From my few knowledge, using the McClellan transformation to a 1D-FIR filter allows us to get a circular as well as the diamond shaped 2D-FIR filters. But, in the context of my work, i look for a square-shaped one. So, is it possible to design a square shaped 2D-FIR filter using the McClellan transformation? if no, is there another approach allowing us to get the circular shaped filters as well as the square shaped ones from a 1D prototype (from the 1D Daubechies 9-7 for exemple)?
A 2-D FIR filter H(z_x,z_y) having a square shaped passband can be designed by simply cascading two 1-D lowpass filters H_x(z_x) and H_y(z_y) having the same characteristics such as the cutoff frequency and passband ripple. In other words,
H(z_x,z_y) = H_0(z_x) H_0(z_y),
where H_0(.) is a 1-D prototype filter.
Tanks for your answer, by my question is not as you have understood. So, in other words, my question is how can we design a 2D square-shaped FIR filter bank that guarantees a perfect reconstruction? (i.e.: how to design four square filters allowing to get the perfect reconstruction)
Yours sincerely
Abdelhak
To design a 2-D filter bank with perfect reconstruction using a 2-D prototype filter having a square-shaped passband you may employ the modified-DFT or the cosine-modulated approach. For more details see the paper "Theory and design of two-dimensional DFT modulated filter bank with arbitrary modulation and decimation matrices".
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