Order of convolution and multiplying [Matlab]

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From: Eyal Spielman on 19 Jun 2008 03:39

From: Eyal Spielman on 19 Jun 2008 04:43

Rune Allnor <allnor(a)tele.ntnu.no> wrote in message
<1ab41a94-4de0-44da-8801-
7033c962de59(a)34g2000hsh.googlegroups.com>...
> On 18 Jun, 17:03, "Eyal Spielman" <eyal_...(a)yahoo.com>
wrote:
> > Hi all,
> >
> > I have three signals in the frequency domain, which
> > arranged in mathematical way as follow:
>
> Your description doesn't correspond to anything
> I am familiar with. Since you ask to help with
> expressing an algorithm in terms of maths, I suspect
> the mathemathical description might be flawed.
>
> Could you please describe the problem in plain text?
>
> Rune

Hi Rune,

The signal M is a fourier transform of a random matrix, and
R is a low pass filter. I make a simulation in the
frequency domain.

m = rand(64);
M = fftshift(fft2(fftshift(m-mean(m(:)))));
R = zeros(64);
R(28:36,28:36)=1;

Also I have a target image o,

o = double(rgb2gray(imread('***.bmp')));
O = fftshift(fft2(fftshift(o-mean(o(:)))));

In the case that I don't use the low pass the order of the
simulation is:

result = conv2(conv2(O,M),M);

Since m is a random matrix, conv2(M,M) gives strong delta
function (DC value) plus very small energy in the rest of
the spectrum. In this case I can change the order of the
simulation (without changing the result, of course),

result = conv2(conv2(M,M),O);

by taking conv2(M,M) first, I can suppress the very small
energy from the spectrum and keep the DC value, and then to
make a convolution with O which exactly reconstruct O.

In the case that I do use the low pass the simulation is:

result_lpf = conv2((conv2(O,M).*R),M);

My problem is, how do I suppress these tiny energy
components from the spectrum (and keep the DC value) in
this case.

From: Rune Allnor on 19 Jun 2008 05:25

On 19 Jun, 10:43, "Eyal Spielman" <eyal_...(a)yahoo.com> wrote:
> Rune Allnor <all...(a)tele.ntnu.no> wrote in message
>
> <1ab41a94-4de0-44da-8801-
> 7033c962d...(a)34g2000hsh.googlegroups.com>...
>
> > On 18 Jun, 17:03, "Eyal Spielman" <eyal_...(a)yahoo.com>
> wrote:
> > > Hi all,
>
> > > I have three signals in the frequency domain, which
> > > arranged in mathematical way as follow:
>
> > Your description doesn't correspond to anything
> > I am familiar with. Since you ask to help with
> > expressing an algorithm in terms of maths, I suspect
> > the mathemathical description might be flawed.
>
> > Could you please describe the problem in plain text?
>
> > Rune
>
> Hi Rune,
>
> The signal M is a fourier transform of a random matrix, and
> R is a low pass filter. I make a simulation in the
> frequency domain.
>
> m = rand(64);
> M = fftshift(fft2(fftshift(m-mean(m(:)))));
> R = zeros(64);
> R(28:36,28:36)=1;
>
> Also I have a target image o,
>
> o = double(rgb2gray(imread('***.bmp')));
> O = fftshift(fft2(fftshift(o-mean(o(:)))));

Change those names! That's a disaster waiting to happen.

To see why, take a look at your keyboard. What key is
located on the line above the 'o' key, immediately
to its right? It doesn't take much of a miss when
you're hacking away, to type the wrong character.
And when (not if) that happens you will find yourself
in serious trouble.

> In the case that I don't use the low pass the order of the
> simulation is:
>
> result = conv2(conv2(O,M),M);

Wrong. First, why would you apply two convolutions? One
ought to be enough. Second, convolutions take place in
spatial domain wheras M comtains frequency domain data.
Substitute 'm' for 'M' and see if things improve.

In general, you need to look up the basics on filtering,
amd maybe make a few tutorials and tests on simple
data, so that you understand how filtering works.
Leave the images out of this while you do the
learning excercises.

Rune

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