Consider the following signal
x(t) = cos(2*pi*1000t) + cos(2*pi* 2000t) + cos(2*pi*3000t)
Assume a sampling frequency 1/12000
(a) Compute the DFT of the given signal and plot the spectrum of the signal. (Choose the
t length so that you can distinguish the frequencies) Note: The plots must be appropriately labeled and show these plots over the range (0,pi).
(b)Let the component at Omega(C) = 2pi* 3000 be the corrupting signal. Design an appropriate lter to lter out this component of the input. You can use fir1 command for this. Plot the frequency response of this lter.
(c) Filter the input signal x(t) using the designed lter. Compute and plot the DFT of the ltered signal. Again the plots must be appropriately labeled and the frequency range must be (0,pi ).