Consider the continuous time signal x(t) = sin(2 pi f_0 t) and consider the samp
ID: 2082607 • Letter: C
Question
Consider the continuous time signal x(t) = sin(2 pi f_0 t) and consider the sampling and reconstruction system 1. Let omega_s = 2 pi/T be the sampling frequency. a. What is the Nyquist rate/frequency omega_s for x(t)? b. Consider the ideal sampling system where H_0 = 1 and H_r (omega) = rect_omega_s/2(omega). Plot x_p (t), x_s (t), and x_r (t) for I. omega_s = 2 omega_n II. omega_s = omega_n III. omega_s = omega_n/2 c. Repeat previous part for H_1 and H_2 being the Zero-Order-Hold sampling interpolation system and reconstruction system, i.e. H_0 (omega) =^-j omega T/2 2 sin (omega T/2), H_r (omega) = rect_omega_s/2 (omega)e^j omega T/2 omega/2 sin(omega T/2).Explanation / Answer
a.) for x(t), nyquist's rate or nyquist frequency for ideal sampling is twice the highest frequency component present in the signal. since x(t) is a pure sinusoid of frequency = fo Hz, the maxm. frequency component is of fo Hz only. Thus, wn= 2*pi*(2*fo)=4*pi*fo rad/s.