fir lattice structure
TRANSCRIPT
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Major Project Report On
FIR LATTICE STRUCTURE
1. Filter co-efficients to Lattice co-efficients2. Lattice co-efficients to Filter co-efficients
Presented By:-Anuj Kumar
Ashutosh Verma
Suman Saurabh
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Introduction
Realization of any FIR discrete time system
Direct form realization
Simplest form of filter realization
Quantization effects are not taken into
consideration.
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Lattice realization
Exhibit robustness in finite word lengthimplementations.
Frequency sampling realization for an FIR
system (computationally efficient). State space formulation for linear time
invariant system.
Lattice filters are used extensively in digitalspeech processing and in the
implementation of adaptive filters.
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What we see..
Direct form filter realization is the
simplest but not very much accurate.
Lattice realization is accurate but not so
simple.
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What If.
If we get both the simplicity of Direct form realization as well as the accuracy of
Lattice realization. We get a way to convert Filter co-
efficients to Lattice co-efficients and vice-
versa, such that we can extract thebenefits of both.
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Direct Form FIR Digital Filter
StructuresA direct form realization of an FIR
filter can be readily developed from
the convolution sum description asindicated below for N= 4
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FIR Filter RealizationsLattice Form
7
u[k]
y[k]
+
+
x
x
ko
+
+
x
x
k1
+
+
x
x
k2
+
+
x
x
k3
xbo
y[k]
~
][....]1[.][.][10
Nkubkubkubky N
i.e. different software/hardware, same i/o-behavior
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Conversion of Direct - from
Filter coefficients to Lattice
coefficients
Here,
x(n) is the input sequence to the filter andy(n) is the output sequence.m(k) is the Unit sample response of the m
th
filter. where., k = 1,2,3,,m.
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We can compute directly lattice
coefficients by using these
equations
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If order=1 and coefficients is 1
and 0.2 respectively.
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Graphics window for order 1 is
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2nd order Filter
If order=2 and coefficients is 1, 0.3 and 0.5respectively.
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Graphics window for order 2 is
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Conversion from Lattice
coefficients to Direct - form
Filter coefficients
Km = Reflection Co-efficient.
Ym(z) = mth Output.
Xm(z) = mth Input.
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Finding co-efficients
1 k m-1,m =1,2,.,M-1
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1st Order Filter
If order=1 and k1=0.5
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Graphical representation for
order = 1
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2nd Order Filter
If order = 2 and k1=0.5 and k2=0.8
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Graphical representation for
order = 2
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Conclusion
We can get Filter co-efficients and
Lattice co-efficients from one another.
So, we can reach to a more accurate
result using easier computation
technique.
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THANK YOU