MATLAB: Draw a Morlet wavelet w(t) with t being set from -0.5 to 0.5 sec

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The mother wavelet of Morlet wavelet transform is formed by multiplying a sinusoidal wave with a Gaussian window: cycles = 8 and 0 f = 40Hz.

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fo = 40;
cycles = 8;
sigmaf = fo/cycles;
sigmat = 1/(2*pi*sigmaf);
t = linspace(-0.5,0.5,1000);
omega_t = 1./(sigmat.*sqrt(2.*pi)).*(exp(-t.^2./(2.*sigmat.^2))).*exp(2i.*pi.*fo.*t);
plot(t,omega_t,'-*m')

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If you are referring to the default level for http://www.mathworks.com/help/images/ref/im2bw.html then it is using a simple ">=" comparison. One of the names for that is "binarization"; there are other names.

MATLAB: Plotting a function with input and output

You need to change * to .* and change e to exp(), and you need to move the 5 exponent:

t=0:0.01*pi:20*pi; % Create t
[x, y] = bird(t); % Call the function.
function [x,y] = bird(t)
x = sin(t) .* (exp(cos(t)) - 2*cos(4*t)-sin(t/12).^5)
y = cos(t) .* (exp(cos(t)) - 2*cos(4*t)-sin(t/12).^5)
plot(x,y)
end

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MATLAB: Threshold of 0.5

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