Polar Convolution

Polar Convolution

Post by Metin Guns » Sun, 28 Jul 1991 03:12:01



Has anyone out there ever done convolution in polar coordinates? I've derived
what I believe to be the correct transformation of rectangular convolution
into polar coordinates, but it is giving me inconsistent results. Is polar
convolution possible? I haven't found any references in the literature.
Any comments or references would greatly be appreciated.

Metin Gunsay.

 
 
 

Polar Convolution

Post by Peter Kootsook » Mon, 29 Jul 1991 15:15:43


|> Has anyone out there ever done convolution in polar coordinates? I've derived
|> what I believe to be the correct transformation of rectangular convolution
|> into polar coordinates, but it is giving me inconsistent results. Is polar
|> convolution possible? I haven't found any references in the literature.
|> Any comments or references would greatly be appreciated.

There is a similar problem in statistics, when the data to be analysed
are "circular" in nature (e.g. compass bearings). When the pdf's of in these sorts of problems have to be calculated, a "modulo" convolution operation
has to be defined. There is a book on this topic by K.V. Mardia, "Statistics of Directional Data", Academic Press, 1972.

I'm not sure whether this is of any use, but it sounds similar to the problem
as you've stated it.

Peter Kootsookos


 
 
 

1. 3-d polar surface plotting

I would like some suggestions here. I was trying to plot the
antenna field pattern. Which is calculated in terms of the
polar parameters theta and phi.
        E(theta,phi)
In order to plot the 3-d polar plot i was  obtaining the
transform value of each of the rectangular coordinates.
ie
        Ez = E(i,:) .* cos(theta);
        Ex = cos (phi(i))* (E(i,:) .* sin (theta));
        Ey = sin (phi(i))* (E(i,:) .* sin (theta));

but this form is not very visually helpful, i was trying to obtain the same
3-d plot using the 'surf' plotting in matlab.
but i am finding it difficult to calculate the array which would correspond to
E(theta,phi) and give me the surface polar plot.

I hope i made some sense there.
pls do let me know if some one has any idea how to do this.

Regards,
Avishek

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