function H = generateHaarMatrix(n)
    % generate the normalized Haar matrix of order 2^n
    % recursive implementation
    if n == 0  
        H = 1;        % base case
    else
        % recursive step
        H_prev = generateHaarMatrix(n-1);  % generate Haar matrix of previous order
        I = eye(2^(n-1));  % identity matrix of size 2^(n-1)
        % Kronecker products for constructing the next level Haar matrix
        top = (1/sqrt(2)) * kron(I, [1 1]);  % approximation
        bottom = (1/sqrt(2)) * kron(H_prev, [1 -1]); % detail
        H = [top; bottom]; % combine to form the next level Haar matrix
    end
end