1.

What is the energy density spectrum of the signal x(n)=a^nu(n), |a|

Answer»

The CORRECT choice is (b) \(\frac{1}{1-2acosω+a^2}\)

The EXPLANATION: Given x(n)= a^nu(n), |a|<1

The auto correlation of the above SIGNAL is

rxx(l)=\(\frac{1}{1-a^2}\) a^|l|, -∞< l <∞

According to Wiener-Khintchine Theorem,

Sxx(ω)=F{rxx(l)}=\([\frac{1}{1-a^2}]\).F{a^|l|} = \(\frac{1}{1-2acosω+a^2}\)



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