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detrending_method.m
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detrending_method.m
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% clear; close all; clc; warning off;
function [detrended_data, record_y] = detrending_method(data, seg_len, fit_order)
if size(data, 1) < size(data, 2)
data = data';
end
% seg_len = 1001; % odd num
nonoverlap_len = (seg_len - 1)/2;
% load brod2005.txt
% data = brod2005;
data_len = length(data);
% calculate the coefficient, given a window size and fitting order
[coeff_output, A] = detrending_coeff(seg_len, fit_order);
A_coeff = A * coeff_output;
for seg_index = 1
% left trend
% seg_index = 1;
xi = 1 + (seg_index - 1) * (seg_len - 1) : seg_index * (seg_len - 1) + 1;
xi_left = xi;
seg_data = data(xi);
%slope = polyfit(xi, seg_data', fit_order);
%left_trend1 = polyval(slope, xi);
% to be replaced by pre-calculated coefficients
left_trend = (A_coeff * seg_data)';
% mid trend
if seg_index * (seg_len - 1) + 1 + nonoverlap_len > data_len
xi = 1 + (seg_index - 1) * (seg_len - 1) + nonoverlap_len : length(data);
xi_mid = xi;
seg_data = data(xi);
%slope = polyfit(xi, seg_data', fit_order);
%mid_trend = polyval(slope, xi);
if (length(seg_data) < seg_len)
[coeff_output1, A1] = detrending_coeff(length(seg_data), fit_order);
A_coeff1 = A1 * coeff_output1;
mid_trend = (A_coeff1 * seg_data)';
else
mid_trend = (A_coeff * seg_data)';
end
xx1 = left_trend((seg_len + 1)/2:seg_len);
xx2 = mid_trend(1:(seg_len + 1)/2);
w = (0 : nonoverlap_len)/nonoverlap_len;
xx_left = xx1 .* (1 - w) + xx2 .* w;
record_x = xi_left(1:nonoverlap_len);
record_y = left_trend(1:nonoverlap_len);
mid_start_index = find(xi_mid == (xi_left(end) + 1));
if (length(mid_start_index) == 0)
record_x = [record_x xi_left((end+3)/2 : end)];
record_y = [record_y xx_left(2 : end)];
else
record_x = [record_x xi_left((end+1)/2 : end) xi_mid(mid_start_index : end)];
record_y = [record_y xx_left(1 : end) mid_trend((seg_len + 3)/2:end)];
end
detrended_data = data - record_y';
return;
else
xi = 1 + (seg_index - 1) * (seg_len - 1) + nonoverlap_len : seg_index * (seg_len - 1) + 1 + nonoverlap_len;
xi_mid = xi;
seg_data = data(xi);
%slope = polyfit(xi, seg_data', fit_order);
%mid_trend = polyval(slope, xi);
mid_trend = (A_coeff * seg_data)';
% right trend
if (seg_index + 1) * (seg_len - 1) + 1 > data_len % not enough data points available in the right part
xi = seg_index * (seg_len - 1) + 1 : data_len;
xi_right = xi;
seg_data = data(xi);
%slope = polyfit(xi, seg_data', fit_order);
%right_trend = polyval(slope, xi);
if (length(seg_data) < seg_len)
% need to re-calculate coefficient and A
[coeff_output1, A1] = detrending_coeff(length(seg_data), fit_order);
A_coeff1 = A1 * coeff_output1;
right_trend = (A_coeff1 * seg_data)';
else
right_trend = (A_coeff * seg_data)';
end
xx1 = left_trend((seg_len + 1)/2:seg_len);
xx2 = mid_trend(1:(seg_len + 1)/2);
w = (0 : nonoverlap_len)/nonoverlap_len;
xx_left = xx1 .* (1 - w) + xx2 .* w;
xx1 = mid_trend((seg_len + 1)/2:seg_len);
xx2 = right_trend(1:(seg_len + 1)/2);
w = (0 : nonoverlap_len)/nonoverlap_len;
xx_right = xx1 .* (1 - w) + xx2 .* w;
record_x = xi_left(1:nonoverlap_len);
record_y = left_trend(1:nonoverlap_len);
record_x = [record_x xi_left((end+1)/2 : end) xi_mid((end+1)/2 + 1 : end)];
record_y = [record_y xx_left(1 : end) xx_right(2:end)];
right_start_index = find(xi_right == xi_mid(end) + 1);
record_x = [record_x xi_right(right_start_index:end)];
record_y = [record_y right_trend(right_start_index:end)];
detrended_data = data - record_y';
return;
else
xi = seg_index * (seg_len - 1) + 1 : (seg_index + 1) * (seg_len - 1) + 1;
xi_right = xi;
seg_data = data(xi);
%slope = polyfit(xi, seg_data', fit_order);
%right_trend = polyval(slope, xi);
right_trend = (A * coeff_output * seg_data)';
xx1 = left_trend((seg_len + 1)/2:seg_len);
xx2 = mid_trend(1:(seg_len + 1)/2);
w = (0 : nonoverlap_len)/nonoverlap_len;
xx_left = xx1 .* (1 - w) + xx2 .* w;
% plot(xi_left(end/2 : end), xx_left, 'r', 'LineWidth', 2)
xx1 = mid_trend((seg_len + 1)/2:seg_len);
xx2 = right_trend(1:(seg_len + 1)/2);
w = (0 : nonoverlap_len)/nonoverlap_len;
xx_right = xx1 .* (1 - w) + xx2 .* w;
% plot(xi_mid(end/2:end), xx_right, 'r', 'LineWidth', 2)
record_x = xi_left(1:nonoverlap_len);
record_y = left_trend(1:nonoverlap_len);
record_x = [record_x xi_left((end+1)/2 : end) xi_mid((end+1)/2 + 1 : end)];
record_y = [record_y xx_left(1 : end) xx_right(2:end)];
end
end
end
for seg_index = 2 : floor((data_len-1)/(seg_len-1)) - 1
% left trend
% seg_index = 1;
xi = 1 + (seg_index - 1) * (seg_len - 1) : seg_index * (seg_len - 1) + 1;
xi_left = xi;
seg_data = data(xi);
%slope = polyfit(xi_left, seg_data', fit_order);
%left_trend = polyval(slope, xi);
left_trend = (A_coeff * seg_data)';
% mid trend
xi = 1 + (seg_index - 1) * (seg_len - 1) + nonoverlap_len : seg_index * (seg_len - 1) + 1 + nonoverlap_len;
xi_mid = xi;
seg_data = data(xi);
%slope = polyfit(xi, seg_data', fit_order);
%mid_trend = polyval(slope, xi);
mid_trend = (A_coeff * seg_data)';
% right trend
xi = seg_index * (seg_len - 1) + 1 : (seg_index + 1) * (seg_len - 1) + 1;
xi_right = xi;
seg_data = data(xi);
%slope = polyfit(xi, seg_data', fit_order);
%right_trend = polyval(slope, xi);
right_trend = (A_coeff * seg_data)';
xx1 = left_trend((seg_len + 1)/2:seg_len);
xx2 = mid_trend(1:(seg_len + 1)/2);
w = (0 : nonoverlap_len)/nonoverlap_len;
xx_left = xx1 .* (1 - w) + xx2 .* w;
% plot(xi_left(end/2 : end), xx_left, 'r', 'LineWidth', 2)
xx1 = mid_trend((seg_len + 1)/2:seg_len);
xx2 = right_trend(1:(seg_len + 1)/2);
w = (0 : nonoverlap_len)/nonoverlap_len;
xx_right = xx1 .* (1 - w) + xx2 .* w;
% plot(xi_mid(end/2:end), xx_right, 'r', 'LineWidth', 2)
record_x = [record_x xi_left((end+3)/2 : end) xi_mid((end+1)/2 + 1 : end)];
record_y = [record_y xx_left(2 : end) xx_right(2:end)];
end
% last part of data
for seg_index = floor((data_len-1)/(seg_len-1))
% left trend
% seg_index = 1;
xi = 1 + (seg_index - 1) * (seg_len - 1) : seg_index * (seg_len - 1) + 1;
xi_left = xi;
seg_data = data(xi);
%slope = polyfit(xi_left, seg_data', fit_order);
%left_trend = polyval(slope, xi);
left_trend = (A_coeff * seg_data)';
% mid trend
if (seg_index * (seg_len - 1) + 1 + nonoverlap_len > length(data))
xi = 1 + (seg_index - 1) * (seg_len - 1) + nonoverlap_len : length(data);
xi_mid = xi;
seg_data = data(xi);
%slope = polyfit(xi, seg_data', fit_order);
%mid_trend = polyval(slope, xi);
% may need to re-calcualte coefficient and A, since the length of
% 'seg_data' may be smaller than seg_len
if (length(seg_data) < seg_len)
% need to re-calculate coefficient and A
[coeff_output1, A1] = detrending_coeff(length(seg_data), fit_order);
A_coeff1 = A1 * coeff_output1;
mid_trend = (A_coeff1 * seg_data)';
else
mid_trend = (A_coeff * seg_data)';
end
xx1 = left_trend((seg_len + 1)/2:seg_len);
xx2 = mid_trend(1:(seg_len + 1)/2);
w = (0 : nonoverlap_len)/nonoverlap_len;
xx_left = xx1 .* (1 - w) + xx2 .* w;
mid_start_index = find(xi_mid == (xi_left(end) + 1));
if (length(mid_start_index) == 0)
record_x = [record_x xi_left((end+3)/2 : end)];
record_y = [record_y xx_left(2 : end)];
else
record_x = [record_x xi_left((end+3)/2 : end) xi_mid(mid_start_index : end)];
record_y = [record_y xx_left(2 : end) mid_trend((seg_len + 3)/2:end)];
end
break;
else
xi = 1 + (seg_index - 1) * (seg_len - 1) + nonoverlap_len : seg_index * (seg_len - 1) + 1 + nonoverlap_len;
xi_mid = xi;
seg_data = data(xi);
%slope = polyfit(xi, seg_data', fit_order);
%mid_trend = polyval(slope, xi);
mid_trend = (A_coeff * seg_data)';
end
% plot(xi, mid_trend);
% hold on;
% right trend
xi = seg_index * (seg_len - 1) + 1 : data_len;
xi_right = xi;
seg_data = data(xi);
%slope = polyfit(xi, seg_data', fit_order);
%right_trend = polyval(slope, xi);
if (length(seg_data) < seg_len)
% need to re-calculate coefficient and A
[coeff_output1, A1] = detrending_coeff(length(seg_data), fit_order);
A_coeff1 = A1 * coeff_output1;
right_trend = (A_coeff1 * seg_data)';
else
right_trend = (A_coeff * seg_data)';
end
xx1 = left_trend((seg_len + 1)/2:seg_len);
xx2 = mid_trend(1:(seg_len + 1)/2);
w = (0 : nonoverlap_len)/nonoverlap_len;
xx_left = xx1 .* (1 - w) + xx2 .* w;
% plot(xi_left(end/2 : end), xx_left, 'r', 'LineWidth', 2)
xx1 = mid_trend((seg_len + 1)/2:seg_len);
xx2 = right_trend(1:(seg_len + 1)/2);
w = (0 : nonoverlap_len)/nonoverlap_len;
xx_right = xx1 .* (1 - w) + xx2 .* w;
% plot(xi_mid(end/2:end), xx_right, 'r', 'LineWidth', 2)
record_x = [record_x xi_left((end+3)/2 : end) xi_mid((end+1)/2 + 1 : end)];
record_y = [record_y xx_left(2 : end) xx_right(2:end)];
right_start_index = find(xi_right == xi_mid(end) + 1);
record_x = [record_x xi_right(right_start_index:end)];
record_y = [record_y right_trend(right_start_index:end)];
end
detrended_data = data - record_y';