%
% Solution exercise 2, Assignment 6, part 2
% 
% CAAM 415, 11/25/08
%

%parameters here are k_x, s_x, k_t, s_t, corresponding ...
%to the peak spatial (c/deg) and temporal (c/sec) values of the
%filter and their spread. 

%circular frequency corresponding to 4.2 cycles/deg
k_x = 2*pi*4.2;

%in degrees
s_x = 0.1; 

dx = 0.004;            %units are degrees
nx = 128;

x = ((-nx/2+1)*dx:dx:nx/2*dx);  %units are degrees, 128 points

%compute the spatial filters
r_es = g_es(k_x,s_x,x);
r_os = g_os(k_x,s_x,x);

%circular frequency corresponding to 8 cycles/sec
k_t = 2*pi*8;

%in sec
s_t = 0.031;

%temporal filter
dt = 0.002;            %units are seconds
nt = 128;
t = ((-nt/2+1)*dt:dt:nt/2*dt)';  %units are seconds

t_es = f_es(k_t,s_t,t);
t_os = f_os(k_t,s_t,t);


%grating
t_gr = (0:dt:2)';
n_tgr =length(t_gr);

%grating moving to the right
g1 = cos(k_x*repmat(x,[n_tgr 1]) - k_t*repmat(t_gr,[1 nx]));

%spatial component
g1_s = g1*r_es';

%temporal convolution
inter1_st = conv(g1_s,t_es);

%correct for time shift using conv
g1_st(1:n_tgr) = inter1_st(64:n_tgr+64-1)*dt;

%grating moving to the left
g2 = cos(k_x*repmat(x,[n_tgr 1]) + k_t*repmat(t_gr,[1 nx]));

%spatial component
g2_s = g2*r_es';

%temporal convolution
inter2_st = conv(g2_s,t_es);

%correct for time shift using conv
g2_st(1:n_tgr) = inter2_st(64:n_tgr+64-1)*dt;


figure;
h1 = plot(t_gr,g1_st);
hold on;
h2 = plot(t_gr,g2_st,'r.');
legend([h1 h2],{'right' 'left'});
title('response of separable Gabor Filter to left/right moving sine waves');
xlabel('time (s)');
ylabel('response (arbitrary units)');

%spatial component odd filter part
g3_s = g1*r_os';

%temporal convolution
inter3_st = conv(g3_s,t_os);

%correct for time shift using conv
g3_st(1:n_tgr) = inter3_st(64:n_tgr+64-1)*dt;

%spatial component odd filter part
g4_s = g2*r_os';

%temporal convolution
inter4_st = conv(g4_s,t_os);

%correct for time shift using conv
g4_st(1:n_tgr) = inter4_st(64:n_tgr+64-1)*dt;

figure;
h3 = plot(t_gr,g1_st+g3_st);
hold on;
h4 = plot(t_gr,g1_st+g4_st,'r.');
legend([h3 h4], {'right' 'left'});
title('response of inseparable GF to left/right moving sine waves');
xlabel('time (s)');
ylabel('response (arbitrary units)');