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ECE405HW6Su2010

# ECE405HW6Su2010 - ECE 405 HOMEWORK#6 SUMMER 2010 DR JAMES S...

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ECE 405 HOMEWORK #6 SUMMER 2010 ©DR. JAMES S. KANG 1 A message x(t) = 2 cos(2 π ×10t) is uniformly sampled by an impulse train of period T s = 0.02 sec. Sketch (a) x(t). (b) the Fourier transform of x(t), X( ω ). (c) the sampled waveform. (d) the spectrum of the sampled waveform. (e) the spectrum of the output of the ideal lowpass filter with bandwidth 1/2T s and gain of T s when the sampled waveform is applied at the input. (f) the waveform of the output of the ideal lowpass filter with bandwidth 1/2T s and gain of T s when the sampled waveform is applied at the input. 2 Repeat Problem 1 when T s = 1/15. 3 Repeat Problem 1 when T s = 1/10. 4 Repeat Problem 1 when x(t) = 4 cos(2 π ×20t) + 2 cos(2 π ×10t) and T s = 1/50. 5 Repeat Problem 1 when x(t) = 4 cos(2 π ×20t) + 2 cos(2 π ×10t) and T s = 1/30. 6 Repeat Problem 1 when x(t) = 2 cos(2 π ×10t) is sampled uniformly by a rectangular pulse train with duty cycle 1/4, amplitude 1, and period T s = 1/50. 7 Determine the theoretical Nyquist sampling rate for the following signals.

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ECE405HW6Su2010 - ECE 405 HOMEWORK#6 SUMMER 2010 DR JAMES S...

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