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P1/2 2012 Spring ELEC3100 Homework 2 (Deadline:26/03/2012 before 5pm) Please submit your HW into the ELEC3100 HW Collection Box before 5pm on the deadline indicated The HW collection box is located out of Rm2513. Sampling Q1. Consider a CT signal t t t t t x π 144 cos 8 120 sin 4 24 cos 2 32 sin 3 ) ( + + = . (a). One engineer suggests to sample it at sampling frequency of 40 samples/sec to generate the sequence x[n]. Determine the exact expression of x[n]. (b). Is the selection of sampling frequency reasonable? Can you correct it? (c). What is the unit of the “ordinary frequency” for the CT signal? What is the unit of the “normalized digital angular frequency” for the DT signal? DFT Q2. Let X[k] denote the DFT of x[n]. (a). Determine the values of X[k], 0 k 7, which is the 8 point DFT of ) N / n 2 cos( ] n [ x π = for N=8 and 0 n 7. (b). How many complex multiplications and complex additions are required for calculating each X[k]? (c). What is the computation load for calculating DFT of x[n] in total?

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