Consider a signal that is sampled at 2 Hz and given by x(n) = cos(n/3) +...

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Consider a signal that is sampled at 2 Hz and given by x(n) = cos(лn/3) + cos(2/3). 1. What frequencies in Hz to the two cosine terms correspond to? 2. Generate 1000 samples of x(n). 3. Write MATLAB code to use an IIR notch filter to eliminate the 27/3 frequency. The filtering can be accomplished by the filter command in MATLAB. Justify your choice of the parameter r. 4. Plot the following using the freqz command. For the plots, the horizontal axis is the frequency in Hz and the vertical axis is the magnitude response (do not convert to decibels). (1) Magnitude Spectrum of x(n) (2) Magnitude response of IIR filter (3) Magnitude Spectrum of signal after filtering Consider a signal that is sampled at 2 Hz and given by x(n) = cos(лn/3) + cos(2/3). 1. What frequencies in Hz to the two cosine terms correspond to? 2. Generate 1000 samples of x(n). 3. Write MATLAB code to use an IIR notch filter to eliminate the 27/3 frequency. The filtering can be accomplished by the filter command in MATLAB. Justify your choice of the parameter r. 4. Plot the following using the freqz command. For the plots, the horizontal axis is the frequency in Hz and the vertical axis is the magnitude response (do not convert to decibels). (1) Magnitude Spectrum of x(n) (2) Magnitude response of IIR filter (3) Magnitude Spectrum of signal after filtering