The figure below shows the Fourier transform of a real bandpass signal, i.e., a signal whose frequencies are not centered around the origin. We want to sample this signal. Let

F, in Hz (a) (4 pts) One option is to sample this signal at the Nyquist rate. Then to recover the signal, we pass its sampled version through a low pass filter. What is the Nyquist rate of this signal? (b) (9 pts) Since the signal might have high frequency components, Nyquist rate for this signal can be high. In other words, we need to have a lot of samples of the signal,which means that the sampling scheme is costy. It turns out that for this type of signal,we can sample it at a sampling frequency lower that the Nyquist rate and we can still recover the signal, however in this case, we will use a band pass filter. To see this, we have the following two options for the sampling frequency: • Fs= 0.5 Hz; • Fs = 1 Hz; For each case, draw the spectrum of the signal after sampling it. To recover the signal,which F, can we use? How we should choose the frequencies of the band pass filter?What is the minimum F, we can use and still recover the signal?