What is the value of |X(ω)| given X(ω)=1/(1-ae^-jω), |a|

1.	What is the value of \|X(ω)\| given X(ω)=1/(1-ae^-jω), \|a\|
Answer» CORRECT ANSWER is (a) \(\frac{1}{\sqrt{1-2acosω+a^2}}\) To elaborate: For the GIVEN X(ω)=1/(1-ae^-jω), \|a\|<1 we obtain XI(ω)=(-asinω)/(1-2acosω+a^2) and XR(ω)=(1-acosω)/(1-2acosω+a^2) We know that \|X(ω)\|=\(\sqrt{X_R (ω)^2+X_I (ω)^2}\) Thus on CALCULATING, we obtain \|X(ω)\| =\(\frac{1}{\sqrt{1-2acosω+a^2}}\).

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What is the value of |X(ω)| given X(ω)=1/(1-ae^-jω), |a|

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