function [approximationCoefficients, detailCoefficients] = haarDWT(signal)
% FWT with Haar wavelet
    N = length(signal); 
    approximationCoefficients = zeros(1, N/2);
    detailCoefficients = zeros(1, N/2);  
    for k = 1:N/2
        % compute approximation (scaling) coefficients
        approximationCoefficients(k) = (signal(2*k-1) + signal(2*k)) / sqrt(2);    
        % compute detail (wavelet) coefficients
        detailCoefficients(k) = (signal(2*k-1) - signal(2*k)) / sqrt(2);
    end
end