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 theo...
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) x(t) undergoes impulse train sampling through the following system below: x(t) 20 n=-00 3 i. (5 pts) What is the sampling frequency w used by this system? What is the equation for the output Fourier Transform X,(jw) in terms of X(jw)? ii. (5 pts) Using your equation from (i), sketch the output spectrum X, (jw) vs. w. Make sure to label all critical points iii. (5 pts) Using your sketch from (ii), determine if there is aliasing or not....
Problem 4 Let x(t) be a continuous time signal whose Fourier transform has the property that Xe(ja)0 for lal 2 2,000. A discrete time signal aIn]x(n(0.5x 10-3)) is obtained. For each of the following constra ints on Xa(e/n), the Fourier transform of xaln], determine the coresponding constraint on Xe(ja) a) X(en) is real b) The maximum value of X4 (ea) over all is 1 c) Xa(ea)= Xa(e/ a-) Problem 4 Let x(t) be a continuous time signal whose Fourier transform...
Don't need to do #1. Please go into detail on how you solved #2 and #3 The Fourier transform of the signal r(t) is given by the following figure (X(jw)0 for w> 20) X(ju) 0.8 0.6 0.4 0.2 -10 10 20 m Page 4 of 5 Final S09 EE315 Signals & Systems The signal is sampled to obtain the signal withFourier transform Xlw 1. (5p) What is the minimum sampling frequency w 2. (10p) Now suppose that the sampling frequency...
points) Consider the signal s(t) with Fourier Transform 10 1+ω. S(a) figure below, we impulse sample s) at a frequency o, rads/second, e signal sa(t). Can you find a finite sampling frequency o such that ly recover s(t) from so()? If so, find it. If not, explain why not. a) (5 pts) In ting in the can perfectly you s (t) sa(t) →| Impulse sample at- rate o b) (5 pts) Now suppose we filter the signal s() with an...
4. The continuous-time signal e(t) has the Fourier transform X(jw) shown below. Xe(ju) is zero outside the region shown in the figure X.Gj) -2T (300) -2r(100) 0 2n(100) 2T (300) We need to filter re(t) to remove all frequencies higher than 200 Hz. (a) Plot the effective continuous-time filter we need to implement. Label your plot. b) Suppose we decide to implement the filtering in discrete-time using the overall process (sample, filter, reconstruct) shown in the figure in Problem 3....