2) Consider the sinusoidal signal x(t) =cos(500rt + 0), and suppose that this signal is sampled, using impulse sampling, at w, = 10007 =(2 rf;), in order to achieve the signal Xp(t) as: +00 п 500 500- a) Find the signal g(t) such that x(t) = cos(0) cos(500rt) + g(t). b) Show that g () = 0 for n = 0,±1,±2, .. c) Using the results of the previous two parts, show that if the sampled signal is applied as the input to an ideal low-pass filter with cutoff frequency w. = 500x, the resulting output is x„(t)=cos(0) cos(500zt).
2) Consider the sinusoidal signal x(t) =cos(500rt + 0), and suppose that this signal is sampled, using impulse sampling, at w, = 10007 =(2 rf;), in order to achieve the signal Xp(t) as: +00 п 500 500- a) Find the signal g(t) such that x(t) = cos(0) cos(500rt) + g(t). b) Show that g () = 0 for n = 0,±1,±2, .. c) Using the results of the previous two parts, show that if the sampled signal is applied as the input to an ideal low-pass filter with cutoff frequency w. = 500x, the resulting output is x„(t)=cos(0) cos(500zt).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2) Consider the sinusoidal signal x(t) =cos(500rt + 0), and suppose that this signal is
sampled, using impulse sampling, at ws = 10007 =(2nfs), in order to achieve the signal
Xp (t) as:
+00
x„(t) = E × (500 ) ( - 500
- 00
a) Find the signal g(t) such that x(t) = cos(0) cos(500rt) + g(t).
b) Show that g () = 0 for n = 0,±1,±2, ...
c) Using the results of the previous two parts, show that if the sampled signal is applied as
the input to an ideal low-pass filter with cutoff frequency w. = 5007, the resulting
output is x„(t)=cos(0) cos(500zt).
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