ECE405HW1Su2010 - ECE 405 HOMEWORK #1 SUMMER 2010 DR. JAMES...

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ECE 405 HOMEWORK #1 SUMMER 2010 ©DR. JAMES S. KANG 1 Given x(t) = 12 cos(2 π × 15,000t 60 o ) 20 cos(2 π × 20,000t + 30 o ) 16 cos(2 π × 30,000t 70 o ), plot (a) one-sided magnitude spectrum. (b) one-sided phase spectrum. (c) two-sided magnitude spectrum. (d) two-sided phase spectrum. 2 Given the pulse train with amplitude = 1V, period = 3ms, pulse width = 1ms, delay = 1ms shown below, t (ms) .......... .......... 1 0 1 2 3 4 –1 –2 –3 x(t) (a) Find the exponential Fourier coefficient X n . (b) Plot the two-sided amplitude spectrum. (c) Plot the two-sided phase spectrum. (d) What is the power contained at second harmonic? (e) Represent x(t) by its Fourier series. (f) Let y(t) = x(t) cos (2 π × 30000t). Determine Y n and plot | Y n | and Y n . (g) If y(t) is applied to an ideal bandpass filter with bandwith 5 kHz and center frequency of 30 kHz, what is the output of the filter in the time domain? Assume that the gain of the filter is one and the phase response of the filter is zero for all frequencies.
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ECE405HW1Su2010 - ECE 405 HOMEWORK #1 SUMMER 2010 DR. JAMES...

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