pbutterworthfilter

Designs lowpass, highpass, bandpass or bandreject Butterworth filter.

Synopsis

pbutterworthfilter [-m mask] ncol nrow ndep highpass cutin cutoff order [im_out|-]

Description

pbutterworthfilter designs either a lowpass, highpass, bandpass or bandreject Butterworth filter. If ndep<1 the filter im_out is a 2D float image with size nrow*ncol otherwise the filter im_out is a 3D float image with size ndep*nrow*ncol.

The Butterworth lowpass filter cuts off high-frequency components of the Fourier transform that are at a distance greater than a specified distance D0 (the cutoff value) from the origin of the centered transform.

The type of filter is given by both parameters highpass and cutin:

highpass=0 and cutin=0 : lowpass filter
highpass=1 and cutin=0 : highpass filter
highpass=0 and cutin=1 : bandreject filter
highpass=1 and cutin=1 : bandpass filter

The transfer function for a 2D Butterworth lowpass filter of the given order n and with cutoff frequency at distance D0 from the origin is defined as:

Hlp(u,v) =             1
           --------------------
            1 + [ D(u,v)/D0]²ⁿ

where D(u,v) is the distance of point (u,v) from the origin:

D(u,v)=sqrt((u-M/2)² + (v-N/2)²)

where N is the number of rows and M is the number of columns.

The transfert function for a Butterworth highpass is defined as:

H(u,v) =  1- Hlp(u,v)

The transfer function for a band reject is defined as:

H(u,v) =          1
        ------------------
         1+ [  D(u,v)W ]²ⁿ
            [----------]
            [D²(u,v)-D0²]

where W is the bands width = cutoff-cutin and D0 is the radius=(cutin+cutoff)/2.

Parameters

ncol, nrow, ndep specify the size of the output image. If ndep<1 then the output image im_out is a 2D image otherwise a 3D image.
highpass is used in conjunction with the cutin parameter. It specifies the type of the filter:
- highpass=0 and cutin=0 : lowpass filter
- highpass=1 and cutin=0 : highpass filter
- highpass=0 and cutin=1 : bandreject filter
- highpass=1 and cutin=1 : bandpass filter
cutin is the cut in frequency of the filter D0 in case of bandreject or bandpass filter. In this case, the band width=cutoff-cutin and D0=(cutoff+cutin)/2.
cutoff is the cut off frequency of the filter D0. It must be a positive real value in the interval ]0.. sqrt(M*m+N*n)/2]. It corresponds to an euclidean distance from the center of the image. The higher cutoff is, the lower the lowpass is or the higher the highpass is.
order is the order of the filter. The higher order is the sharper the transition is. It must be an integer >= 1. A typical value is 1.

Outputs

im_out: a float image (Img2dsf or Img3dsf).

Result

Returns SUCCESS or FAILURE in case of bad parameter values.

Examples

Performs Butterworth lowpass filtering:

   psetcst 0 tangram.pan i1.pan
   pfft tangram.pan i1.pan i2.pan i3.pan
   pbutterworthfilter 256 256 0 0 0 50 2 i4.pan
   pmult i2.pan i4.pan i5.pan
   pmult i3.pan i4.pan i6.pan
   pifft i5.pan i6.pan out.pan i8.pan

Performs Butterworth highpass filtering:

   psetcst 0 tangram.pan i1.pan
   pfft tangram.pan i1.pan i2.pan i3.pan
   pbutterworthfilter 256 256 0 1 0 50 2 i4.pan
   pmult i2.pan i4.pan i5.pan
   pmult i3.pan i4.pan i6.pan
   pifft i5.pan i6.pan out.pan i8.pan

Performs Butterworth bandreject filtering:

   psetcst 0 tangram.pan i1.pan
   pfft tangram.pan i1.pan i2.pan i3.pan
   pbutterworthfilter 256 256 0 0 25 50 2 i4.pan
   pmult i2.pan i4.pan i5.pan
   pmult i3.pan i4.pan i6.pan
  pifft i5.pan i6.pan out.pan i8.pan

Performs Butterworth bandpass filtering:

   psetcst 0 tangram.pan i1.pan
   pfft tangram.pan i1.pan i2.pan i3.pan
   pbutterworthfilter 256 256 0 1 25 50 2 i4.pan
   pmult i2.pan i4.pan i5.pan
   pmult i3.pan i4.pan i6.pan
   pifft i5.pan i6.pan out.pan i8.pan

C++ prototype

Errc PButterworthFilter( Img2dsf &im_out, int ndep, int nrow, int ncol, int highpass, float cutin, float cutoff, int order);

Version française

Génère un filtre passe-bas, passe-haut, coupe-bande ou passe-bande de Butterworth.

Author: Régis Clouard