Question: Consider a 20-point finite-duration sequence x[n] such that x[n] = 0 outside 0 n 19, and let X(e j ) represent the Fourier

Consider a 20-point finite-duration sequence x[n] such that x[n] = 0 outside 0 ≤ n ≤ 19, and let X(e^jω) represent the Fourier transform of x[n].

(a) If it is desired to evaluate X(e^jω) at ω = 4π/5 by computing one M-point DFT, determine the smallest possible M , and develop a method to obtain X(e^jω) at ω = 4π/5 using the smallest M.

(b) If it is desired to evaluate X(e^jω) at ω = 10π/27 by computing one L-point DFT, determine the smallest possible L, and develop a method to obtain X(e^j10π/27) using the smallest L

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