The first-order filter shown in Fig. P9.35 is implemented in four-bit (including sign) I...

The first-order filter shown in Fig. P9.35 is implemented in four-bit (including sign) Iced-point two's-complement fractional arithmetic. Products are rounded to four-bit representation. Using the input x(n) = 0.10δ(n), determine:

(a) The first five outputs if α = 0.5. Does the filter go into a limit cycle?

(b) The first five outputs if α = 0.75. Does the filter go into a limit cycle?