Consider the filter y(n) 0 9y (n 1) bx (n) (a) Determine b so that H(0) 1 (b) Determine the frequency at which H() 1 2 (c) Is this filter low pass, band pass, or high pass (d) Repeat parts (b) and (c) for the filter y(n) 0 9y(n 1) 0 1x (n) ...

y n 09 y n 1 bx n a b c The filter is ...

Consider the filter y(n) = 0.9y (n 1) + bx (n) (a) Determine b so that

Question:

Consider the filter y(n) = 0.9y (n – 1) + bx (n)
(a) Determine b so that |H(0) = 1.|
(b) Determine the frequency at which |H(ω)| = 1/√2.
(c) Is this filter low pass, band pass, or high pass?
(d) Repeat parts (b) and (c) for the filter y(n) = -0.9y(n – 1) + 0.1x (n).