how to generate two waveforms which have the same variance and different kurtosis

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song 2016-9-25

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https://ww2.mathworks.cn/matlabcentral/answers/304430-how-to-generate-two-waveforms-which-have-the-same-variance-and-different-kurtosis

编辑： song 2016-9-26

I want to generate two signals. They have the same variance and different kurtosis. My ideal signals are shown in figure.

Does anybody can solve this problem for me? Thanks.

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Answer 1

Image Analyst 2016-9-25

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在 MATLAB Online 中打开

Try creating an amplitude vector and a sine wave and multiply them.

t = 1 : 400
period = 30 % or whatever....
amplitude = ... some function of t you decide on.
y = amplitude .* sine(2*pi*t/period)
plot(t, y);

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Image Analyst 2016-9-25

You forgot to post your code. Please post it.

song 2016-9-26

编辑：song 2016-9-26

在 MATLAB Online 中打开

Hi, Here is my code. y1 and y2 look like what I want. But std(y1)~=std(y2). Could you please help me to fix it? Thank you

    %%amplitude function.
x=-10:0.1:10;
a=1;sigma=2;
amplitude=(1/((sqrt(2*pi))*sigma))*exp(-((x-a).^2)/(2*sigma.^2))-0.02;
amplitude=mapminmax(amplitude,0.2,1); % rescale to [0.2,1]
plot(amplitude)
%%your codes.
period = 3; % or whatever....
y1=sin(2*pi*x/period);
y2 = amplitude .* sin(2*pi*x/period);% 
plot(x,[y1;y2]','linewidth',1);
legend('Y1','Y2');
std(y1)
std(y2)