Chapter 8

% Program 8_1

% Factorization of a Rational FIR Transfer Function

%

format long

num = input('Filter coefficient vector = ');

Numfactors = factorize(num);

disp('Factors'),disp(Numfactors)

% Program 8_2

% Factorization of a Rational IIR Transfer Function

%

format short

num = input('Numerator coefficients = ');

den = input('Denominator coefficients = ');

Numfactors = factorize(num);

Denfactors = factorize(den);

disp('Numerator Factors'),disp(Numfactors)

disp('Denominator Factors'),disp(Denfactors)

% Program 8_3

% Parallel Realizations of an IIR Transfer Function

%

num = input('Numerator coefficient vector = ');

den = input('Denominator coefficient vector = ');

[r1,p1,k1] = residuez(num,den);

[r2,p2,k2] = residue(num,den);

disp('Parallel Form I')

disp('Residues are');disp(r1);

disp('Poles are at');disp(p1);

disp('Constant value');disp(k1);

disp('Parallel Form II')

disp('Residues are');disp(r2);

disp('Poles are at');disp(p2);

disp('Constant value');disp(k2);

% Program 8_4

% Cascaded Lattice Realization of an

% Allpass Transfer Function

%

format long

den = input('Denominator coefficient vector = ');

k = poly2rc(den);

knew = fliplr(k);

disp('The lattice section multipliers are');disp(knew');

% Program 8_5

% Realization of Gray-Markel Cascaded Lattice Structure

%

% den is the denominator coefficient vector

% num is the numerator coefficient vector

% k is the lattice parameter vector

% alpha is the vector of feedforward multipliers

%

format long

% Read in the transfer function coefficients

num = input('Numerator coefficient vector = ');

den = input('Denominator coefficient vector = ');

num = num/den(1);

den = den/den(1);

[k,alpha] = tf2latc(num,den);

disp('Lattice parameters are');disp(k');

disp('Feedforward multipliers are');disp(fliplr(alpha'));

% Program 8_6

% Transfer Function of Gray-Markel Cascaded

% Lattice Structure from the Lattice and

% Feedforward Parameters

% k1 is the lattice parameter vector

% alpha is the vector of feedforward multipliers

% den is the denominator coefficient vector

% num is the numerator coefficient vector

%

format long

% Read in the lattice and feedforward parameters

k1 = input('Lattice parameter vector = ');

alpha = input('Feedforward parameter vector = ');

[num,den] = latc2tf(k1,fliplr(alpha));

disp('Numerator coefficients are');disp(num)

disp('Denominator coefficients are');disp(den)

% Program 8_7

% FIR Cascaded Lattice Realization

%

format long

num = input('Transfer function coefficients = ');

k = tf2latc(num);

disp('Lattice coefficients are'); disp(fliplr(k'));