Chapter 9Digital Signal Processing

with Xilinx FPGAs

Yin-Tsung Hwang

The materials are largely based on the Xilinx Seminar Notes presented by Bruce Newgard

2

Configurable Hardware DSP Solutions Introduction to digital filters Distributed Arithmetic (DA) DA FIR filter example 8 Tap Slice High speed FIR filter Low speed FIR filter IIR bi-quad filter correlator Summary

Digital Filter Basics

4

Introduction to Digital Filters Key component in many DSP applications

channel equalization, echo cancellation

digital vs analog filters programmability better frequency response

Classifications Finite Impulse Response (FIR) filter

Infinite Impulse Response (IIR) filter

1

0

)()(M

kk knxcny

1

0 1

)()()(M

k

N

ppk pnybknxcny

5

Finite Impulse Response Filter

ck: filter coefficients (constants) x(n): input at time instance n y(n): output at time instance n M: filter tap order

M could be as large as 1000

a series of multiply and accumulate operations No. of MAC operations /sec = sampling frequency

filter tap order

)1()1()(

)()(

110

1

0

Mnxcnxcnxc

knxcny

M

M

kk

6

High Pass Filter Example

0 10 20 30 40 50 60 70-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

n

|h(n

)|

coefficients

-2 -1.5 -1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

Real part

Ima

gin

ary

pa

rt

0 1000 2000 3000 4000 5000 6000 7000 8000 9000-60

-50

-40

-30

-20

-10

0

frequency

de

cib

els

Magnitude Response in dB

Ws=1500Hz Wp=4000HzSampling freq. : 5KHzTap order : 67filter type :HPF filter(FIR)

7

Low Pass Filter Example

Wp=1500Hz Ws=3000HzSample_freq=5KHzTap order=67filter type : LPF filter(FIR)

0 10 20 30 40 50 60 70-0.02

0

0.02

0.04

0.06

0.08

0.1

n

|h(n

)|coefficient

-2 -1.5 -1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

Real part

Ima

gin

ary

pa

rt

0 0 .5 1 1 .5 2 2 .5

x 104

-140

-120

-100

-80

-60

-40

-20

0

20

frequency

de

cib

els

Magn itude Response in dB

8

Basic FIR Filter Block Diagram

9

FIR Implementation Using Programmable DSP Processor

Software solution

1 parallel multiplier, accumulator

Time sharing through micro-coding

relative low sample rate

multiple chip solution

no migration path

complex real time programmingFor each sample data word

For each tapMultiply c(i) times x(i)Add result to accumulator

Distributed Arithmetic Basics

11

2’s Complement Multiplication

12

A Series of Multiply & Add

×

+

+

×

+

+

×

+

coefficient Input sampleWeighted

partial product

multiply result

+final result

Parallel multiplier

accumulator

13

Distributed Arithmetic Approach (1)

+ + + +

LSB MSBLSB+1

+final result

partial sumCan be implementedby a look up table

Accumulator + shifter

14

Distributed Arithmetic Approach (2) x x x x3,3 0,0 3,2 0,0 3,1 0,0 3,0 0,0a a a a

Sum Sum Sum Sum SumSum

x x x x2,3 1,0 2,2 1,0 2,1 1,0 2,0 1,0a a a a x x x x1,3 2,0 2,2 2,0 1,1 2,0 1,0 2,0a a a a x x x x0,3 3,0 0,2 3,0 3,1 0,0 3,0 0,0a a a a

x x x x3,3 0,1 3,2 0,1 3,1 0,1 3,0 0,1a a a a x x x x2,3 1,1 2,2 1,1 2,1 1,1 2,0 1,1a a a a x x x x1,3 2,1 1,2 2,1 1,1 2,1 1,0 2,1a a a a x x x x0,3 3,1 0,2 3,1 0,1 3,1 0,0 3,1a a a a

Sum Sum Sum Sum SumSum x x x x3,3 0,2 3,2 0,2 3,1 0,2 3,0 0,2a a a a x x x x2,3 1,2 2,2 1,2 2,1 1,2 2,0 1,2a a a a x x x x1,3 2,2 1,2 2,2 1,1 2,2 1,0 2,2a a a a x x x x0,3 3,2 0,2 3,2 0,1 3,2 0,0 3,2a a a a

x x x x3,3 0,3 3,2 0,3 3,1 0,3 3,0 0,3a a a a

Sum Sum Sum Sum SumSum

x x x x2,3 1,3 2,2 1,3 2,1 1,3 2,0 1,3a a a a x x x x1,3 2,3 1,2 2,3 1,1 2,3 1,0 2,3a a a a x x x x0,3 3,3 0,2 3,3 0,1 3,3 0,0 3,3a a a a

Sum Sum Sum Sum SumSum

SumSum Sum Sum SumSumSumSum Sum Sum SumSum

SumSum Sum Sum SumSumSumSum Sum Sum SumSum

+1

+1

+1

+1

1

1

1

1

P 0P 1P 2P 3P 4P 5P 6P 7P 8P 9

Need a 4-operandparallel adder

Need a scalingaccumulator

15

DA One-Tap FIR Filter Reduces to multiply a variable x(n) with a constant c0

16

DA Two-Tap FIR Filter

17

DA Three-Tap FIR Filter

Look up table implementation can be both faster and area efficient than a multi-operand adder

18

Recall XC4000X Family

4028EX* 4036EX* 4044EX 4052XL 4062XL 4085XL 40125XV4028EX* 4036EX* 4044EX 4052XL 4062XL 4085XL 40125XV

Typ Logic Gates

Typ System Gates(Logic + Select -

RAM)

Avail RAM bits

Number CLBs

Flip-Flops

I/O

Supply Voltage

Packages:

Typ Logic Gates

Typ System Gates(Logic + Select -

RAM)

Avail RAM bits

Number CLBs

Flip-Flops

I/O

Supply Voltage

Packages:

56,000 72,000 90,000 110,000 130,000 175,000 250,000

32,768 41,472 51,200 61,952 73,728 100,352 157,968

1,024 1,296 1,600 1,936 2,304 3,136 4,6242,560 3,168 3,840 4,576 5,376 7,168 10,336256 288 320 352 384 448 544

HQ208 HQ208 HQ208HQ240 HQ240 HQ240 HQ240 HQ240HQ304 HQ304 HQ304 HQ304 HQ304 BG352 BG352 BG352 BG352 BG352

BG432 BG432 BG432 BG432BG560 BG560 BG560 BG560

PG299 PG411 PG411 PG411 PG475 PG559 PG599

* 30% of CLBsas RAM

28,000 36,000 44,000 52,000 62,000 85,000 125,000

5/3 5/3 5/3 3 3 3 2.5

The Development of a Distributed Arithmetic FIR Filter

10 bit 10 tap XC4000E Family example

20

DA FIR Filter Design in XC 4000E

10-Tap 10-bit example

• N clocks per sample word• Fast clock• No multiplier required• Embedded hardware solution• LUT holds coefficients & Mult.

21

LUT Size in DA FIR Design• Look up table scales exponentially• 10-tap 10-bit needs 210×10 bits• need to reduce the LUT size• take advantages of linear phasesymmetrical FIR filter

22

10-Tap 10-Bit Symmetrical FIR Filter

23

Look Up Table Implementation

Holds all partial products

LUT is as wide as coefficient

use MEMGEN to generate LUT

32×10 memory

Look UpTable

A0

A1

A2

A3

A4

320 bits

DATA10

24

Serial Time Skew Buffer

Sample data word size = Nfilter tap size = k

• one N-bit shift register per tap• use XC4000E RAM to build

shift register• one 16-bit shift register per

1/2 CLB

Using FFs10-bit 10-tap50 CLBs

Using FFs10-bit 10-tap50 CLBs

Using RAMs10-bit 10-tap10 CLBs

Using RAMs10-bit 10-tap10 CLBs

Shift register implemented in RAM

25

Bit Serial Adder

Distributed arithmetic lookup table

26

27

1‘s Complementer MSB has negative

weighting inverts data on the last

cycle 2 bits per CLB

28

Scaling Accumulator

Adds data to 1/2*(SUMOUT)

2 bits per CLB

needs N+1 bits

double precision with an extra shift register

can use LogiBlox for RPM

10-bit 10-tap linear phase FIR filter

29

30

Implementation Block Diagram

Total of 44 CLBs: Fits in a 4003E (with extra 56 CLBs for system use) about 1,300 equivalent gates: little interconnect between blocks

31

Performance No. of 10-tap 10-bit sym. FIR per 4000E device

XC4000part

4003E 4005E 4006E 4008E 4010E 4013E 4020E 4025E

Number ofinstances

2 4 5 7 9 11 15 22

FIR 10B10T macro can be clocked at 70 MHz

10 bit word requires 11 clocks 10 bit sample word rate is 6.4

MHz

word sizesample rate

6 8 10 12 14 16

10.0 7.8 6.4 5.4 4.7 4.1

bitsMHz

32

Double Rate DA FIR Filter (1)

Process 2 bits per clock # of clocks = (N/2)+1

33

Double Rate DA FIR Filter (2)

two taps require 4-input LUT without symmetry

four taps require 4-input LUT with symmetrical FIR

time skew buffer is twice as many CLBs

twice the data word sample rate

both LUTs are the same

Designing large multi-tap filter Xilinx 8-tap FIR filter SLICE building blocks

34

Issue: LUT scales exponentially

35

32-tap FIR filter using 8-tap slices

36

8-tap FIR filter slice building blocks

37

8-tap FIR filter slice

38

8-tap FIR filter slice

39

Very high speed sampling rates

Multiple parallel multipliers

40

Multiply variable with a constant

41

Multiply variable with a constant (1)

42

Multiply variable with a constant (2)

43

High speed parallel FIR filter

44

Fully parallel distributed arithmetic

45

8-tap parallel DA slice (1)

46

8-tap parallel DA slice (2) Support sampling rates 50 ~ 70 Msps Data and coefficient sizes are independent of each

other 8-bit data, 8-bit coefficient require 122 CLBs per 8-

tap slice 16-tap, 8-bit filter requires 250 CLBs 32-tap, 8-bit filter requires 508 CLBs

47

CLB count for 8-tap PDA slice

Approximate number of XC4000 CLBs48

Serial sequential architecture

• Efficient CLB counts• Large number of taps• Moderate sampling rates• Non-symmetric filter OK

49

Lower sampling rate applications

Serial sequential architecture

50

Serial sequential FIR filter (1)

51

Serial sequential FIR filter (2)

52

Serial sequential FIR filter (3)

53

64-tap serial sequential FIR filter

54

Serial sequential FIR filter designs

55

Size estimate

Serial sequential FIR filter designs

56

Speed estimate

8-bit word FIR filter structures

57

FIR filter implementation options

58

8-bit word example

12-bit word FIR filter structures

59

FIR filter implementation options

60

12-bit word example

IIR Filter Designs

61

Bi-quad IIR filter – direct form

62

(lowest quantization noise)

IIR filter – bi-quad implementation

Requires 32-deep LUT 2 parallel to serial converters 60 CLBs for 16-bit word

63

64

IIR filter – bi-quad implementation

Correlator design

65

Using LUTs for correlator design Any n-stage correlator can be decomposed into

(n/4) 4-stage correlators LUTs contain all possible outputs for each 4-stage

correlation Example: correlation pattern = 1011

Store 4h at address 13h in LUT (4 bit matches) Store 3h at addresses 3, F, 9, A in LUT (1 bit error)

Bit rate can exceed 120MHz (XC 3100A)

66

Correlator LUT example

67

Input search pattern= 1101

16-stage correlator using LUT

68

Summary

70

Xilinx v.s. DSP Processor When does it make senses to use FPGAs?

High to medium sample rate systems

small word lengths

lots of taps

fast correlators

single chip solution required

low cost migration path (HardWire)

incremental cost of DSP chip

DSP application specific chips

Design Once !

71

XDSP FPGA Applications

Signal Synthesis

Modulation / Demodulation

Fast Fourier Transforms

Neural Networks

Video Signal Processing (2D, 3D Filters)

and more …….

72

Possibilities

An alternative to software DSP processor solution

existing 4000E/EX are efficient at signal processing

system level application specific solution on a single chip

standard product configurable solution

automatic migration path to a lower cost high volume solution