Determine and plot the value of x using synthesis equation

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Reference no: EM13275338

Synthesize a periodic discrete-time signal with period N=5 and the following DTFS coefficients
a0 = 2, a2 = a-2* = ejπ/4 , a4= a-4 * = e jπ/3

a) Based on the DTFS coefficients, do you expect x[n] to have complex-value, purely real, or purely imaginary? Explain your answer?

b) Using the DTFS coefficients given above, determine the values of a0 through a4.

c) Using MATLAB Synthesis function and values of ak found in the pervious section to determine and plot the value of x[n] for 0 ≤ n ≤ 25.

d) Determine and plot the value of x[n] using the synthesis equation directly {do not use ifft()}. What is the percent difference in x[n] energy between the direct method used here and MATLAB function used in part (c).

e) Plot x[n] magnitude, phase, real part and imaginary part using stem. Was your statement in part a correct?

Reference no: EM13275338

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