## Transcribed Text

Digital Signal Processing
Chapter 3
1. Sketch each of the following special digital sequences:
(a) 58(n)
(b) -2õ(n-5)
(c) -5u(n)
(d)5u(n-2)
2. Calculate the first cight sample values and sketch each of the following
sequences:
(a.) x(n)=0.5"u(n)
(b. x(n)=5sin (0.2m n)u(n)
7. Sketch the following sequences:
(a) x( n)=2õ(n+3) -0.56(n+1)-58(n-2)-4(6n-5)
(b) x(n)=2ô(n+2) 20(n+ 1)+5u(n-3)
3.8. Given the x(n) Figures 3.26 and 1.27 write expression for each digital
signal
using
sequence
and
its
shifted
sequences
.
4
FIGURE 3.26
The first digital signal ir Problem
82
CHAPTER Digital Signals and Systems
.
FIGURE 3.27
The second digital signal Problem 3.8.
.10. Determine which of the following systems is linear system.
(a) (n) =5x(n)+2x²(n)
(b)y(n)= x(n-1)+4x(n)
(c) ((()) =4x³ (n- 1)-2x(n)
13. Determine which of the following linear systems is time invariant.
(a)y(n)= -5x(n- 10)
(b) y(n)=4x(n2)
14 Determine which of the following linear systems is causal.
(a) y(n) =0 5x(n) +100x(n-2 20x(n- 10)
(b) y(n): x(n+4) +0.5x(n)-2x(n-2)
16. Find the unit impulse response for each of the following linear systems.
(a)y(n) 0.5x(n) 0.5x(n- 2): forn> 0,x(-2) =0,x(-1)
(b)y(n) =0. 75x(n- 1)+x(n); for n> 0,y(-1)=0
Chapter 6
2. Given the difference equation
y(n) =x(n) 0.5y(n- +0.6y(n- 1)
(a)Calculate the system response y(n) 0,1, .4 with the input x(n)=(0.5)"u(n)
and initial condition x(- 1)= and y( 1)=1,
9. A digital system is described by the following difference equation:
y(n): x(n)- 0.3x (n 1) +0.28x(n-2)
Find the transfer function H(z) the denominator polynomial A(z) and the
numerator polynomial B(z)
10.
Convert each of the following transfer functions into difference equations:
(a) H(z) 550.5z
(b)H(z) 1-0.3z
21.
For the difference equations:
(a) y(n) =0. 5x(n) +0. 5x(n- 1)
(b)y(n) =0 5x(n) 5x(n- 1)
(c) y(n) =0 5x(n) +0, 5x(n 2)
(d)y(n) 5x(n) 5x(n-2)
1. Find H(z):
25.
Given the filter
H(z)=
realize H(z) and develop difference equations using the following forms:
a. direct form
b direct -form II;

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.