Consider a 20-point finite-duration sequence x[n] such that x[n] = 0 outside 0 ≤ n ≤ 19, and let X(ejω) represent the discrete-time Fourier transform of x[n].
(a) If it is desired to evaluate X(ejω) at ω = 4π/5 by computing one M-point DFT, determine the smallest possibleM,and develop a method to obtain X(ejω) atω = 4π/5 using the smallest M.
(b) If it is desired to evaluate X(ejω) at ω = 10π/27 by computing one L-point DFT, determine the smallest possible L, and develop a method to obtain X(ej10π/27) using the smallest L.
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