Digital filters - Continuous and Discrete Time Signals and Systems - page 662

z −1

−0.5 0.2

+ +

z −1

0.24 0.8

14.9 Using the principle of transposition for the flow graphs, derive two alter-
native representations for the FIR filter specified in Problem 14.8.
14.10 Draw the linear-phase flow graph for the FIR filter specified in Problem
14.8.

14.11 The transfer function of an IIR filter is given by

− 1 ) 8 .

H ( z ) = (1 − 0 . 25 z

Draw the flow graphs based on the following forms: (i) cascade of eight
first-order FIR systems; (ii) cascade of four second-order FIR systems;
(iii) cascade of two third-order FIR systems and one second-order FIR
system; (iv) cascade of two fourth-order FIR systems; (v) cascade of one
sixth-order FIR system and one second-order FIR system. Compare the
computational complexity of each realization.

14.12 The transfer function of an IIR filter, with impulse response given by

π
4 k

h [ k ] = 0 . 5 k sin

u [ k ] ,

is given by the following expression:

π
4

0 . 5 z sin

0 . 3536 z
z 2 − 0 . 7071 z + 0 . 25 .

H ( z ) = ≈

π
4

z 2 − 2 0 . 5 cos z + 0 . 25

Draw the flow graphs for (i) direct form I, (ii) direct form II, (iii) the
cascaded form, and (iv) the parallel form realizations of the IIR filter.

14.13 Using the principle of transposition for the flow graphs, derive four
alternative flow graph representations for the IIR filter specified in
Problem 14.12.

14.14 The transfer function of a digital system is given by
H ( z ) = 1 − 0 . 8 z − 1 + 0 . 15 z − 2

1 − 0 . 7 z − 1 − 0 . 18 z − 2 .
Draw the flow graphs for (i) direct form I, (ii) direct form II, (iii) the
cascaded form, and (iv) the parallel form realizations of the IIR filter.