fir lattice structure

8/3/2019 Fir Lattice Structure

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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

fir lattice structure

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