A desirable signal x(t) = cos(100t) 2 cos(50 t) is recorded as y(t) = x(t) +

A desirable signal x(t) = cos(100πt) – 2 cos(50π t) is recorded as y(t) = x(t) + cos(120πr t), i.e., as the desired signal but with a 60 Hz hum. We would like to get rid of the hum and recover the desired signal. Use symbolic ATLAB to plot x(t) and y(t). Consider the following three different alternatives (use symbolic MATLAB to implement the filtering and use any method to design the filters):

• Design a band-eliminating filter to get rid of the 60 Hz hum in the signal. Plot the output of the band-eliminating filter.

• Design a high-pass filter to get the hum signal and then subtract it from y(t). Plot the output of the high-pass filter.

• Design a band-pass filter to get rid of the hum. Plot the output of the band-pass filter.

Is any of these alternatives better than the others? Explain.