www.gusucode.com > wavelet 源码程序 matlab案例代码 > wavelet/LocalizeDiscontinuityInSineWaveExample.m

    %% Localize Discontinuity in Sine Wave
% This example shows wavelet analysis can localize a discontinuity in a
% sine wave.
%%
% Create a 1-Hz sine wave sampled at 100 Hz. The duration of the sine wave
% is one second. The sine wave has a discontinuity at $t=0.5$ seconds.

% Copyright 2015 The MathWorks, Inc.

t = linspace(0,1,100)';
x = sin(2*pi*t);
x1 = x-0.15;
y = zeros(size(x));
y(1:length(y)/2) = x(1:length(y)/2);
y(length(y)/2+1:end) = x1(length(y)/2+1:end);
stem(t,y,'markerfacecolor',[0 0 1]); 
xlabel('Seconds'); 
ylabel('Amplitude');
%%
% Obtain the nondecimated discrete wavelet transform of the sine wave using
% the |'sym2'| wavelet and plot the wavelet (detail)
% coefficients along with the original signal.
[swa,swd] = swt(y,1,'sym2');
subplot(211)
stem(t,y,'markerfacecolor',[0 0 1]); 
title('Orignal Signal');
subplot(212)
stem(t,swd,'markerfacecolor',[0 0 1]);
title('Level 1 Wavelet Coefficients');
%%
% Compare the Fourier coefficient magnitudes for the 1-Hz sine wave with
% and without the discontinuity.
dftsig = fft([x y]);
dftsig = dftsig(1:length(y)/2+1,:);
df = 100/length(y);
freq = 0:df:50;
stem(freq,abs(dftsig));
xlabel('Hz'); ylabel('Magnitude');
legend('sine wave','sine wave with discontinuity');
%%
% There is minimal difference in the magnitudes of the Fourier
% coefficients. Because the discrete Fourier basis vectors have support
% over the entire time interval, the discrete Fourier transform does not
% detect the discontinuity as efficiently as the wavelet transform.
%%
% Compare the level 1 wavelet coefficients for the sine wave with and
% without the discontinuity.
[swax,swdx] = swt(x,1,'sym2');
subplot(211)
stem(t,swd); title('Sine Wave with Discontinuity (Wavelet Coefficients)');
subplot(212)
stem(t,swdx); title('Sine Wave (Wavelet Coefficients)');
%%
% The wavelet coefficients of the two signals demonstrate a significant
% difference.
% Wavelet analysis is often capable of revealing characteristics of a
% signal or image that other analysis techniques miss, like trends,
% breakdown points, discontinuities in higher derivatives, and
% self-similarity. Furthermore, because wavelets provide a different view
% of data than those presented by Fourier techniques, wavelet analysis can
% often significantly compress or denoise a signal without appreciable
% degradation.