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(Solved): Find the inverse Discrete Time Fourier Transform(DTFT) of the following systems: (a) \( X[\Omega]=\ ...
![Find the inverse Discrete Time Fourier Transform(DTFT) of the following systems:
(a) \( X[\Omega]=\frac{12 e^{j \Omega}-5}{4](https://media.cheggcdn.com/study/482/482af906-3301-4811-a877-62a3cf65ac21/image)
Find the inverse Discrete Time Fourier Transform(DTFT) of the following systems: (a) \( X[\Omega]=\frac{12 e^{j \Omega}-5}{4 e^{j \Omega}-3+0.5 e^{-j \Omega}} \) (b) \( X[\Omega]=\frac{e^{j n}}{e^{j n}-2 \alpha+\alpha^{2} e^{-j \Omega}}, \quad|\alpha|<1 \). (20 points) Solution:
Expert Answer
(a) The given DTFT of the sequence is: X(?)=12ej??54ej??3+0.5e?j? Taking 4ej?common from the denominator, we get: X(?)=3?54e?j?1?34e?j?+18e?j2?=3?54e?