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I want to estimate the parameters of a chirp signal using the fractional fourier transform. Following the paper estimating chirp parameters, the chirp rate $\mu$ can be obtained with (minus) the cotangent of the rotated angle $\theta$, $\mu=-\cot{\theta}$. The simulation code I wrote is

   fs=256;
   t = 0:1/fs:1023/fs;
   y = exp(-j*24*pi*t.^2);
   XF = [];
   for alpha = 0:0.001:1
        XF = [XF,frft(y,alpha)] ;
   end;  
   
   figure;
   surf((abs(XF)).^2);
   colormap('jet'); view(0,90);
   shading interp;

The discrete fractional fourier transform function frft is adopted from code.

The figure peaks at $\alpha = 0.772$. As a result, the rotated angle is $\theta=0.772*\pi/2$ and the estimated chirp rate is $\cot\theta=0.3743$. Obviously, this is not the desired result.

What may be the problem with my code? Thank you!

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