If x(n)=Ae^jωn is the input of an LTI system and h(n) is the response of the system, then what is the output y(n) of the system?(a) H(-ω)x(n)(b) -H(ω)x(n)(c) H(ω)x(n)(d) None of the mentionedI had been asked this question in exam.My doubt is from Frequency Domain Characteristics of LTI System in chapter Frequency Analysis of Signals and Systems of Digital Signal Processing

If x(n)=Ae^jωn is the input of an LTI system and h(n) is the response

1.	If x(n)=Ae^jωn is the input of an LTI system and h(n) is the response of the system, then what is the output y(n) of the system?(a) H(-ω)x(n)(b) -H(ω)x(n)(c) H(ω)x(n)(d) None of the mentionedI had been asked this question in exam.My doubt is from Frequency Domain Characteristics of LTI System in chapter Frequency Analysis of Signals and Systems of Digital Signal Processing
Answer» Right answer is (c) H(ω)x(N) To explain I would say: If x(n)= AE^jωn is the input and h(n) is the response o the system, then we KNOW that y(n)=\(\sum_{k=-∞}^∞ h(k)x(n-k)\) =>y(n)=\(\sum_{k=-∞}^∞ h(k)Ae^{jω(n-k)}\) = A \([\sum_{k=-∞}^∞ h(k) E^{-jωk}] e^{jωn}\) = A. H(ω). e^jωn = H(ω)x(n)

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