Problem 1 Nyquist Sampling (15 points) By the Sampling Theorem the Nyquist sampling rate must be twice the highest bandwidth of the message signal. For the three message signals below determine the Nyquist rate and the Nyquist interval for each. (a) m(t) = 3 x cos(50лt) +10 x sin(300лt) + 1.5 x cos(120лt) (b) m(t)=8x sin(600лt) x cos(200πt) (c) m(t)=sinc (100) = sin(100) πι Hint: Fourier Transform of a sinc waveform is a rectangular pulse, g(t)=sinc(2Bt) <FG(f) =: -rect 2B 2B where "rect" is the symbol for a rectangular spectrum that is flat from frequency -B Hz to +B Hz. It is said to have a spectral bandwidth of B Hz.