DSP Lecture 22

7/30/2019 DSP Lecture 22

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Lecture 22 EE-802 ADSP SEECS-NUST

EE 802-Advanced Digital SignalProcessing

Dr. Amir A. KhanOffice : A-218, SEECS

9085-2162; [email protected]

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From Direct Form to Lattice Lattice structures are extensively used in DSP especially for

the adaptive filter description Consider an FIR filter

Direct form

Impulse

Response?Same asfilter coeffs

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Lattice Structure for FIR Filters

First order FIR

One step forward predictor

Reflection coefficient

2nd order FIR

Take o/p on

upper branch

Discardlower branch

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Lattice Structure for FIR Filters2nd order FIR

Reflection coefficients of latticefilter can be linked to the direct form

Filter coefficients

Filter coefficients of A 2(z)

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m-stage Lattice StructureRelation between m th order direct form FIR and m th order lattice filter

Output of M-1 stage FIR filter

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Filter Coefficients for Upper and Lower Branches

Coefficients {1 K 1} = {1, a 1(1)}

Coefficients {K 1 1} = {a 1(1), 1}

Filter coefficients of upper branch

Filter coefficients of lower branch Filter coefficients of upper and lower

branches are in reversed order 7


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Forward/Backward PredictionInter-relationship of Upper/Lower Branches

Filter coefficients of B m(z)

Linear Prediction Context

Backward Prediction

Bm(z) is reciprocal filter of A m(z)

Forward Prediction)(

)( n x n x Prediction Error )(

)( mn x mn x Prediction Error

Their product is an all pass system 8


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Lattice Structure FIR-Matrix Form

Divide both side by X(z)

Matrix form of a lattice structure

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Conversion of Lattice Coefficients to DirectForm Coefficients and Vice Versa

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DSP Lecture 22

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