High Flyers School and Degree College Jutial Gilgit
sdfs
SDF sdfsd

Spring 2016
Unit  4
(part 1)
1
IIR structure
Derived from difference equation
Q
y n bi x n i
Direct form I
i 0
b0
xn
z1
z1
z1
z1
yn
b1
a1
b2
a2
b3
bQ1
a3
aQ1
z1
P
ak y n k
k 1
1
H ( z ) B ( z )
A( z )
z1
non canonical form
z1
z1
IIR structure
Dire
High Flyers School and Degree College Jutial Gilgit
sdfs
SDF sdfsd

Spring 2016
Unit  3
(part 1)
1
The zTransform and transfer function
A DSP system can be represented by ztransform
Use general rule
k
Z
transform
of
x(nk)=z
Consider a system given byX(z)
the difference
equation
y (n) x(n) x(n 1) 2 x(n 2) 2 y (n 1) y (n 2)
App
High Flyers School and Degree College Jutial Gilgit
sdfs
SDF sdfsd

Spring 2016
Unit  2
Transforms
Example of a substitution:
Original equation: x4 + 4x 8 = 0
Let: y = x give y + 4y 8 = 0
Familiar form: ay + by + c = 0
Solve for y
Solution to original form problem is
x = y
2
Fourier transform
Fourier transform convert a signal in
High Flyers School and Degree College Jutial Gilgit
sdfs
SDF sdfsd

Spring 2016
Unit  3
(part 1)
1
The zTransform
The ztransform of sequence x(n) is defined by
X ( z ) x ( n) z
n
n
2
zPlane
X ( z ) x ( n) z
n
Im
z = ej
n
j
X (e )
x ( n )e
n
j n
Re
Definition
Give a sequence, the set of values of z for
which the ztransfo
High Flyers School and Degree College Jutial Gilgit
sdfs
SDF sdfsd

Spring 2016
Unit  2
Transforms
Example of a substitution:
Original equation: x4 + 4x 8 = 0
Let: y = x give y + 4y 8 = 0
Familiar form: ay + by + c = 0
Solve for y
Solution to original form problem is
x = y
2
Fourier transform
Fourier transform convert a signal in
High Flyers School and Degree College Jutial Gilgit
sdfs
SDF sdfsd

Spring 2016
Unit  1
Spring 2016
(part 1)
1
Signals  Introduction
Signal: Anything that carries some information can be called
as signal. A signal is also defined as any physical
quantity that varies with time, space or any other
independent variable or variables.
High Flyers School and Degree College Jutial Gilgit
sdfs
SDF sdfsd

Spring 2016
Signal Processing
Signal
Processing
is
a
method
of
extracting information from the signal which
in turn depends on the type of signal and the
nature of information it carries.
What is a system?
A system is formally defined as an entity that manipulates on
High Flyers School and Degree College Jutial Gilgit
sdfs
SDF sdfsd

Spring 2016
THE ZTRANSFORM
zTransform Theorems and
Properties
LINEARITY
Z[ x(n)] X ( z ),
z Rx
Z[ y (n)] Y ( z ),
z Ry
Z[ax(n) by (n)] aX ( z ) bY ( z ),
z Rx R y
Overlay of
the above two
ROCs
SHIFT
Z[ x(n)] X ( z ),
n0
z Rx
Z[ x(n n0 )] z X ( z )
z Rx
MULTIPLICATIO