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Asymmetric gaussian type function through signal filtering

Started by s068...@sms.ed.ac.uk May 31, 2011
Hi there, i'm trying to get an asymmetric gaussian type shape that i can parameterise, i thought perhaps signal filtering might be an efficient way to do it. Only problem is i don't know enough about filtering!

So, if you take a look at:
http://web.me.com/bilal.khan/diagram.png

Top left is the gaussian shape we're all wonderfully familiar with, and top right is the kind of curve i'm looking for where a) b) & c) are the things i'm trying to parameterise.

a) is the height of the peak
b) is the size of the pattern (while keeping the other 2 params constant)
c) is the rate of decay

optional extra d) it's not essential, but it would be nice to be able to move the position of the peak.

One thing to note, the diagram is one dimensional but i'm actually working in 2, which is to say the gaussian is 2D.

I've tried doing it with a logarithmic gaussian, with which i can move the position of the peak, but controlling the decay (c) and height of the peak independently (a) eludes me. A friend said i might try signal filtering to solve the problem but im not sure how i'd go about that.

Thanks in advance for any help!
Maybe you should consider something other than a Gaussian PDF. There are many others to choose from. Take a look at http://www.causascientia.org/math_stat/Dists/Compendium.pdf

Hugh

--- On Wed, 5/18/11, s...@sms.ed.ac.uk wrote:

From: s...@sms.ed.ac.uk
Subject: [audiodsp] Asymmetric gaussian type function through signal filtering
To: a...
Date: Wednesday, May 18, 2011, 10:13 AM

 

Hi there, i'm trying to get an asymmetric gaussian type shape that i can parameterise, i thought perhaps signal filtering might be an efficient way to do it. Only problem is i don't know enough about filtering!

So, if you take a look at:

http://web.me.com/bilal.khan/diagram.png

Top left is the gaussian shape we're all wonderfully familiar with, and top right is the kind of curve i'm looking for where a) b) & c) are the things i'm trying to parameterise.

a) is the height of the peak

b) is the size of the pattern (while keeping the other 2 params constant)

c) is the rate of decay

optional extra d) it's not essential, but it would be nice to be able to move the position of the peak.

One thing to note, the diagram is one dimensional but i'm actually working in 2, which is to say the gaussian is 2D.

I've tried doing it with a logarithmic gaussian, with which i can move the position of the peak, but controlling the decay (c) and height of the peak independently (a) eludes me. A friend said i might try signal filtering to solve the problem but im not sure how i'd go about that.

Thanks in advance for any help!
You may want to take a look at the chi-squared family of pdfs. They provide
similar features as you've described here. I'm not sure how you could
accomplish this using filtering, unless you're planning on using a
non-linear filter.
-Brant

On Wed, May 18, 2011 at 9:13 AM, wrote:

> Hi there, i'm trying to get an asymmetric gaussian type shape that i can
> parameterise, i thought perhaps signal filtering might be an efficient way
> to do it. Only problem is i don't know enough about filtering!
>
> So, if you take a look at:
> http://web.me.com/bilal.khan/diagram.png
>
> Top left is the gaussian shape we're all wonderfully familiar with, and top
> right is the kind of curve i'm looking for where a) b) & c) are the things
> i'm trying to parameterise.
>
> a) is the height of the peak
> b) is the size of the pattern (while keeping the other 2 params constant)
> c) is the rate of decay
>
> optional extra d) it's not essential, but it would be nice to be able to
> move the position of the peak.
>
> One thing to note, the diagram is one dimensional but i'm actually working
> in 2, which is to say the gaussian is 2D.
>
> I've tried doing it with a logarithmic gaussian, with which i can move the
> position of the peak, but controlling the decay (c) and height of the peak
> independently (a) eludes me. A friend said i might try signal filtering to
> solve the problem but im not sure how i'd go about that.
>
> Thanks in advance for any help!
>
>

--
Brant Jameson
PhD Candidate
UC Santa Cruz Computer Engineering
http://people.ucsc.edu/~pheese