sec3 - EE 2200 / Spring 2010: Section THREE 1 ECE 2200 /...

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EE 2200 / Spring 2010: Section THREE 1 ECE 2200 / Spring 2010 SECTION Three (Week 4: Feb 15-18) 1. The continuous-time sinusoid x ( t ) = 4 . 5 sin (16 . 6 πt ) is to be sampled at f s to produce the discrete-time sinusoid x [ k ]= M cos( γk + θ ) (i) For f s = 15 Hz, determine M , γ , and θ . Has x ( t ) been undersampled or oversampled? (ii) For f s =7 . 5 Hz, determine M , γ , and θ . Has x ( t ) been undersampled or oversampled? (iii) For f s = 22 . 5 Hz, determine M , γ , and θ . Has x ( t ) been undersampled or oversampled? 2. Consider the discrete-time sinusoid y [ n ] = 11 . 8 cos(0 . 21 πn - π/ 5) generated by sampling y ( t )= M cos(2 παt + θ ) at a sampling rate of 4200 Hz. Determine three di±erent continuous-time sinusoids y ( t ) with frequencies all less than 5.8 kHz that could have produced x [ n ]. Specify your three possibilities with unique triples of M , α and θ . 3. Sketch the spectrum of x ( t ) = sin 3 (470 ) Clearly label the frequencies and complex amplitudes of each component. Deter- mine the minimum sampling rate that can be used to sample x ( t ) without aliasing any of its components. 4. Consider the three zero-phase cosines of di±erent frequencies x 1 ( t ) = cos(2 π 8500 t ) x 2 ( t ) = cos(2 π 24500 t ) x 3 ( t ) = cos(2 π 31000 t ) For each x i
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sec3 - EE 2200 / Spring 2010: Section THREE 1 ECE 2200 /...

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