engineering recuitment GATE EE 2023-24 Test Series Signals and Systems Discrete Time Fourier Transform (DTFT)
The inverse DTFT of \(X\left( {{e^{j\omega }}} \right) = 1;\frac{\pi }{4} \le \left| \omega \right| \le \frac{{3\pi }}{4}\) is
1
\(\frac{1}{{\pi n}}\left[ {\cos \frac{{3\pi n}}{4} - \sin \frac{{\pi n}}{4}} \right]\)
2
\(\frac{1}{{\pi n}}\left[ {\cos \frac{{3\pi n}}{4} - \cos \frac{{\pi n}}{4}} \right]\)
3
\(\frac{1}{{\pi n}}\left[ {\sin \frac{{3\pi n}}{4} - \sin \frac{{\pi n}}{4}} \right]\)
4
\(\frac{1}{{\pi n}}\left[ {\sin \frac{{3\pi n}}{4} - \cos \frac{{\pi n}}{4}} \right]\)