2-D FIR filter using frequency transformation
produces the two-dimensional FIR filter
h = ftrans2(
h that corresponds to the
one-dimensional FIR filter
b using the transform
b must be a one-dimensional, Type I
(even symmetric, odd-length) filter such as can be returned by
the Signal Processing Toolbox software. The transform matrix
contains coefficients that define the frequency transformation to use.
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
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)
b— One-dimensional FIR filter
1-D FIR filter, specified as a numeric matrix.
be a 1-D Type I (even symmetric, odd-length) filter such as can be returned
firpm in the Signal Processing Toolbox
t— Transform matrix
The transform matrix, specified as a numeric matrix.
t contains coefficients that define the frequency
transformation to use.
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.