Re: bandpass filter for 2D Data

[John Swensen]

On Aug 28, 2009, at 11:30 AM, Sergei Steshenko wrote:

> --- On Thu, 8/27/09, John Swensen <address@hidden> wrote:
>
> > From: John Swensen <address@hidden>
> > Subject: Re: bandpass filter for 2D Data
> > To: "Dr. Johannes Zellner" <address@hidden>
> > Cc: address@hidden
> > Date: Thursday, August 27, 2009, 12:58 PM
> >
> > On Aug 27, 2009, at 3:15 AM, Dr. Johannes Zellner wrote:
> >
> > > Hi
> > >
> > > does anyone have an implementation of a 2D bandpass
> > filter?
> > > Suppose I've 2d data in a matrix of 1000 x 1000 pixels
> > which
> > > represents a spatial extension of 1 m (1 mm per
> > pixel).
> > > Now I'd like to filter away all frequencies below a
> > wavelength of 50
> > > mm and above a wavelength of 150 mm,
> > > so the resulting data should only have frequencies
> > corresponding to
> > > wavelengths between 50 and 150 mm.
> > >
> > > Any octave examples for this?
> > >
> > > --   
> > > Johannes
> > > _______________________________________________
> > > Help-octave mailing list
> > > address@hidden
> > > https://www-old.cae.wisc.edu/mailman/listinfo/help-octave
> >
> > I don't know if there is an example of how to do this, but
> > I think I
> > remember doing the following pseudocode in my computer
> > visions class:
> >
> > 1) perform the 2D FFT
> > 2) figure out, based on your spatial sampling frequency,
> > how much one
> > "pixel" in the magnitude portion of the 2D FFT is
> > 3) set everything but an annulus whose larger radius
> > equates to 150mm
> > wavelength and inner radius equates to 50mm to zero.
> > 4) Perform the inverse 2D FFT
> >
> > Someone please correct me if this doesn't work, but I think
> > this ends
> > up being a fairly quick way to do what you ask and easy to
> > implement.
> >
> > John Swensen
> > _______________________________________________
>
>
> Your approach is essentially correct, however, with any inverse FFT
> brickwall filter (the one you propose) causes a lot of ringing in the
> reconstituted signal.
>
> Regards,
>  Sergei.

Yeah, I thought about that afterward, but hadn't got around to  
correcting myself.  To solve that problem you use a difference of 2D  
Guassians to generate the annulus.  I don't quite remember now how to  
set the variance of the Gaussians to get the desired cutoff  
frequencies, though.

Thanks for pointing out my error,
John