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    %% Local Holder Exponents for Cusp Signal and Delta Functions
% Using a cusp signal and a signal containing delta functions, generate
% their local Holder exponents.
%% Cusp Signal
% Load and plot a cusp signal. Note the difference between the two cusps.
load cusp;
plot(cusp)
grid on
xlabel('Sample')
ylabel('Amplitude')
%%
% The equation for this cusp signal specifies a Holder exponent of 0.5 at 
% sample 241 and a Holder exponent of 0.3 at sample 803.
% 
% |-0.2*abs(x-241)^0.5 - 0.5*abs(x-803)^0.3 + 0.00346*x + 1.34|
%%
% Obtain the local Holder exponents and plot the modulus maxima. 
wtmm(cusp,'ScalingExponent','local');

%%
% The Holder exponents at samples 241 and 803 are very close to
% the values specified in the cusp signal equation. The higher Holder
% value at sample 241 indicates that the signal at that point is closer 
% to being differentiable than the signal at sample 803, which has a 
% smaller Holder value.

%% Delta Functions
% Create and plot two delta functions.
x = zeros(1e3,1);
x([200 500]) = 1;  
plot(x)
grid on
xlabel('Sample')
ylabel('Amplitude')

%%
% Obtain the local Holder exponents using the default number of octaves, 
% which in this case is 7. Plot the modulus maxima. A delta function has a 
% Holder exponenent of &ndash1.
wtmm(x,'ScalingExponent','local');
%%
% Obtain the local Holder exponents using 5 octaves and compare the modulus
% maxima plot to the plot using the default number of octaves. 
wtmm(x,'ScalingExponent','local','NumOctaves',5);
%%
% Reducing the number of scales provides more separation in frequency and
% less overlap between the modulus maxima lines of the delta functions.