Question

(30 points) Consider the transmitter of the Differential Pulse Code Modulation (DPCM) system with input sequence x(n) 13 3 2 5 8] when n-0 to 4. A 3-bit mid-riser quantizer and encoder shown in Fig. 1 where step size Δ 1 and a 2-order predictor with coefficients α -0.2 and a2 0.4 are used. 3. a) By hand calculation, find R(n), d(n), d(n),(n) and cn) for n-0 to 4, and complete the table below. 7l x (n) 3 3 258 2(n) d(n) d(n) 4 c(n) b) Write and submit a complete MATLAB program that implements the given DPCM transmitter. The MATLAB program must include proper documentation. Using the MATLAB program, determine R(n), d(n), d(n), R(n) and c(n) for n-0 to 4. Sketclh x(n), R(n), R(n) on the same plot. You must verify whether or not the program is working by comparing the answers generated by your MATLAB program with the results obtained from hand calculation. c) Now consider the input sequence x(n) - [5.8000 5.6990 5.9285 5.9000 3.3304 3.1010 5.8000 6.5990 4.3696 7.7000 1.7715 4.0010 5.8000 5.6990 5.9285]. Using the MATLAB program obtained in step b), determine R(n), d(n). d(n), k(n) and c(n). Sketch x(n),2(n),2(n) on the same plot.

Answer 1

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