The sequence [x=0.125,0.25,0.5,1,2,4] is filtered by a filter with transfer function [H(z)=frac{1}{3}left(1+z^{-1}+z^{-2} ight)] and the result is

The sequence

\[x=0.125,0.25,0.5,1,2,4\]

is filtered by a filter with transfer function

\[H(z)=\frac{1}{3}\left(1+z^{-1}+z^{-2}\right)\]

and the result is decimated by 2 . The output is then upsampled by 2 and filtered by the same \(H(z)\). Generate the resulting sequence and interpret the results.