The FT of the signal x(t) = e^(-9t), is (where w=2) 18/85 a/(a^2+jW^2) 1/(-a-jw) 9/85 O...
Question 3: The continuous-time signal x(t) with FT as displayed below is sampled. X(jw) 1 107 -1079 Sketch the FT of the sampled signal for the following sampling periods (10 marks) (a) T, = 1/14 (b) T. = 1/10. (10 marks) (c) In each case, state whether we can recover the original signal x(t) or not. (10 marks
(b) (2 pts) (t) is given as r(t) e sin(t) Find X(jw). Show that X(jw) = 25 + (w- 1)225(w+1)2 (c) (4 pts) x(t) is given as x(t)-π inc(t) cos(nt). Find X(jw) (d) (4 pts) 2(t) is given as 2(t) e Áil+ 3) + e' ỗ(t-3). Find X (jw). Simplify the answer as (e) (4 pts) 2(t) is given as r(t) = rect(2(t )) reetgehj)). Hint: use Fourier Transform pair: sine(t)艹rect( ) much as possible Find X(jw). Simplify the answer...
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1. Sketch the Fourier transform Xr(jw) of x[n] for T-to. 2. Can x(t) be recovered for T? How? What is the maximum value of T so that r(t) can be recovered?
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1....
1. A signal (t) with Fourier transform X(ju) undergoes impulse-train sampling to generate where T = 4 x 10-4. For each of the following sets of constraints on r(t) and/or X(ju), does the sampling theorem guarantee that r(t) can be recovered exactly from p(t)? a. X(ju) = 0 for l니 > 1000-r b, X(ju) = 0 for lal > 5000π c. R(X(ju))-0 for lwl > 1000-r d, x(t) real and X(jw)-0 for w > 1000π e. x(t) real and X(jw)-0...
(a) The continuous-time signal x(t) with FT as depicted in the figure shown below is sampled. Sketch the FT of the sampled signal for the following sampling intervals: identify whether aliasing occurs, Ts = 1/12 X(jw) -117 107 W -10 0 117 97 97T (b) Determine the z-transform and ROC for the following time signals: x[n] = (4)"u[n] + (1)"u[ -– 1] Sketch the ROC, poles, and zeros in the z-plane.
7.21. A signal x(t) with Fourier transform X(jw) undergoes impulse-train sampling to generate where T = 10-4. For each of the following sets of constraints on x(t) and/or X(j), does the sampling theorem (see Section 7.1.1) guarantee that x(t) can be recovered exactly from xp(t)? (a) X(jo) = 0 for lal > 5000π (b) x(ja)-0 for lol > 15000m (c) Re(X(jw)} = 0 for lal > 5000m (d) x(t) real and X(ju)-0 for ω > 5000TT (e) x(t) real and...
Consider the input signal x(t) with Fourier transformation X(w) as shown in the figure below where WM = 100 rad/s. The sampling frequency ws = 200 rad/s. The filter H(w) has a cut- off frequency we = 100 rad/s a) [10 points) Plot the signal P(0) b) [15 points] Plot the signal Xplo) c) [10 points] Plot the output signal X-(0) pt) - 281t - nT) x(t) H(jw) X Hij M You need to show all the steps that lead...
1x(jw) 2 Use the equation describing the FT representa- tion to determine the time-domain signals cor- responding to the following FTs. ſcos(w), w < 1/2 (a) Xíjw) = { 10, otherwise (b) X(jw) = e-2"u(w) (c) X(jw) = (d) X(jw) as depicted in Fig. P3.8(a) (e) Xijw) as depicted in Fig. P3.8(b) (f) X(jw) as depicted in Fig. P3.8(c) arg{X(jw) } 14 X(jw) 141414 (b) X(jw) 2 1 arg/ X{jw) 77/2 2 M -7/2
(1 point) Write limits of integration for the integral Jw g(x, y, z) DV, where W is the half cylinder shown, if the length of the cylinder is 2 and its radius is 2. Z y Jw 8(x, y, z) dV = Sa So So 8(x, y, z) dr d theta d X where a = 0 b= 2 C= ,d = 3 e = 0 , and f = 2
(1 point) Write limits of integration for the integral Jw g(x, y, z) DV, where W is the half cylinder shown, if the length of the cylinder is 2 and its radius is 2. Z y Jw 8(x, y, z) dV = Sa So So 8(x, y, z) dr d theta d X where a = 0 b= 2 с ,d = 3 e = 0 , and f = 2