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function [num,den] = latc2tf(k,varargin)
// Convert lattice filter parameters to transfer function coefficients
//
//
// Calling sequence
// [num,den] = latc2tf(k,v)
// [num,den] = latc2tf(k,'iiroption')
// num = latc2tf(k,'firoption')
//
//
// Description
// [num,den] = latc2tf(k,v)
// Finds the transfer function of the IIR filter from the lattice
// coefficients k and ladder coefficients v.
// [num,den] = latc2tf(k,'iiroption')
// Finds the transfer function of the allpass or allpole (specified by
// the iiroption flag) IIR filter.
// num = latc2tf(k,'firoption')
// Finds the transfer function of the FIR filter from the lattice
// coefficients k. The firoption flag specifies the type of the FIR
// filter (can be 'min, 'max', or 'FIR')
//
// Parameters:
// k - double - vector
// Lattice coefficients
// Lattice coefficients for FIR/IIR filter. Can be real or complex.
// v - double - vector
// Ladder coefficients
// Ladder coefficients for IIR filters. Can be real or complex.
// iiroption - string flag - 'allpole', or 'allpass'
// Specification of the type if IIR filter
// firoption - string flag - 'min', 'max', or 'FIR' (default)
// Speficication of the type of FIR filter
//
// Examples
// 1) FIR filter
// k1 = [1/2 1/2 1/4];
// [num1,den1] = latc2tf(k1);
//
// See also
// latcfilt | tf2latc
//
// References
// [1] J.G. Proakis, D.G. Manolakis, Digital Signal Processing,
// 3rd ed., Prentice Hall, N.J., 1996, Chapter 7.
// [2] S. K. Mitra, Digital Signal Processing, A Computer
// Based Approach, McGraw-Hill, N.Y., 1998, Chapter 6.
//
// Authors
// Ayush Baid
[numOutArgs,numInArgs] = argn(0);
// ** Check on number of input arguments **
if numOutArgs<1 | numOutArgs>2 then
msg = "cummin: Wrong number of output argument; 1-2 expected";
error(78,msg);
end
if numInArgs<1 | numInArgs>2 then
msg = "cummin: Wrong number of input argument; 1-2 expected";
error(77,msg);
end
// ** Parsing the input arguments **
// 1) k:
// must be a vector
// can be real or complex valued, (negative values allowed)
// checking data type
if ~(type(k)==1 | type(k)==8) then
msg = "latc2tf: Wrong type for argument #1 (k); Real or complex vector expected";
error(53,msg);
end
// checking the dimensions (must be a vector)
if ~(size(k,1)==1 | size(k,2)==1) then
msg = "latc2tf: Wrong type for argument #1 (k); Real or complex vector expected";
error(53,msg);
end
// convert to column vector
if size(k,1)==1 then
k = k(:);
end
L = length(varargin);
// Parsing the 2nd argument
if L>=1 then
arg2 = varargin(1);
// string check
if type(arg2)==10 then
if strcmpi(arg2,'FIR')==0 then
[num,den] = latc2tf_fir(k,2);
elseif strcmpi(arg2,'min')==0 then
[num,den] = latc2tf_fir(k,0);
elseif strcmpi(arg2,'max')==0 then
[num,den] = latc2tf_fir(k,1);
elseif strcmpi(arg2,'allpole')==0 then
[num,den] = latc2tf_iir2(k,1);
elseif strcmpi(arg2,'allpass')==0 then
[num,den] = latc2tf_iir1(k);
else
msg = "latc2tf: Wrong value for argument #2 (string flag) ";
error(53,msg);
end
elseif (type(arg2)==1 | type(arg2)==8) then
// arg2 is ladder coefficients
// check for vector input
if ~(size(arg2,1)==1 | size(arg2,2)==1) then
msg = "latc2tf: Wrong type for argument #2 (v); Real or complex vector expected";
error(53,msg);
end
// convert to column vector
if size(arg2,1)==1 then
arg2 = arg2(:);
end
[num,den] = latc2tf_iir2(k,arg2);
else
msg = "latc2tf: Wrong type for argument #2; Real or complex vector" + ...
"(ladder coeffs k) or string flag expected";
error(53,msg);
end
else
[num,den] = latc2tf_fir(k,2);
end
num = num';
den = den';
endfunction
function [num,den] = latc2tf_fir(k,option)
// latc2tf for FIR filters
// Input Arguments
// k: lattice coefficients
// option: 0 for min-phase (default), 1 for max-phase; 2 for fir
if isempty(k) then
num = 1;
den = 1;
return
end
den = 1;
p = length(k);
num = 1;
for j=2:p+1
num = [num; 0] + k(j-1)*[0; conj(num($:-1:1,:))];
end
if option==1 then
num = conj(num($:-1:1));
end
endfunction
function [num,den] = latc2tf_iir1(k)
// for all pass IIR filters
if isempty(k) then
num = 1;
den = 1;
return
end
p = length(k);
den = 1;
for j=2:p+1
den = [den; 0] + k(j-1)*[0; conj(den($:-1:1,:))];
end
num = conj(den($:-1:1));
endfunction
function [num,den] = latc2tf_iir2(k,v)
// for allpole and general IIR fitlers
if isempty(k) & isempty(v) then
num = [];
den = [];
elseif isempty(k) & length(v)==1 then
num = v;
den = 1;
else
// k is a column vector
M = size(k,1)+1;
// pad v with appropriate number of zeros
l_v = size(v,1);
diff = M - l_v;
if diff>0 then
v = [v; zeros(diff,1)];
elseif diff<0 then
k = [k; zeros(-diff,1)];
end
p = length(k);
den = 1;
for j=2:p+1
den = [den; 0] + k(j-1)*[0; conj(den($:-1:1,:))];
end
exec('rlevinson.sci',-1);
[r,temp] = rlevinson(den,1);
num = (temp*v);
end
endfunction
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