# Fraser Suzuki Function written in MATLAB

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Christian Reece on 15 May 2015
Commented: Junmeng Cai on 12 Apr 2021
I am trying to write a piece of code which will simulate a Fraser Suzuki function, which is an asymmetrically skewed Gaussian. There are a multitude of papers citing the equation, but I cannot seem to get it working in MATLAB.
I've attached an image of the function above. In the paper they also perform a parameter test on the function to make sure they get the desired peak shape. An example I've attached below.
When I write this function myself the
T-p/w
section of the code goes negative, causing the log function to give imaginary values. As this function has been cited multiple times in literature it seems that it's not the function itself that's wrong but my interpenetration in the code. I've attached the code I've been using the simulate the function.
%%FSuzuki
T = linspace(450,700,1000);
h = 0.005;
p = 600;
w = 40;
s = -0.3;
arg1 = log(2*s*T-p/w+1).^2;
y = h*exp(-log(2)/(s^2)*arg1);
Any help would be greatly appreciated.
Joseph Cheng on 15 May 2015
well first of all your matrix operation for arg1 is off. it should be 2*s*(T-p)/w+1. which doesn't solve the issue but should be corrected.

Joseph Cheng on 15 May 2015
Alright, found the paper you mentioned and plotted it in different programs. So... What is happening is that the authors of the paper are ignoring the complex solutions for their Fraser Susuki equation. such that if i re-write your code to be
T = linspace(450,700,1000);
h = [0.005 0.0075 0.01 0.0125 0.015]';
figure(1),hold on
for ind = 1:numel(h)
p = 600;
w = 40;
s = -.3;
lntpw = log(1+2*s*(T-p)/w).^2;
FS = h(ind)*exp(-log(2)/s^2*lntpw);
FS(FS~=real(FS))=0;
plot(T,FS)
end
you get the same curves that they have in the paper.
Chuan Ma on 6 Oct 2020
Hello,
Racio，
Can you tell me how to avoid the complex numbers?
Thank you.
Chuan
Junmeng Cai on 12 Apr 2021
Dear Joseph Cheng, thank you very much!
Great!