modified new lut

Project Seminar on

New Approach to Look-Up-Table Design &Memory-Based Realization of FIR Digital Filter

Presented By SARADA A

Reg.No: 010911407 Class:M.E(PTPG)

• Digital Systems (ECE )• UCE(Autonomous), OU • Internal Guide

Dr.P.Chandra Sekhar Associate Professor,

Dept of ECE, UCE(Autonomous),OU

Contents

Aim of the Project

Technical Approach

Introduction

DA based Approach

Conventional LUT based Apporach

Proposed Method

Simulation Results

Conclusion

References

Aim of the projectTo design an LUT using the proposed

new approachImplementation of the proposed LUT

based FIR Filter and comparing with the existing design.

Technical ApproachThe project is implemented using VHDL and

Simulated for its Functional Verification

Introduction FINITE-IMPULSE response (FIR) digital filter is widely used

as a basic tool in various digital signal processing applications

The order of an FIR filter primarily determines the width of the transition-band . The higher the filter order, the sharper is the transition between a pass-band and adjacent stop-band.

Many applications in digital signal processing require large order FIR filters Since the number of (MAC) operations required per filter output increases linearly with the filter order, real-time implementation of these filters of large orders is a challenging task.

The memory-based computing structures are more regular than the multiply-accumulate structures; and offer many other advantages over MAC structures like greater potential for high throughput and low-latency implementation; and less dynamic power consumption.

Memory-based computing is well-suited for many digital signal processing (DSP) algorithms, which involve multiplication with fixed set of coefficients.

There are two basic variants of memory-based techniques.

Distributed arithmetic (DA) for inner product computation

Computation of multiplication by look-up-table (LUT)

DA based Approach

The “basic” DA technique is bit-serial in natureDA is basically a bit-level rearrangement of the

multiply and accumulate operation.DA hides the explicit multiplications by ROM

look-ups an efficient technique to implement on Field Programmable Gate Arrays (FPGAs).

DA Based Approach contd..

Let xk consisits of N-bits xk : {bk(N-1), ……bk2,bk1,bk0 }

K

kkk xAy

1

1

0

2N

n

nknk bx

…(1)

…(2)

K

k

N

n

nknk bAy

1

1

0

2

K

k

N

n

nknk bAy

1

1

0

2 …(3)

DA Based Approach contd..

K

k

N

n

nkkn Aby

1

1

0

2

112

21

1

1212

2222

1121

1111

2112

1111

0220110

222

222

222

NKNKKKKK

NN

NN

KK

AbAbAb

AbAbAb

AbAbAb

AbAbAby

K

k

NNkkkkkkkk bAbAbAAby

1

)1()1(

22

110 222

…(3)

Expanding this part

DA Based Approach contd..

DA Based Approach contd..

DA Based Approach contd..

1

0 1

2N

n

nK

kknk bAy

K

k

N

n

nkkn Aby

1

1

0

2

Bit Level Rearrangement

Original Equation

Modified Equation

DA Based Approach contd..In the DA-based approach, an LUT is used to

store all possible values of inner-products of a fixed -point vector with any possible -point N bit-vector.

Address and Contents of Look Up Table

LUT

If the inner-products are implemented in a straight-forward way the memory-size of the DA-based approach increases exponentially with the inner-product-length.

Conventional LUT Based Approach

Conventional LUT Multiplier

Conventional LUT based Approach contd..

In the LUT-multiplier-based approach, multiplications of input values with a fixed-coefficient are performed by an LUT consisting of all possible pre-computed product values corresponding to all possible values of input multiplicand.

If the inner-products are implemented in a straight-forward way, the memory-size of LUT-multiplier based implementation increases exponentially with the word length of input values.

In the proposed LUT based multiplier the multiplication of an L -bit input with W-bit coefficient is carried out by the following strategy:

A memory-unit of 2L/2 words of (W+L) -bit width is used to store all the odd multiples of A.

A barrel-shifter for producing a maximum of (L-1)leftshifts is used to derive all the even multiples of A .

The L-bit input word is mapped to (L-1) -bit LUT-address by an encoder.

The control-bits for the barrel-shifter are derived by a control-circuit to perform the necessary shifts of the LUT output.

A RESET signal is generated by the same control circuit to reset the LUT output when X=0000.

The Proposed LUT Based Approach

Proposed LUT design for multiplication of W-bit fixed coefficient(A) and 4-bit input operand(X)

The 4-to-3 bits input encoder

Control Circuit Structure of NOR Cell

Simulation Results

ConclusionThe proposed LUT-based-multiplication reduces

the LUT-size over that of conventional design by making use of odd-multiple-storage scheme.

For address-length 4, the LUT size is reduced to half by using a two-stage logarithmic barrel-shifter and (w+4) number of NOR gates, where W is the word-length of the fixed multiplying coefficients.

References P. K. Meher, “New look-up-table optimizations for memory-based

multiplication,” in Proc. Int. Symp. Integr. Circuits (ISIC’09), Dec.2009, to be published.

P. K. Meher, “New approach to LUT implementation and accumulation for memory-based multiplication,” in Proc. 2009 IEEE Int. Symp. Circuits Syst., ISCAS’09, May 2009, pp. 453–456

H. Yoo and D. V. Anderson, “Hardware-efficient distributed arithmetic architecture for high-order digital filters,” in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, (ICASSP’05), Mar. 2005, vol. 5, pp. v/125–v/128.

J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications. Upper Saddle River, NJ: Prentice- Hall, 1996.

H. H. Dam, A. Cantoni, K. L. Teo, and S. Nordholm, “FIR variable digital filter with signed power-of-two coefficients,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 54, no. 6, pp. 1348–1357, Jun. 2007.

K. K. Parhi, VLSI Digital Signal Procesing Systems: Design and Implementation. New York: Wiley, 1999.

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