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.

%Load the data

load('CHILL20100218_174815_01_rg435.mat')

%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 10x512 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:

load('exam_ts.mat'); %Load the data

x = h_ts_data; %Select the horizontal echo complex ts data 

Note that after reading the data file (‘exam_ts.mat’) all the other required information/data will be automatically loaded on the MATLAB workspace.

Problem 3 [20pts.]: Design a high pass filter (See Fig. 1) to obtain 40dB suppression. These types of filters are used to suppress ground clutter in Doppler radars. Design a filter with either Kaiser Window or Min-Max design (your choice). Show the filter response and demonstrate it meets the specifications. Also plot the filter coefficients (use MATLAB)

This filer is also called the ground clutter filter. Apply this filter to the digital radar signal given in problem 2 to produce the output and plot the spectra and the Time Dependent Fourier Transform. Interpret the results.