1) An analog signal x(t) = cos(320nt) + 2 cos(480rt) – cos(960t ) is sampled with sampling frequency of 640 samples per second. a. Find the Nyquist frequency and Nyquist rate in Hz. b. Draw the Continuous Fourier Transform of x(t) c. Find the sampled discrete signal x[n] d. Draw the DTFT of x[n]. Find the frequencies present in the discrete signal and explain your observations 2) The Fourier Transform of a continuous time signal x(t) which is bandlimited with maximum frequency 2m= 5007 (rad/sec) is shown in below figure. x(t) is sampled with an impulse train at sampling frequency of Fs=250 Hz. Draw the sampled signal's Fourier transform. Determine if it can be recovered with any of the filtering methods, low pass filtering band pass filtering, or high pass filtering. If so what should be the cutoff frequency ? X(Q) 1 O [rad/s] -5007 500 T

1) An analog signal x(t) = cos(320nt) + 2 cos(480rt) – cos(960t ) is sampled with sampling frequency of 640 samples per second. a. Find the Nyquist frequency and Nyquist rate in Hz. b. Draw the Continuous Fourier Transform of x(t) c. Find the sampled discrete signal x[n] d. Draw the DTFT of x[n]. Find the frequencies present in the discrete signal and explain your observations 2) The Fourier Transform of a continuous time signal x(t) which is bandlimited with maximum frequency 2m= 5007 (rad/sec) is shown in below figure. x(t) is sampled with an impulse train at sampling frequency of Fs=250 Hz. Draw the sampled signal's Fourier transform. Determine if it can be recovered with any of the filtering methods, low pass filtering band pass filtering, or high pass filtering. If so what should be the cutoff frequency ? X(Q) 1 O [rad/s] -5007 500 T