- Consider the SFG in Fig. 11.25 which corresponds to the all-pole transfer function
where − 1 <

*a*< 1 for stability.(a) Calculate the output roundoff noise. Show that the noise variance gets amplified through the

*feedback*section, i.e., even though*e*(*n*) may be*small*, its effect on*y*(*n*) can be*large*.(b) Compute roundoff noise for (i)

*a*= 0.1, (ii)*a*= 0.5, and (iii)*a*= 0.998. Comment on the relation between roundoff noise and pole locations.(c) For narrowband filters, |

*a*| is typically very close to 1. For example, a = 0.998 is not uncommon. For such filters, the noise variance gets amplified enormously. (In that case, low-noise/sensitivity filter structures such as lattice filters and wave digital filters need to be considered.) Explain conceptually why poles are located very close to the unit circle for narrowband filters. - Assume that the ...

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