🚀 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.

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. You cannot get any better, but this is definitely
a closed-form expression. So mean square criterions will not get you
too far, but will show you the direction.