denoising_wl_sin.m

function [sin_5] = denoising_wl_sin(A, n, initial_sin)
%% denoising the nth column of cell A by subsampling and wavelet filtering, then fit the data using sine function.
%% initial_sin is the initial parameters for sine function fitting. it is a
%% vector [a, b ,c, d] which a is the ampl, b is the frequ, c is the phase,
%% d is the intercept.
% view2(:, 9:12) = denoising_wl_sin(conv_feature, 2, [20 2 3 70]);
maxiter = size(A, 2);
b = cell(1, maxiter);
%% subsampling
for i =1 : maxiter
    temp = A{1, i};
    conv_d = temp(:, n);
    Leng =  length(conv_d)/5;
    if Leng~= floor(Leng)
        conv_e = zeros(ceil(Leng) * 5, 1);
        for j = 1 : length(conv_d)
            conv_e(j) = conv_d(j);
        end
        conv_d = conv_e;
    end
    Mat = reshape(conv_d, 5, []);
    aver_5 = sum(Mat, 1)/5;
    if Leng~= floor(Leng)
        aver_5(ceil(Leng)) = sum(Mat(:, end))/(length(temp(:,3))-floor(Leng) * 5);
    end
       aver_5 = aver_5';
       b{1, i} = aver_5;
end

%% wavelet filtering
c = cell(size(b));
for i = 1 : length(b)
    s = b{1, i};
    l_s = length(s);
    [cA1, cD1] = dwt(s,'haar');
    A1= upcoef('a',cA1,'haar',1,l_s);
    D1= upcoef('a',cD1,'haar',1,l_s);
    % subplot(1,2,1); plot(A1); title('Approximation A1')
    % subplot(1,2,2); plot(D1); title('Detail D1')
    [thr,sorh,keepapp] = ddencmp('den','wv',s);
    [C,L] = wavedec(s,1,'haar');
    clean = wdencmp('gbl',C,L,'haar',1,1e06,sorh,keepapp);
    % figure;
    % subplot(2,1,1); plot(s); title('Original')
    %  subplot(2,1,2); plot(clean); title('denoised')
    c{1, i} = clean;
end
% c{1,32}= c{1, 32}';
clean_conv_5 = c;
%% sine fitting
lengc = size(c, 2); % Number of users
A = zeros(lengc, 4);
A_result = cell(1, lengc);
for i = 1 : lengc 
   days = length(c{1, i});
   axis_x = 1 : 5 : days*5; 
   axis_y = c{1, i}';
   fx =@(a, t) a(1) * sin(2*pi*t/a(2)+a(3))+a(4);
   A(i, :) = lsqcurvefit( fx, initial_sin, axis_x, axis_y);
   A_res = fx(A(i, :), axis_x);
   A_result{1, i} = A_res;
end
sin_5= A;
end