2-D FIR filter using frequency transformation
Design Circularly Symmetric 2-D Bandpass Filter
ftrans2 to design an approximately circularly symmetric two-dimensional bandpass filter with passband between 0.1 and 0.6 (normalized frequency, where 1.0 corresponds to half the sampling frequency, or π radians). Since
ftrans2 transforms a one-dimensional FIR filter to create a two-dimensional filter, first design a one-dimensional FIR bandpass filter using the Signal Processing Toolbox function
colormap(jet(64)) b = firpm(10,[0 0.05 0.15 0.55 0.65 1],[0 0 1 1 0 0]); [H,w] = freqz(b,1,128,'whole'); plot(w/pi-1,fftshift(abs(H)))
ftrans2 with the default McClellan transformation to create the desired approximately circularly symmetric filter.
h = ftrans2(b); freqz2(h)
t — Transform matrix
The transform matrix, specified as a numeric matrix.
t contains coefficients that define the frequency
transformation to use. By default,
ftrans2 uses a
McClellan transform matrix.
The transformation below defines the frequency response of the two-dimensional filter
where B(ω) is the Fourier
transform of the one-dimensional filter
is the Fourier transform of the transformation matrix
The returned filter
h is the inverse Fourier transform of
 Lim, Jae S., Two-Dimensional Signal and Image Processing, Englewood Cliffs, NJ, Prentice Hall, 1990, pp. 218-237.