Contents

% alternative lattice structures for all-pole systems
% lab9_1.m * mw * 04/13/2007

Filter coefficients

a = [1 1/2 1/4 1/8]; % numerator polynomial for all-pole filter
k = tf2latc(a);      % reflection coefficients (MATLAB built-in function)

Impulse responses - simulate

x = [1 zeros(1,10)];     % impulse (input signal)
[u,v]   = latcfilt(k,1,x); % MATLAB built-in function
[ua,va] = latcalp(k,x);    % all-pole form
[u1,v1] = latc1m(k,x);     % one-multiplier form
[u3,v3] = latc3m(k,x);     % three-multiplier form
[un,vn] = latcnorm(k,x);   % normalized form
[ukl,vkl] = latckl(k,x);   % Kelly-Lochbaum form

Impulse responses - compare

fprintf('lab9_1 : Impulse responses - minumum phase output\n')
fprintf('   u[n]    ua[n]    u1[n]    u3[n]    un[n]    ukl[n]\n')
for n=0:10
    fprintf('%7.4f  %7.4f  %7.4f  %7.4f  %7.4f  %7.4f \n',u(n+1),ua(n+1),u1(n+1),u3(n+1),un(n+1),ukl(n+1))
end
fprintf('lab9_1 : Impulse responses - maximum phase output\n')
fprintf('   v[n]    va[n]    v1[n]    v3[n]    vn[n]    vkl[n]\n')
for n=0:10
    fprintf('%7.4f  %7.4f  %7.4f  %7.4f  %7.4f  %7.4f \n',v(n+1),va(n+1),v1(n+1),v3(n+1),vn(n+1),vkl(n+1))
end

lab9_1 : Impulse responses - minumum phase output
   u[n]    ua[n]    u1[n]    u3[n]    un[n]    ukl[n]
 1.0000   1.0000   1.0000   1.0000   1.0000   1.0000 
-0.5000  -0.5000  -0.5000  -0.5000  -0.5000  -0.5000 
-0.0000  -0.0000  -0.0000  -0.0000  -0.0000   0.0000 
-0.0000  -0.0000  -0.0000   0.0000   0.0000  -0.0000 
 0.0625   0.0625   0.0625   0.0625   0.0625   0.0625 
-0.0312  -0.0312  -0.0312  -0.0313  -0.0313  -0.0312 
-0.0000  -0.0000  -0.0000  -0.0000  -0.0000  -0.0000 
-0.0000  -0.0000  -0.0000   0.0000   0.0000  -0.0000 
 0.0039   0.0039   0.0039   0.0039   0.0039   0.0039 
-0.0020  -0.0020  -0.0020  -0.0020  -0.0020  -0.0020 
-0.0000  -0.0000  -0.0000  -0.0000  -0.0000  -0.0000 
lab9_1 : Impulse responses - maximum phase output
   v[n]    va[n]    v1[n]    v3[n]    vn[n]    vkl[n]
 0.1250   0.1250   0.1250   0.1250   0.1250   0.1250 
 0.1875   0.1875   0.1875   0.1875   0.1875   0.1875 
 0.3750   0.3750   0.3750   0.3750   0.3750   0.3750 
 0.7500   0.7500   0.7500   0.7500   0.7500   0.7500 
-0.4922  -0.4922  -0.4922  -0.4922  -0.4922  -0.4922 
 0.0117   0.0117   0.0117   0.0117   0.0117   0.0117 
 0.0234   0.0234   0.0234   0.0234   0.0234   0.0234 
 0.0469   0.0469   0.0469   0.0469   0.0469   0.0469 
-0.0308  -0.0308  -0.0308  -0.0308  -0.0308  -0.0308 
 0.0007   0.0007   0.0007   0.0007   0.0007   0.0007 
 0.0015   0.0015   0.0015   0.0015   0.0015   0.0015 

Published with MATLAB® 7.3