This is the presentation on digital filters that we used in digital signal processing algorithm , Digital filters structures

1. MEWAR
UNIVERSITY
Presented by: Presented to:
Kamal Jeet Mr. Sayed arif ali
Btech 5th
sem Deptt. Of ECE
MUR1401264

2. BASIc IIR DIgITAl FIlTERBASIc IIR DIgITAl FIlTER
STRUcTURESSTRUcTURES
• The causal IIR digital filters we are
concerned here are characterized by a real
rational transfer function of or, equivalently
by a constant coefficient difference equation
• From the difference equation representation,
it can be seen that the realization of the
causal IIR digital filters requires some form
of feedback
1−
z

3. BASIc IIR DIgITAl FIlTERBASIc IIR DIgITAl FIlTER
STRUcTURESSTRUcTURES
• An N-th order IIR digital transfer function
is characterized by 2N+1 unique
coefficients, and in general, requires 2N+1
multipliers and 2N two-input adders for
implementation
• Direct form IIR filters: Filter structures in
which the multiplier coefficients are
precisely the coefficients of the transfer
function

4. DIREcT FoRM IIR DIgITAlDIREcT FoRM IIR DIgITAl
FIlTER STRUcTURESFIlTER STRUcTURES
• Consider for simplicity a 3rd-order IIR filter
with a transfer function
• We can implement H(z) as a cascade of two
filter sections as shown on the next slide
3
3
2
2
1
1
3
3
2
2
1
10
1 −−−
−−−
+++
+++
==
zdzdzd
zpzpzpp
zD
zP
zH
)(
)(
)(

5. Direct Form iir DigitalDirect Form iir Digital
Filter StructureSFilter StructureS
where
3
3
2
2
1
101
−−−
+++=== zpzpzppzP
zX
zW
zH )(
)(
)(
)(
)(zH1 )(zH2
)(zW
)(zX )(zY
3
3
2
2
1
1
2
1
11
−−−
+++
===
zdzdzdzDzW
zY
zH
)()(
)(
)(

6. Direct Form iir DigitalDirect Form iir Digital
Filter StructureSFilter StructureS
• The filter section can be seen to be
an FIR filter and can be realized as shown
below
]3[]2[]1[][][ 3210 −+−+−+= nxpnxpnxpnxpnw
)(zH1

7. Direct Form iir DigitalDirect Form iir Digital
Filter StructureSFilter StructureS
• The time-domain representation of is
given by
Realization of
follows from the
above equation
and is shown on
the right
)(zH2
][][][][][ 321 321 −−−−−−= nydnydnydnwny
)(zH2

8. Direct Form iir DigitalDirect Form iir Digital
Filter StructureSFilter StructureS
• A cascade of the two structures realizing
and leads to the realization of
shown below and is known as the direct
form I structure
)(zH2
)(zH1
)(zH

9. Direct Form iir DigitalDirect Form iir Digital
Filter StructureSFilter StructureS
• Note: The direct form I structure is
noncanonic as it employs 6 delays to realize
a 3rd-order transfer function
• A transpose of the direct form I structure
is shown on the right and is called the
direct form I structure
t

10. Direct Form iir DigitalDirect Form iir Digital
Filter StructureSFilter StructureS
• Various other noncanonic direct form
structures can be derived by simple block
diagram manipulations as shown below

11. Direct Form iir DigitalDirect Form iir Digital
Filter StructureSFilter StructureS
• Observe in the direct form structure shown
below, the signal variable at nodes and
are the same, and hence the two top delays
can be shared
1 '1

12. Direct Form iir DigitalDirect Form iir Digital
Filter StructureSFilter StructureS
• Likewise, the signal variables at nodes
and are the same, permitting the sharing
of the middle two delays
• Following the same argument, the bottom
two delays can be shared
• Sharing of all delays reduces the total
number of delays to 3 resulting in a canonic
realization shown on the next slide along
with its transpose structure
2
'2

13. Direct Form iir DigitalDirect Form iir Digital
Filter StructureSFilter StructureS
• Direct form realizations of an N-th order
IIR transfer function should be evident