The synthetic aperture radar (SAR) ambiguity function can be approximated by

\[
\chi=\frac{\sin (k x)}{x} \frac{\sin (N r y)}{\sin (r y)}
\]

where \(x\) is the variable for the range-compressed axis, \(y\) is the azimuth-compressed axis, and \(k\) and \(r\) are related to the SAR range and azimuth resolutions. (a) Generate the \(x\)-axis from \(-40 \mathrm{~m}\) to \(40 \mathrm{~m}\) using a sampling interval of \(0.1 \mathrm{~m}\). Assume \(k=1\). Plot the magnitude of this range profile. (b) Generate the \(y\)-axis from \(-40 m\) to \(40 \mathrm{~m}\) using a sampling interval of \(0.1 \mathrm{~m}\). Assume \(r=0.00015\) and \(N=1000\). Plot the magnitude of this azimuth profile. (c) Use the findings in (a) and (b) to generate the two-dimensional ambiguity surface plot.