Loads the EEG signal provided as auxiliary material (EEG.mat). With the knowledge acquired in previous classes, calculate its fundamental frequency using autocorrelation and draw a 2-figure subplot showing the signal (EEG) and below the autocorrelation coefficient. Using the provided ftplot function, paint the Fourier transform and check that the fundamental frequency is the same.

Generate the series obtained by sampling a sinusoid of 100 Hz and unit amplitude with a sampling period of 1 ms for one second. Plot the spectrum of the signal using the abs(fft(y)) statement. Plot the spectrum again using the ftplot function provided as an aid.

(2nd) Repeat the previous section but now taking the signal to be sampled as the sum of four cosines of amplitude one and frequencies 100, 200, 600 and 2100 Hz. Comment on the results and justify them theoretically by virtue of Nyquist's theorem. Add this justification as comments in the generated script.Remember that the components undergoing aliasing appear with an apparent frequency equal to fc k fm where fc is the frequency of the component and fm is the sampling frequency

Generates a sinusoidal signal resulting from the sum of 3 components at 1Khz, 2kHz and 3kHz, on which certain operations will be performed (uses an fs of 10kHz). It delivers a "script" type .m file for this section that, when executed, performs all these operations. Represent the first second of the signal. With the help of the 'ftplot' function provided with the laboratory material, show the spectrum of the resulting signal. Also Create filters using the 'sinc' function as seen in class in such a way that you get: Apply a filter that manages to leave the 1kHz component alone (we will call the output yfiltered1) Apply a filter that manages to leave the 1kHz and 2kHz components (we will call the output yfiltered2) Could you get from yfiltered1 and yfiltered2 a signal that has only the 2kHz component? And could you get using the input and filtered signals a signal that has only the 3kHz component? (2pt) In the files Hr_med.mat and Hr_pre.mat are the heart rate values of an individual during meditation and normal rest respectively. With these files: Load them (using load) Represents both (variables t_med and t_pre are time axis and hr_med and hr_pre are heart rate) The time axes are NOT equispaced so the Fourier Transform cannot be done correctly. Investigate the 'interpl' function and how to make a signal that is not equispaced. Once both heart rates are equispaced, eliminate their continuous component (remove the mean) Do the Fourier transform using ftplot Compare the spectra. Are there differences? Are they the same in frequencies and amplitude?