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

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.

Answer 1

[Image Analyst]

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);

[song]

Thanks for your reply. I tested it. But y and sine signal have different variance. I hope that they have the same variance.

[Image Analyst]

You forgot to post your code. Please post it.

[song]

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)