engineering recuitment GATE IN Test Series 2023-24 Mock Test Signals and Systems Discrete Time Fourier Transform (DTFT) Properties of DTFT
The discrete-time Fourier transform (DTFT) of the following sequence x(n) is
\(x\left( n \right) = \{ \;\begin{array}{*{20}{c}} {n\;;}&{ - 4 \le n \le 4\;}\\ {0\;;}&{otherwise} \end{array}\;\)
1
\(j2\;\mathop \sum \limits_{k = 1}^4 ksin\;\left( {k\omega } \right)\)
2
\(- j2\;\mathop \sum \limits_{k = 1}^4 ksin\;\left( {k\omega } \right)\)
3
\(j4\;\mathop \sum \limits_{k = 1}^4 k\sin \left( {k\omega } \right)\)
4
\(- j4\;\mathop \sum \limits_{k = 1}^4 k\sin \left( {k\omega } \right)\)