## Design and computations – digital signal processing

Problem 1 [10pts.]: 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 1.042 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.

%Select the receiver voltage time-series for 10000 samples

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

Problem 2 [20pts.]: The CSU-CHILL radar transmits a pulse of power and receives power from returned echoes. The radar data file contains data from CSU-CHILL observations. Both horizontal and vertical echo power data are provided. Assume the observations were taken with the sampling interval of 1 millisecond per pulse. In total 512 pulses were stored at 10 range samples. Please note that all samples are complex numbers. There is a matrix of 10×512 complex numbers.

Compute the Spectra of the complex digital signal for the 3 rd range sample (vector of 512 numbers). Plot the Spectra with the true analog frequency on the x-axis (Hz). 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. MATLAB code for reading the radar data file: 