Unformatted text preview: M = 3. 2. Compute the fourpoint DFT, X [ k ], of the sequence: x [0] = 1, x [1] = − j , x [2] = − 1, x [3] = j . X [ k ] = x [ n ] W 4 kn n = 3 ∑ = x [ n ] e − jkn π /2 n = 3 ∑ = x [ n ]( n = 3 ∑ − j ) nk X [0] = (1)(1) + ( − j )(1) + ( − 1)(1) + ( j )(1) = X [1] = (1)(1) + ( − j )( − j ) + ( − 1)( − 1) + ( j )( j ) = X [2] = (1)(1) + ( − j )( − 1) + ( − 1)(1) + ( j )( − 1) = X [3] = (1)(1) + ( − j )( j ) + ( − 1)( − 1) + ( j )( − j ) = 4 X [ k ] = 4 δ [ n − 3]...
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 Winter '12
 Dr.BrianJeffs
 Digital Signal Processing, Aliasing, Impulse response, finite length impulse

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