Re: bandpass filter for 2D Data

[Sergei Steshenko]

--- 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.