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2-dimensional Filter Design using McClellan transformation

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12 Feb 2012 (Updated )

This function can be used to design 2D lowpass, highpass, bandpass, bandstop filters.

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Description

[Filter_1D,Filter_2D]=Filter_Design_2D_McClellan(Type,edges,Ap,Aa,transformation_vector)

This function can be used to design a lowpass, highpass, bandpass, or bandstop
two-dimensional filter which satisfies prescribed specifications.

_ Type can be "Lowpass", "Highpass", "Bandpass", or "Bandstop"
_ edges is a vector of normalized frequencies (rad/s) including passband and stopband edges.
(frequencies must be in an increasing order)
_ Ap: peak to peak passband ripple (db)
_ Aa: minimum stopband attenuation (db)
_ transformation_vector: this is a vector with 4 elements which maps 1D
space to 2D space [1]. These coefficients can be found based on the method
presented in [2]. Some examples are as follows:

2D Filter with circularly symmetric spectrum=[-0.5 0.5 0.5 0.5];
2D Filter with elliptic spectrum=[-2.4973 2.9006 0.3127 0.2840];
2D Filter with fan shape spectrum=[0 0.5 -0.5 0];

The algorithm first designs 1D filter based on kaiser method and
Dig_Filter(http://www.mathworks.com/matlabcentral/fileexchange/30321-digfilter).
Then by using the transformation vector and Chebyshev Polynomials
(http://www.mathworks.com/matlabcentral/fileexchange/4913-chebyshevpoly-m)
2D filter will be designed.

The amplitude response of 2D and 1D filters as well as contours of the
transformation function will be shown at the output.

[Filter_1D,Filter_2D] are 1D and 2D filters’ coefficients, respectively.

Example:
[Filter_1D,Filter_2D]=Filter_Design_2D_McClellan('lowpass',[0.1*pi,0.2*pi],0.5,30,[-0.5 0.5 0.5 0.5]);
Which designs a lowpass 2D FIR filter with circularly symmetric spectrum using Kaiser Method. Passband edge is 0.1*pi, and stopband edge is 0.2*pi,
Ap=0.5 (db) and Aa=30 (db).

----------------------------------------
References:
[1] D.E. Dudgeon, R.M. Mersereau, "Multidimensional digital signal processing", Prentice-Hall.

[2] R.M. Mersereau, W.F.G.Mecklenbrauker, T.F. Quatieri, "McClellan transformations
for two-dimensional digital filtering: I-Design", IEEE transactions on circuit and systems, 1976.

To find other Matlab functions about filter design, please visit
http://www.ece.uvic.ca/~imanmoaz/index_files/index1.htm

Acknowledgements

Chebyshev Poly.M and Dig Filter inspired this file.

Required Products Signal Processing Toolbox
MATLAB
MATLAB release MATLAB 7.2 (R2006a)
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Comments and Ratings (1)
18 Apr 2013 Pei Yu

Thank you for your sharing. I tried and found this code is just for designing FIR. Would you tell me what I should do to get an IIR type? Hope to hear your reply. Thanks.

Updates
11 Oct 2012

some changes in comments

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