one_dim_with_lapl.m

h = 1/16 * [1, 4, 6, 4, 1];

sample_pts = -36:1:37;
sample_pts_1 = sample_pts(1:2:end);

signal = my_signal(sample_pts);

num_pts = size(signal, 2);

h_ = [h zeros(1, num_pts - 5)];
e = [1, zeros(1, num_pts - 1)];

T = toeplitz(1/16 * e, h_);

% fix this
D = eye(num_pts); 
S = kron(D, [1, 0]);

g_1 = S * T * signal.';

% plot signal and gauss lv 1
plot(sample_pts, signal);
plot(sample_pts_1, g_1);

% upscale gauss
UPD = eye(size(sample_pts_1, 2) / 2);
UPS = kron(UPD, [0.5, 0.5]);
% find laplacian
UPG = UPS * g_1;
l_1 = signal - UPG;

function signal = my_signal(x)
    % random polynomial or any func
    signal = sin(x) ./ x; 
end