🚀 go-pugleaf

>sjreeves@eng.auburn.edu (Stan Reeves) writes:
>>In order to optimize the tradeoff between main lobe width and side lobe
>>height, one has to have a criterion.  Do you want more resolution and more
>>variance or do you want less variance and less resolution?  I suppose that
>>one could come up with a criterion based on expected mean-square error
>>between the estimated and actual power spectrum, but I don't know of any
>>neat closed-form expressions for this.

dak@messua.informatik.rwth-aachen.de (David Kastrup) writes:
>Well, if you define bandwidth (and timespread) as the variance of a
>similar-spread probability density function, you get a sort of
>square mean error. The product of the time width and the bandwidth
>is limited downwards, it cannot get better than an optimum, that is
>provided by a gaussian curve which again transforms into a Gaussian
>in the frequency domain. 
[..]

The probability density function described above must be positive and sum 
(integrate) to 1: is therefore the normalised square of the (time domain) 
function an appropriate measure (in a mean square error sense) ? 

i.e. 
variance = SUMi { [xi-mean(xi)]^2 * f(xi)^2 } 
where SUMi ( f(xi)^2 ) = 1.

Also , does anybody  know of some good references on this subject ?

James Andrew
Wollongong
g9024557@wampyr.uow.oz.au