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2-D FIR filter using frequency transformation


h = ftrans2(b,t) produces the two-dimensional FIR filter h that corresponds to the one-dimensional FIR filter b using the transform t. The transform matrix t contains coefficients that define the frequency transformation to use.


h = ftrans2(b) uses the McClellan transform matrix t.

t = [1 2 1; 2 -4 2; 1 2 1]/8;


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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 function firpm.

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');

Use ftrans2 with the default McClellan transformation to create the desired approximately circularly symmetric filter.

h = ftrans2(b);

Input Arguments

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FIR filter, specified as a numeric matrix. b must be a 1-D Type I (even symmetric, odd-length) filter such as can be returned by fir1 (Signal Processing Toolbox), fir2 (Signal Processing Toolbox), or firpm (Signal Processing Toolbox).

Data Types: double

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.

Data Types: double

Output Arguments

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2-D FIR filter, returned as a numeric matrix. ftrans2 returns h as a computational molecule, which is the appropriate form to use with filter2. If t is m-by-n and b has length Q, then h is size ((m-1)*(Q-1)/2+1)-by-((n-1)*(Q-1)/2+1).


The transformation below defines the frequency response of the two-dimensional filter returned by ftrans2.


where B(ω) is the Fourier transform of the one-dimensional filter b:


and T(ω1,ω2) is the Fourier transform of the transformation matrix t:


The returned filter h is the inverse Fourier transform of H(ω1,ω2):



[1] Lim, Jae S., Two-Dimensional Signal and Image Processing, Englewood Cliffs, NJ, Prentice Hall, 1990, pp. 218-237.

Version History

Introduced before R2006a