## NAME

         Butterworth_Low - performs Butterworth lowpass filtering

## SYNOPSIS

          #include <math.h>
          #include <stdio.h>
          #include <stdlib.h>
          #include "CVIPdef.h"
          #include "CVIPimage.h"

         Image *Butterworth_Low(Image *in_Image, int block_size,  int
         dc, int cutoff, int order)

          <in_Image> - pointer to an Image structure
          <block_size> - desired block size
          <dc> - drop(0) or retain(1) dc component
          <cutoff> - cutoff frequency
          <order> - filter order

## PATH

         $CVIPHOME/XFORMFILTER/filter.c

## DESCRIPTION

          Butterworth_Low()  performs   two-dimensional   butterworth
         lowpass  filtering  in transform domain on input image.  The
         parameter cutoff defines  the  cut-off  frequency  locus  at
         points  for  which the filter transfer function H(u,v) is at
         0.7071 of its maximum value. All components inside  the  the
         circle  (or 1/4 circle if dc component is on the upper-left-
         hand corner of its transform plane) of radius  "cutoff"  are
         passed  with  no  attenuation, while all frequencies outside
         the circle (or 1/4 circle) are attenuated by the  transition
         from  passband  to  stopband  which  depend on the degree of
         filter order f_order. If dc equals 1, the dc component  will
         be retained, if dc = 0, dc componenet will be dropped.

## TYPES AND CONSTANTS

         None

## RETURN VALUES

         A filtered image

## HISTORY

         History information recorded: None

## DIAGNOSTICS

         Butterworth_Low()   performs   two-dimensional   butterworth
         lowpass  filtering  in transform domain on input image.  The
         parameter cutoff defines  the  cut-off  frequency  locus  at
         points  for  which the filter transfer function H(u,v) is at
         0.7071 of its maximum value. All components inside  the  the
         circle  (or 1/4 circle if dc component is on the upper-left-
         hand corner of its transform plane) of radius  "cutoff"  are
         passed  with  no  attenuation, while all frequencies outside
         the circle (or 1/4 circle) are attenuated by the  transition
         from  passband  to  stopband  which  depend on the degree of
         filter order f_order. If dc equals 1, the dc component  will
         be retained, if dc = 0, dc componenet will be dropped.

## EXAMPLE

          #include <CVIPtoolkit.h>
          #include <CVIPimage.h>
          #include <CVIPdef.h>
          #include <CVIPconvert.h>
          #include <CVIPview.h>
          #define VIEWER "picture"
          #define VIDEO_APP "SunVideo &"

          void main()
          {
          Image *cvipImage;
          IMAGE_FORMAT format;
          char *inputfile,*outputfile;

          (void) setDisplay_Image(VIEWER, "Default");
          print_CVIP("\n\t\tEnter the  Input File Name:  ");
          inputfile =(char *) getString_CVIP();
          format = getFormat_CVIP(inputfile);
          cvipImage = read_Image(inputfile,1);
          view_Image(cvipImage, inputfile);
          free(inputfile);
          /* the following call performs the fft_transform on the
          input image with the block size equal to 256 */
          cvipImage=(Image *)fft_transform(cvipImage,256);
          /* the following call performs the butterworth low pass
          filtering of order 2 on the transformed image with
          the cut off frequency equal to 64 */
          cvipImage = (Image *)Butterworth_Low(cvipImage,256,1,64,2);
          /* the following call performs the inverse fft_transform
          in the filtered image with the block size equal to 256 */
          cvipImage = (Image *)ifft_transform(cvipImage,256);
          print_CVIP("\n\t\tEnter the Output File Name:  ");
          outputfile = getString_CVIP();
          view_Image(cvipImage,outputfile);
          write_Image(cvipImage,outputfile,CVIP_NO,CVIP_NO,format,1);
          free(outputfile);
          }

## SEE ALSO

         libxformfilter

## AUTHOR

         Copyright (C) 1996 SIUE - by Scott E. Umbaugh and Simon Low.