Problem $6[$Extra credit : $10$ pts$]$: The CSU$-$CHILL radar made observations of the Ponnequin Wind Farm located on the boarder of Wyoming and Colorado near I$-25.$ The wind farm is approximately $62$ km away from the radar. Complex valued digital signals observed by the radar from a rotating wind turbine are provided. The data is sampled with a period of $1\mathrm{.}042$ milliseconds.

Compute the time dependent Fourier transform of the complex digital signal. Plot it as a $2-$dimensional function of true analog frequency $(Hz)$ on the y $-$axis and time $(sec)$ on the x $-$axis between $0$ to $10$ sec $.$

Interpret the results. Think about the interpretation of a frequency shift in a radar signal?

In MATLAB, the following code will open the file containing CSU$-$CHILL radar time$-$series data and extract the time$-$series as variable $"x"$ to be used.

$\%$Load the data

load$(\text{'}$CHILL$20100218\_174815\_01\_$rg$435.$mat'$)$

$\%$Select the receiver voltage time$-$series for $10000$ samples

$x=$ double$($pulse$.$H$(1$:$10000))$;