Is there any way of producing periodic Gaussian pulses such that the bell shape repeats itself with a defined period. Does there exist any solution for some differential equation which resembles the aforementioned function?
You can start by reading this link:
http://math.stackexchange.com/questions/454289/how-to-make-any-function-to-repeat-periodically
Thanks Gioacchino de Candia for the reply... Albeit the link you sent was helpful still it has some ambiguity...
By definition there is no Gaussian periodic function, you could use binomial formula which is exactly zero. The natural way is Fourier-expansion - you prescribe the shape and project to Fourier basis. That is how I would do it.
The above comments are true. Bu beyond that I want add something. First I say what purpose it will serve , it is to understand first. So define the problem . I think you mean the Co-ordinate geometry-point of view. If it is so take a polar form with proper definition and constraints of the Gaussian curve. Then try to proceed. Thanks.
A periodic Gaussian function seems to be the wrapped normal distribution: http://en.wikipedia.org/wiki/Wrapped_normal_distribution
Karthik Soman, my answer clarifies your problem and is the starting point, there is no ambiguity.
How about the von MIses distribution? It is also known as circular normal distribution which hints at similarities with the gaussian.Following link from wikipedia:
http://en.wikipedia.org/wiki/Von_Mises_distribution
you can use the following function and change the parameters (a, b and c) to fit your data: y=exp(-((a*sin(x)-b)/c).^2)
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