Signals and systems electrical engineering miscellaneous Difficult Questions and Answers | Page - 36

Signals and systems electrical engineering miscellaneous

Determine-time Fourier Transform for the signal x[n] = {– 2, – 1, 0, 1, 2} will be

1. 2j(2sin 2Ω + sin Ω)
1. 2(2cos 2Ω – cos Ω)
1. – 2j(2sin 2Ω– sin Ω)
1. – 2(2cos 2Ω – cos Ω)

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= – 2e^j2Ω – 1e^jΩ + 1e^-jΩ + 2e^-j2Ω
= – 2(e^j2Ω – e^-j2Ω) – 1(e^jΩ – e^-jΩ)
= – 2j2sin 2Ω– 2jsinΩ
= – 2j(2sin2Ω – sinΩ)

Correct Option: B

= – 2e^j2Ω – 1e^jΩ + 1e^-jΩ + 2e^-j2Ω
= – 2(e^j2Ω – e^-j2Ω) – 1(e^jΩ – e^-jΩ)
= – 2j2sin 2Ω– 2jsinΩ
= – 2j(2sin2Ω – sinΩ)