes to the wiggles is the cross-talk
between the crequency components. Umless the two sines are
orthogonal, they will interact with a coupling factor that is
given by the sinc window function at any given N.

And since N varies all the time - if I understand your code
correctly - the coupling factor also changes all the time,
switching between positive and negative, and sliding further
and further apart in spectrum domain.

Rune

Re: Need help with Fourier transform

Steve Amphlett — Wed, 02 Sep 2009 17:59:19 -0400

Rune Allnor <allnor@tele.ntnu.no> wrote in message <b6dff0b3-e1f3-40c7-bff3-6118dda5a8a3@c37g2000yqi.googlegroups.com>...
> On 2 Sep, 16:46, "Steve Amphlett" <Firstname.Lastn...@Where-I-
> Work.com> wrote:
>
> > If I want to track single frequencies, I can write code like this:
> ...
> > So I can recover the amplitudes of the real and imag components in my fake signal with the summations. ?But what about the wiggles in the plots?
>
> ...so what you do is to use an integrator to accumulate
> the energy of each nominal frequency band...?
>
> One effect that contributes to the wiggles is the cross-talk
> between the crequency components. Umless the two sines are
> orthogonal, they will interact with a coupling factor that is
> given by the sinc window function at any given N.
>
> And since N varies all the time - if I understand your code
> correctly - the coupling factor also changes all the time,
> switching between positive and negative, and sliding further
> and further apart in spectrum domain.
>
> Rune
Cycle-by-cycle update perhaps? Integrators reset.