%% Example 3.2
% Here is a signal consisting of 4 cycles of sine followed by a step function.

s = [sin([1:512]*8*pi/512) ones(1,256) ones(1,256)/2]
plot(s)
xticks([0 256 512 768 1024])
xticklabels({'0','256','512','768','1024'})
axis([0 1024 -1.5 1.5])

%
% Here it is with added noise.

s10 = [sin([1:512]*8*pi/512) ones(1,256) ones(1,256)/2]+0.1*randn(1,1024);

%

plot(s10)
xticks([0 256 512 768 1024])
xticklabels({'0','256','512','768','1024'})
axis([0 1024 -1.5 1.5])
title('random signal with noise')

%
% Here is a plot of one-scale Haar transform of the signal, using the command haarwave from Computer Exploration 3.7.4.

plot(haarwave(s10,1))
xticks([0 256 512 768 1024])
xticklabels({'0','256','512','768','1024'})
axis([0 1024 -1.5 1.5])
title('one-scale Haar transform of signal')
annotation('doublearrow',[0.13 0.52], [0.52 0.52]);
annotation('doublearrow',[0.52 0.905],[0.52 0.52]);
annotation('textbox',[0.32 0.42 0.11 0.06],...
    'String',{'trend s_9'},'LineStyle','none');
annotation('textbox',[0.65 0.38 0.16 0.10],...
    'String',{'detail s_9'},'LineStyle','none');