railway RRB JE (CBT I + CBT II) Mock Test 2024 Signals and Systems Discrete Fourier Transform (DFT) and Discrete Fourier Series (DFS)
Consider the signal x(n) with DTFT X(ejω). Let the signal y(n) be defined as;
\(y\left( n \right) = \left\{ {\begin{array}{*{20}{c}} {x\left( n \right)\;for\;n = 2k}\\ {0\;for\;n = 2k + 1} \end{array}} \right.\)
The DTFT of y(n) is
1
\(\frac{1}{2}X\left( {{e^{j\omega }}} \right) + \frac{1}{2}X\left( {{e^{j\left( {\omega + \pi } \right)}}} \right)\)
2
X(ej(ω +π))
3
\(\left( {{e^{j\frac{\omega }{2}}}} \right)\)
4
X(ej2ω)