Use the proof for the previous problems relationships and show that the following relationship holds for any sample set that has only real values (that is, no complex part)

where: depicts the complex conjugation.

Load the data from the file 'data_for_dft.dat'. * provided at the books web page. It contains a table with y vs t data points (the first column holds the time, the second holds y). These data points are taken with the same sampling rate.

1. What is the sampling rate? 2. Calculate forward DFT of the data (use MATLAB built-ins) and find which two frequency components of the spectrum (measured in Hz not rad1 ) are the largest. Note: I refer to the real frequency of the sin or cos component, that is, only positive frequencies. 3. What is the largest frequency (in Hz) in this data set that we can scientifically discuss? 4. What is the lowest frequency (in Hz) in this data set that we can scientifically discuss?