hwB06 - ENEE 241 02* HOMEWORK ASSIGNMENT 6 Due Wed 02/13...

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ENEE 241 02* HOMEWORK ASSIGNMENT 6 Due Wed 02/13 (i) (5 pts.) Compute the sum of the two discrete-time sinusoids: x 1 [ n ] = cos(2 πn/ 5 + π/ 3) and x 2 [ n ] = cos(8 πn/ 5 + π/ 4) ( Hint : Start with reducing the angular frequency of x 2 [ n ] to a value between 0 and π , then use phasors.) (ii) (5 pts.) Consider the frequency f 0 = 50 Hz and the sampling rate f s = 200 samples/sec. List all the aliases of f 0 with respect to f s in the frequency range 0.0 to 1.0 kHz. (iii) (5 pts.) The discrete-time sinusoid x [ n ] = 2 . 5cos((2 π/ 5) n +0 . 9) is obtained by sampling the continuous-time sinusoid x ( t ) at a rate of 200 samples per second. If it is known that the frequency of x ( t ) is in the range 300 to 400 Hz, write an equation for x ( t ). (iv) (5 pts.) ( Unrelated to part (i) ) Consider the two continuous-time signals x 1 ( t ) = cos(2 πt ) and x 2 ( t ) = cos(3 πt ) The two signals are sampled at the same rate f s = 1 /T s to produce the sequences x i [ n ] = x i ( nT s
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hwB06 - ENEE 241 02* HOMEWORK ASSIGNMENT 6 Due Wed 02/13...

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