Answers to Selected Problems - Digital Signal Processing: Fundamentals and Applications - page 850

CHAPTER 13
13.1. a.

B ¼ f sM = 2 ¼ f s =ð 2 MÞ; f c ¼ 2 ðf s =ð 2 MÞÞ ¼ 2 B; f c =B ¼ 2 ¼ even

wn () xm ()

↓ 4

f

f = f /4

sM s

Xf ()

f

f /2

s

f /4

s

b. B ¼ f sM = 2 ¼ f s =ð 2 MÞ; f c ¼ f s =ð 2 MÞ¼B; f c =B ¼ 1 ¼ odd

xm ()

wn ()

↓ 4

f f = f /4

s sM s

Xf ()

f

f /2

s

f /4

s

1
2 ðWðzÞþWðe jp zÞÞ ,

1
2 ðWðe jU ÞþWðe jðUpÞ ÞÞ ,

Yðe jU Þ¼

13.3. From Equation (13.7), YðzÞ¼

Wðe jðUpÞ Þ is the shifted version of Wðe jU Þ by f s = 2.
(a)

(b)