OCTOBER 19-20, 2012 - YMCA University of Science & Technology

Proceedings of the National Conference on
Trends and Advances in Mechanical Engineering,
YMCA University of Science & Technology, Faridabad, Haryana, Oct 19-20, 2012
4. Problem Description
When a mobile user moves from one region to another region, a different channel is allotted to the user
depending upon the availability of the channel. A Band Pass IIR filter is designed which is used to give the
response of a particular channel. Two band pass filters are used to give the responses of two available channels.
5. System Modeling
The filter consists of two stages connected in cascading. The single stage is designed in the direct form two. In
the first stage x (n) is input and y 11 (n) is the output and Z -1 represents the delay element. The output of delay
element is multiplied by the coefficients of numerator and denominator respectively and then fed the adder. The
output of first stage y 11 (n) is fed to the input of second stage. The output of second stage is represented by y 1 (n).
Thus the system is designed using cascaded structure while the individual stage is designed using direct form
two structure.
Fig. 1. Structure of band pass filter
6. Mathematical Analysis
The filter is having two stages in cascade form while the individual stage is designed in the direct form two
structure.
The band pass filter transfer function is
− 1
1 − z
H ( z ) =
(1)
−1
− 2
1 − 0 .07 z + 0 .07 z
Substituting
j T
e ω for z in equation (1)
H
1 − e
= (2)
1 − 0.07 e + 0.07 e
− jω
T
( ω T )
− jω
T
− 2 jω
T
Rearranging the terms to produce positive and negative exponents of equal magnitude in equation (2)
H ( ωT
) =
H ( ωT
) =
e
e
− jωT
jωT
/ 2 jωT
/ 2 − jωT
/ 2
[ e − e ]
jωT
− jωT
[ e − 0.07 + 0.07e
]
−
jωT
/ 2 jωT
/ 2 − jωT
/ 2
e [ e − e ]
jωT
− jω
[ e − 0.07( 1 − e )]
T
(3)
(4)
Substituting inside the parentheses, the relation e
j ω T = cos( ωT
) + j sin( ωT
)
jωT
/ 2
e [ cos( ωT
/ 2) + jsin(
ωT
/ 2) − cos( ωT
/ 2) + j sin( ωT
/ 2) ]
H(
ωT)
=
[ cos( ωT)
+ jsin(
ωT)
] − 0.07 [(1
− cos( ωT)
+ j sin( ωT)
]
(5)
386