Dear all: I was studying the notch filter. As far as I understood, there are 2 possible ways to accomplish this task: 1) Set the DC component of the spectrum to be equal to zero, i.e: F(0,0) =0. To obtain the filtered image, apply the IDFT. 2) Create a kernel (k) having the same size as the filtered image. Set all the kernel values equal to 1, except for the pixel in position (M/ 2,N/2), which will be equal to 0. Note that M,N represent respectively the width and height of the filtered image. Compute the DFT of the kernel (k) obtaining a kernel K in the frequency domain. Convolve the spectrum with the kernel K in the frequency domain, and apply the IDFT to the convolved image in order to obtain the filtered image in the spacial domain. I would like to know, if those 2 operations are equivalent, because the obtained filtered images in method 1, and 2 differ from each other. Best regards, Javier -- ================================================= Javier A. Montoya Zegarra - http://www.lis.ic.unicamp.br/~jmontoya Institute of Computing, State University of Campinas, SP - Brazil ================================================= "Set all Afire" - St. Ignatius of Loyola

# About Notch Filtering in the Frequency Domain (2D images)

Started by ●May 17, 2007

Reply by ●May 17, 20072007-05-17

On 17 May, 17:04, Javier Montoya <jmonto...@gmail.com> wrote:> Dear all: > > I was studying the notch filter. As far as I understood, there are 2 > possible ways to accomplish this task: > 1) Set the DC component of the spectrum to be equal to zero, i.e: > F(0,0) =0. To obtain the filtered image, apply the IDFT. > 2) Create a kernel (k) having the same size as the filtered image. Set > all the kernel values equal to 1, except for the pixel in position (M/ > 2,N/2), which will be equal to 0. Note that M,N represent respectively > the width and height of the filtered image. Compute the DFT of the > kernel (k) obtaining a kernel K in the frequency domain. Convolve the > spectrum with the kernel K in the frequency domain, and apply the IDFT > to the convolved image in order to obtain the filtered image in the > spacial domain. > > I would like to know, if those 2 operations are equivalent, because > the obtained filtered images in method 1, and 2 differ from each > other.Formally, they are equivalent, except for wrap-around effects. If, for the sake of argument, your image is of size 2N+1 x 2N+1, then the resulting image after convolition (your approach #2) is of size 4N+1 x 4N+1. Your approach #1 is formally equal to your approach #2 PROVIDED both the image and the mask, which are of size 2N+1 x 2N+1, are zero-padded to size 4N+1 x 4N+1 prior to computing the 2D DFTs. Since you haven't done that, the "overshoot" wraps around the edges and start messing up your image. Rune

Reply by ●May 18, 20072007-05-18

Please tell me you would not do 1) in this way! Dirk On May 17, 11:04 am, Javier Montoya <jmonto...@gmail.com> wrote:> Dear all: > > I was studying the notch filter. As far as I understood, there are 2 > possible ways to accomplish this task: > 1) Set the DC component of the spectrum to be equal to zero, i.e: > F(0,0) =0. To obtain the filtered image, apply the IDFT.<xnipped>> Javier > > -- > ================================================= > Javier A. Montoya Zegarra -http://www.lis.ic.unicamp.br/~jmontoya > Institute of Computing, State University of Campinas, SP - Brazil > ================================================= > > "Set all Afire" - St. Ignatius of Loyola