Two Rate based low complexity variable fractional delay filter

8/11/2019 Two Rate based low complexity variable fractional delay filter

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Guided By Presented by

Dr. Manju Manuel Reshma Ravi KAssociate Professor Roll.no:13

Dept of ECE S2 AECE

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Overview Introduction

Two rate approach

Variable Fractional delay(VFD) filters

Design and Methods to reduce complexity

Extended structure using HB FRM filters

Conclusion

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Introduction Many DSP systems tend to have a very high

computational complexity when they target wideband

application.

FRM(Frequency response masking) approach reduce the

complexity.

The overall complexity reduction obtained by combining

two rate technique with FRM approach In this paper, we focus the implementation complexity of

VFD(variable fraction delay) filters

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Two Rate Approach To reduce the complexity, we consider here a structure

that is derived via a two-rate approach.

Fig1.Basic multirate approach

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H(z) = F(z)G(z)

Using polyphase decomposition ,

The order and delay of the overall filter H(z) is

)()()(

)()()(

)()()()()(

1

1

0

1

1

0

11

1

00

zGzzGzG

zFzzFzF

where

zFzGzzFzGzH

2

2

GF

H

GF

H

DDD

NNN

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Fig2 (a) Two-rate approach. (b) Equivalent representation

of the system

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Variable fractional delay (VFD)filter

The two-rate based structure offers dramatic complexity

reductions in the Farrow-structure based variable

fractional-delay (VFD) filters.

Applications like interpolation, resampling, delay

estimation, and signal reconstruction.

Incorporating the FRM approach, further complexity

savings are obtained.

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Contd

The VFD filter, with a transfer function H(z, d), is forto approximate the ideal VFD filter frequency response

Where DH is fixed delay & d fractional delay [0.5 0.5]!!

Using the Farrow structure H(z, d) is expressed in the

form

where HK(z) are fixed subfilters

jwez

)(),(

dDjwjw

idealHedeH

L

k

k

k zHddzH0

)(),(

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In the case of multi-function system, the partial outputs

are finally combined via the FD multiplications to formonly one output.

Fig4. Farrow structure realizing the VFD filter transfer function

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Hk(z) is realized as

where F0(z) and are again the polyphase

components of a linear-phase HB interpolation filter F(z)with a passband gain of two and delay DF, whereas Gk0(z)

andGk1(z) are the polyphase components of the subfilters

Gk(z)

where G(z, d) approximates an FD filter

)()()(2)( 1)1(

00 zGzzGzFzH kD

kk

F

)1( FDz

L

k

k

kzGddzG

0

)(),(

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Fig5.Two-rate based structure realizing the VFD filter transferfunction

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Implementation complexity In fig5.number of adders multipliers and delays required

to implement the polyphase components of F(z) and

G(z,d)

The complexity of G(z,d) is lower than H(z).

Major part of the overall complexity is moved to the filter

F(z) and thus to F0(z)

Complexity saving can achieved the FRM technique It cannot be used directly, and one therefore has to seek

other methods to reduce the complexity

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Basic FRM Approach In a linear phase model filter each delay is replaced by

L delays

This results in a periodic filter with much sharpertransition bands

Finally a masking filter extracts the desired band

The overall transfer function is

Model filter and masking filter

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)()()()()( 10 zFzGzFzGzH L

c

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Extended Structure Using HB

FRM Filters Realizing F(z) as an FRM filter, express the transfer

function as[4]

is a period model filter and is itscomplement, whereas B0(z) and B1(z) are masking filters.

)()1()(

)()]([2)()(2)(

01

10

zBzzB

where

zBzAzzBzAzF

BB

A

DD

LLDL

AD

zzAzA

5.0)()( 2

0

)( LzA )( L

LDzAz A

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Using polyphase decomposition, for even:

)(0]2/

)(002[2)(012/)1(

2)(0L

zABD

zzBzBApD

zzF

BD

Fig6.realization of F0(z) using FRM approach

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F0(z) makes use of three subfilters in which , of order

NArequires roughly only NA/(2L) multiplications

andNA/L additions.

Linear Phase case

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)(L

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Design result

We consider the design of a VFD filter with a bandwidth

of

It is seen from the table that that the two-rate based

structure is considerably more efficient than the regularFarrow structure.

9.0c

w

Table 1: 18


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Conclusion Two rate based structure offer substantial saving in

arithmetic complexity compared to other VFD structures

for wide band applications.

Extended FRM HB filters was also introduce further

complexity reduction .

55% 0f saving compared to regular VFD filter when

using two rate based structure and 70% saving whenusing FRM approach with two rate structure.

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References[1]Hkan Johansson, Senior Member, IEEE, and EwaHermanowicz, Two-Rate Based Low-ComplexityVariable Fractional-Delay FIR Filter Structures IEEEtransactions on circuits and systems

,vol. 60, no. 1,

january 2013.

[2]H. Johansson and P. Lwenborg, On the design ofadjustable fractional delay FIR filters, IEEE Trans.Circuits Syst. II, Analog Digit. Signal Process., vol. 50,

no. 4, pp. 164169, Apr. 2003.[3]N. P. Murphy, A. Krukowski, and I. Kale,Implementation of a wideband integer and fractionaldelay element,Electron. Lett., vol. 30, no.20, 1994.

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[4]Hakan Johansson1 Two classes of frequency

responsemasking linear-phase fir filters for interpolation

and decimation, circuits systems signal processing vol.

25, no. 2, 2006, pp. 175200

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Thank You

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Two Rate based low complexity variable fractional delay filter