Unable to shift discrete time Bessel Function

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Raghav Kumar 2016-12-2

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https://ww2.mathworks.cn/matlabcentral/answers/315181-unable-to-shift-discrete-time-bessel-function

Hello,

I have been trying to make a Kaiser Window FIR Filter just for my own understanding. I get the Kaiser Window function in the time domain from 1:N where N is the total number of samples. However, when I try to center (shift) the window function about 0, I only get half the function. Here is my code -

 %window x axis
 n = floor(N/2);
 nn = n;
 n = -n:n;
 %kaiser window code
 Beta = 6;
 K = Beta*sqrt(1 - ((2*n/N) - 1).^2); %define numerator term
 %I_0(K) Bessel Function (numerator)
 num = I_0(K,100);
 %I_0(Beta) Bessel Function (denominator)
 den = I_0(Beta,200);
 w = num / den; 
 figure;
 stem(n,w);

I would like something like this, which is centered around 0 -

I know there have been previous posts on shifting discrete time functions. However, none of these have helped me with this problem. I tried changing the index value of the matrix (the matrix which defines the x-coordinates essentially), but it still does not work.

Any help is appreciated. Thanks in advance!