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diff --git a/macros/bilinear.sci b/macros/bilinear.sci new file mode 100644 index 0000000..387b8d0 --- /dev/null +++ b/macros/bilinear.sci @@ -0,0 +1,40 @@ +function [Zb, Za, Zg]= bilinear(Sb,varargin) +// Transform a s-plane filter specification into a z-plane specification +//Calling Sequence +// [ZB, ZA] = bilinear (SB, SA, T) +// [ZB, ZA] = bilinear (SZ, SP, SG, T) +// [ZZ, ZP, ZG] = bilinear (...) +//Description +//Transform a s-plane filter specification into a z-plane specification. Filters can be specified in either zero-pole-gain or transfer function form. The input form does not have to match the output form. 1/T is the sampling frequency represented in the z plane. +// +//Note: this differs from the bilinear function in the signal processing toolbox, which uses 1/T rather than T. +// +//Theory: Given a piecewise flat filter design, you can transform it from the s-plane to the z-plane while maintaining the band edges by means of the bilinear transform. This maps the left hand side of the s-plane into the interior of the unit circle. The mapping is highly non-linear, so you must design your filter with band edges in the s-plane positioned at 2/T tan(w*T/2) so that they will be positioned at w after the bilinear transform is complete. +//Examples +//[ZB,ZA]=bilinear([1],[2,3],3) + funcprot(0); + lhs= argn(1); + rhs= argn(2); + if(rhs < 3 | rhs > 4) + error("Wrong number of input arguments"); + end + if(lhs < 2 | lhs > 3) + error("Wrong number of output arguments"); + end + select(rhs) + case 3 then + select(lhs) + case 2 then + [Zb, Za]= callOctave("bilinear", Sb, varargin(1), varargin(2)); + case 3 then + [Zb, Za, Zg]= callOctave("bilinear", Sb, varargin(1), varargin(2)); + end + case 4 then + select(lhs) + case 2 then + [Zb, Za]= callOctave("bilinear", Sb, varargin(1), varargin(2), varargin(3)); + case 3 then + [Zb, Za, Zg]= callOctave("bilinear", Sb, varargin(1), varargin(2), varargin(3)); + end + end +endfunction
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