The sequence x(n) is obtained by sampling an analog signal with period T. From this signal a new signal is derived having the sampling period T/2 by use of a linear interpolation method described by the equation y(m) = ( x(m/2), m even 1 2 x m−1 2 + x m+1 2 , m odd (a) Show that this linear interpolation scheme can be realized by basic digital signal processing elements. (b) Determine the spectrum of y(n) when the spectrum of x(n) is X(ω) = 1, 0 ≤ |ω| ≤ 0.2π 0, otherwise in [−π, π] (c) Determine the spectrum of y(n) when the spectrum of x(n) is X(ω) = 1, 0.7π ≤ |ω| ≤ 0.9π 0, otherwise in [−π,