Digital Signal Processing Systems, Basic Filtering Types, and Digital Filter Realizations - Digital Signal Processing: Fundamentals and Applications - page 212

6.21. For the difference equations

a. yðnÞ¼ 0 : 5 xðnÞþ 0 : 5 xðn 1 Þ
b yðnÞ¼ 0 : 5 xðnÞ 0 : 5 xðn 1 Þ
c. yðnÞ¼ 0 : 5 xðnÞþ 0 : 5 xðn 2 Þ
d. yðnÞ¼ 0 : 5 xðnÞ 0 : 5 xðn 2 Þ

1. find HðzÞ ;
2. calculate the magnitude response;
3. specify the filtering type based on the calculated magnitude response.
6.22. Given an IIR system expressed as

yðnÞ¼ 0 : 5 xðnÞþ 0 : 2 yðn 1 Þ; yð 1 Þ¼ 0

a. find HðzÞ ;
b. find the system response yðnÞ due to the input xðnÞ¼ð 0 : 5 Þ n uðnÞ .
6.23. Given the IIR system

yðnÞ¼ 0 : 5 xðnÞ 0 : 7 yðn 1 Þ 0 : 1 yðn 2 Þ

with zero initial conditions,
a. find HðzÞ ;
b. find the unit step response.
6.24. Given the first-order IIR system

1 þ 2 z 1
1 0 : 5 z 1

HðzÞ¼

realize HðzÞ and develop the difference equations using the following forms:
a. direct-form I;
b. direct-form II.
6.25. Given the filter

1 0 : 9 z 1 0 : 1 z 2

HðzÞ¼

1 þ 0 : 3 z 1 0 : 04 z 2

realize HðzÞ and develop difference equations using the following forms:
a. direct-form I;
b. direct-form II;