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ECE405HW2Su2010 - ECE 405 HOMEWORK#2 SUMMER 2010 DR JAMES S...

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ECE 405 HOMEWORK #2 SUMMER 2010 ©DR. JAMES S. KANG 1 A message modulates a carrier ( ) ( ) 2 sinc m t t = ( ) 2cos 2 10 t π . (a) Find the Fourier transform of m(t) and plot it. (b) Sketch the two-sided spectrum of the modulated waveform when the modulation is (1) AM (2) DSB–SC (3) LSSB (4) USSB (c) Sketch the modulated waveform in the time domain when the modulation is (1) AM (b) DSB–SC 2 The system shown below can be used to send two messages on one carrier. (a) If and ( ) ( ) 1 cos 2 1000 m t t π = ( ) ( ) 2 cos 2 4000 m t t π = , find the output y(t). (b) Device block diagram for a suitable demodulator for y(t). Lowpass filter at 100 kHz Highpass filter at 100 kHz m 1 (t) m 2 (t) cos(2 π × 10 5 t) y(t) + + Σ 3 Sketch the spectrums X(f) and Y(f) in the system shown below. m(t) x(t) y(t) M(f) X(f) Y(f) Lowpass filter at 1 kHz 2 cos(2 π × 10 3 t) M(f) 0 –1 1 f (kHz) 4 Sketch the spectrums and ( ) Y f ( ) Z f in the system shown below. x(t) y(t) Lowpass filter at 25 kHz z(t) 2 cos(2 π × 3 0,000 t) 1
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