Re: [Gnuplot-info] sin(x)/x smoothing option?

[Ethan A M. <eam...@gm...>]

On Tuesday, 31 July 2018 20:49:48 Kevin Oberman wrote:
> On Tue, Jul 31, 2018 at 12:38 PM, Ethan Merritt <eam...@gm...> wrote:
> 
> > On Mon, Jul 30, 2018 at 5:10 PM, Reginald Beardsley via gnuplot-info <
> > gnu...@li...> wrote:
> >
> > > Is there an option to apply a sin(x)/x aka Whittaker interpolator to the
> > > points when plotting?  I'm working on a digital signal processing
> > tutorial
> > > and it would be helpful to be able to apply a sinc interpolator to the
> > data
> > > points.
> > >
> > > If there is not, I'd like to suggest considering that as an enhancement
> > as
> > > it is widely used in DSP applications.
> > >
> >
> > Not my field, so I'm working with the assistance of Wikipedia.
> > Do I understand correctly that the idea would be to plot the function
> >
> >       f(x) = Summation_over_all_data { yn * sinc( (x - nT)/T )}
> >
> > where the original data points were [xn, yn] and T = 1/(2*bandwidth) is a
> > constant specified by the user?
> > Analogous to the kdensity smoothing option, the plot command would be
> >
> >      plot $DATA smooth Whittaker {bandwidth <value>}
> >
> > In the case of kernel density smoothing there is an obvious default for the
> > bandwidth.
> > Is there something similar for this formula or would the bandwidth always
> > be required?
> > Would it be more natural to provide T or to provide bandwidth?
> >
> >     Ethan
> >
> 
> The 5.2 manual does not seem to mention "smooth Whittaker".

Well yeah, that's the point.  There is no such smoothing option now but
Reginald is suggesting that it would be useful to add one.
I was trying to understand what such an option would look like to the
user, and how well it would fit with the existing mechanisms for smoothing
in gnuplot.

	Ethan

> Any idea where
> I might find some information on it, especially as used in gnuplot?