A finite duration discrete time signal {x}( {n}) is obtained by sampling the continuous time signal, x(t)=\cos (200 n t) at sampling instants, t=\;{n}/{400}, n=0, . . ., 7 . The 8 -point DFT and x[n] is defined as {X}[ {k}]=∑↙{ {n}=0}↖{7} ×[ {n}] {e}^{\;{- {j} π {kn}}/{4}} {k}=0,1 . . ., 7 Which is true?

Question

A finite duration discrete time signal  {x}( {n}) is obtained by sampling the continuous time signal,   x(t)=\cos (200 n t) at sampling instants, t=\;{n}/{400}, n=0, . . ., 7 . The 8 -point DFT and x[n] is defined as    {X}[ {k}]=∑↙{ {n}=0}↖{7} ×[ {n}]  {e}^{\;{- {j} π  {kn}}/{4}}    {k}=0,1 . . ., 7   Which is true?

Examsnet · Accepted Answer

Correct Answer is :  Only X[2] and X[6] are non-zero.

GATE Electronics and Communications (EC) 2020 Solved Papers