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Engineering · Electrical Engineering
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QUESTIONS The following finite duration sequences are given: X1=[2-1 3 1]and x2=[36-21] n-0 n-0 Find the linear convolution of these sequences (x (n) x2(n)). (7.5 points). a. b. Find the circular convolution of these sequences ( (n° x2 (n) ).(7.5 points). If the sequences x xi (n) O xs(n) = x1 (n) * x2 (n), r2 (n). (5 points). 1(n) and X2(n) are altered as x,(n) and x(n), so that express the altered sequences x, (n) and c. Find the FFT of sequence x(n)-(2,-1.4, 1} using the decimation-in-time method, and sketch the corresponding signal flow diagram. (10 points). A lowpass analog filter is described by the following transfer function: . Determine the digital system function H(z) corresponding to H(s) using the impulse- invariant design method. (10 points). 4. The first and second derivatives of yt) at time instant i nT, are approximated respectively as follows: and dy(t) Subscquently, think about the linear and time invariant system described by the differential equation: a Write out the difference equation that approximates the above system at sample instants t-nT. (10 points). b. If T-025 s, what is the impulse response of the system.. (10 points). c Draw frequency response of the discrete-time system of part a in the 0-2T radian interval. (5 points). d. Draw the reduced complexity block diagram of the discrete-time system of part a. (5 points).

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