Prev: How to add noise???
Next: FFT with TMS320F2812
From: ejs on 18 Jun 2008 13:22
Hi all,

I have three signals in the frequency domain, which arranged in
mathematical way as follow:

The first signal (named as M) is multiplied with a signal (named as R)
that blocks some frequency components and transmits the others, and the
result is convolved with the first signal (M).

My question is, what are the mathematical operations that I have to do if
I need to rearrange the order such that M is convolved with itself, and
then to take in account R.



From: emre on 18 Jun 2008 13:58
>The first signal (named as M) is multiplied with a signal (named as R)
>that blocks some frequency components and transmits the others, and the
>result is convolved with the first signal (M).

Multiplication with R can not block some frequency components and leave
others unless they are separated in time. You might want to double check
your requirements and compare to what you are doing. What kind of signals
are R and M? Why do you need such an operation?

Multiplication and convolution do not commute in general. It may be
possible if either of your signals is a sinusoid.

Emre
From: Oli Charlesworth on 18 Jun 2008 17:14
On Jun 18, 6:58 pm, "emre" <egu...(a)ece.neu.edu> wrote:
> >The first signal (named as M) is multiplied with a signal (named as R)
> >that blocks some frequency components and transmits the others, and the
> >result is convolved with the first signal (M).
>
> Multiplication with R can not block some frequency components and leave
> others unless they are separated in time. You might want to double check
> your requirements and compare to what you are doing. What kind of signals
> are R and M? Why do you need such an operation?
>
> Multiplication and convolution do not commute in general. It may be
> possible if either of your signals is a sinusoid.
>

If M and R are frequency-domain representations, then R can mask
certain frequency bands if it's zero for certain regions.

However yes, in general, convolution and multiplication do not
commute.


--
Oli
From: Tim Wescott on 19 Jun 2008 03:13
ejs wrote:
> Hi all,
>
> I have three signals in the frequency domain, which arranged in
> mathematical way as follow:
>
> The first signal (named as M) is multiplied with a signal (named as R)
> that blocks some frequency components and transmits the others, and the
> result is convolved with the first signal (M).
>
> My question is, what are the mathematical operations that I have to do if
> I need to rearrange the order such that M is convolved with itself, and
> then to take in account R.

You are doing this in the frequency domain? So in the time domain you
are filtering m (M's time-domain equivalent) with r (r's time domain
equivalent), then multiplying by m?

That's all very interesting, but it makes no sense. Particularly when
the answer to your third paragraph is just "do what you said".

Perhaps if you gave some more context, someone could give you a sensible
answer, or at least tell you why your problem statement can never be
sensible.

--

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

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html
From: ejs on 19 Jun 2008 04:46
>On Jun 18, 6:58 pm, "emre" <egu...(a)ece.neu.edu> wrote:
>> >The first signal (named as M) is multiplied with a signal (named as
R)
>> >that blocks some frequency components and transmits the others, and
the
>> >result is convolved with the first signal (M).
>>
>> Multiplication with R can not block some frequency components and
leave
>> others unless they are separated in time. You might want to double
check
>> your requirements and compare to what you are doing. What kind of
signals
>> are R and M? Why do you need such an operation?
>>
>> Multiplication and convolution do not commute in general. It may be
>> possible if either of your signals is a sinusoid.
>>
>
>If M and R are frequency-domain representations, then R can mask
>certain frequency bands if it's zero for certain regions.
>
>However yes, in general, convolution and multiplication do not
>commute.
>
>
>--
>Oli
>

Thanks all,

Let me explian my problem in more detais.

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

 |  Next  |  Last
Pages: 1 2
Prev: How to add noise???
Next: FFT with TMS320F2812