DSP Lecture 22
Transcript of 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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Lecture 22 EE-802 ADSP SEECS-NUST
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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Lecture 22 EE-802 ADSP SEECS-NUST
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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Lecture 22 EE-802 ADSP SEECS-NUST
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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Lecture 22 EE-802 ADSP SEECS-NUST
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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Lecture 22 EE-802 ADSP SEECS-NUST
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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