Session A3 Part 2 Multirate DSP Wireless 2011

8/20/2019 Session A3 Part 2 Multirate DSP Wireless 2011

1/49

Applications toCommunication Systems

fred [email protected]

Part 2

June -1, 2011

Multirate Digital Signal Processing

filter_ten_a, filter_ten_b, filter_ten_c


2/49

Critically Sampled

Analysis/Synthesis Filter BankH (Z)0 G (Z)0 H (Z)0

H (Z)1 G (Z)1 H (Z)1

H (Z)2 G (Z)2 H (Z)2

H (Z)3 G (Z)3 H (Z)3

4-Point

IFFT4-Point

FFT

f

f

Non-Critically SampledAnalysis/Synthesis Filter Bank

H (Z)0

H (Z)4

G (Z)0

G (Z)4

H (Z)0

H Z)4

H (Z)1

H (Z)5

G (Z)1

G (Z)5

H (Z)1

H (Z)5

H (Z)2

H (Z)6

G (Z)2

G (Z)6

H (Z)2

H (Z)6

H (Z)3

H (Z)7

G (Z)3

G (Z)7

H (Z)3

H (Z)7

8-Point

IFFT

8-Point

FFT

f

f f


3/49

0 20 40 60 80-0.2

0

0.2channel 0

0 20 40 60 80-2

0

2channel 1

0 20 40 60 80-0.4

-0.2

0

0.2channel 2

0 20 40 60 80-0.1

0

0.1

channel 3

0 20 40 60 80-0.1

0

0.1channel 4

0 20 40 60 80-0.1

0

0.1channel 5

0 20 40 60 80-0.1

0

0.1channel 6

0 20 40 60 80-0.1

0

0.1channel 7

Channel Time Series

Channelizer Time Response toTone Burst

-1 -0.5 0 0.5 1

-150

-100

-50

0channel 0

d B

-1 -0.5 0 0.5 1

-150

-100

-50

0channel 1

-1 -0.5 0 0.5 1

-150

-100

-50

0channel 2

-1 -0.5 0 0.5 1

-150

-100

-50

0channel 3

d B

-1 -0.5 0 0.5 1

-150

-100

-50

0channel 4

-1 -0.5 0 0.5 1

-150

-100

-50

0channel 5

-1 -0.5 0 0.5 1

-150

-100

-50

0channel 6

Frequency

d B

-1 -0.5 0 0.5 1

-150

-100

-50

0channel 7

Channelized Spectra

Frequency

Channelizer Spectral Response toTone Burst


4/49

0 50 100 150 200 250 300 350 400-1.5

-1

-0.5

0

0.5

1

1.5Reconstructed Signal

A m p l i t u d e

-4 -3 -2 -1 0 1 2 3 4

-100

-50

0

Spectrum: Reconstructed Signal

Normalized Freq uency (f/f BW

)

d B

Reconstructed Tone Burst fromAnalysis Filter Bank

16 fsfs

h (n)0

h (n)2

h (n)= h(r+ nM)r

h (n)30

h (n)1

h (n)16

h (n)15

h (n)31

FDM

32-PNT IFFT

.

.

.

.

.

.

.

.

.

.

. . .

16 ActiveInput Ports

InputSample Rate

12 Mhzper Channel

f lg= 0

flg= 0

f l g = 1 f l g

= 1

Circular Buffer

1-to-16 Up-Sample in 32-Point IFFT


5/49

Z

Z

Z

Z

Z

-1

-15

-16

-30

-31

H ( Z )032

H ( Z )132

H ( Z )1532

H ( Z )1632

H ( Z )30

32

H ( Z )3132

. . . .

. . . .

. . . .

. . . .

1:16

Z

Z

Z

Z

Z

-1

-15

-16

-30

-31

H ( Z )0

2

H ( Z )1

2

H ( Z )15

2

H ( Z )16

2

H ( Z )30

2

H ( Z )31

2

. . . .

. . . .

. . . .

. . . .

1:16

1:16

1:16

1:16

1:16

1:16

32-Path Polyphase Partition with

First Step of 1-to-16 Up-Sampling

Z

Z

Z

Z

Z

Z

Z

-1

-15

-1

-1

-1

-14

-15

H ( Z )02

H ( Z )12

H ( Z )152

H ( Z )162

H ( Z )302

H ( Z )312

. . . .

. . . .

. . . .

. . . .

1:16

1:16

1:16

1:16

1:16

1:16

Z

Z

Z

Z

Z

Z

Z

-1

-15

-1

-1

-1

-14

-15

H ( Z )02

H ( Z )12

H ( Z )152

H ( Z )162

H ( Z )30 2

H ( Z )312

. . . .

. . . .

. . . .

. . . .

1:16

1:16

1:16

1:16

1:16

1:16

32-Path Polyphase Partition with Secondand Third Steps of 1-to-16 Up-Sampling


6/49

Z

Z

Z

-1

-1

-1

H ( Z )02

H ( Z )12

H ( Z )152

H ( Z )162

H ( Z )302

H ( Z )312

. . . .

. . . .

H (Z )k2

Z H (Z )-1

(k+ 16)2

h(k)

h(k+ 16)

h(k+ 32)

h(k+ 48)

h(k+64)

h(k+80)

h(k+ 96)

h(k+112)

h(k+128)

h(k+ 144)

32-Path Polyphase Partition withFinal Step of 1-to-16 Up-Sampling

Two Versions of PathFilters in Partition

0

T

T 2T 3T 4T

T T T

0 0 0IIIIIIIV

fs

32-PNT IFFT

.

.

.

.

.

flg= 0

flg= 0

f l g = 1 f l g

= 1

Circular Buffer

Phase Continuity

Embedded 2-to-1 Down-Sampler in 32-path Polyphase Filter

Requires Circular Buffer to Align Phase of SinusoidsIn Successive Output Blocks from IFFT


7/49

Single Channel Polyphase Filters

Down-Sampler and Up-SamplerEmbedded in Filter

Constant Workload Single Channel Filter

Nyquist Sample Criterion

f sf s f s/M

M-to-1Filter

H(Z)

x(n) y(n) y(nM)

f s

f sf

s/M

0

0

2BWΔf

2BW f +Δ

= + Δ2S f BW f

harris

> 2S f BW

Nyquist


8/49

Interesting Relationship

( )

22

2 ; (Protect from Aliasing When Down Sampling)

S

S

f A dB N

f

f BW

M α

=Δ

=

Filter Length at Input Sample Rate :

Signal 2-Sided BW as Fraction of Output Sample Rate:

Transition BW, ∆f as Fraction of Output Sample

(1 ) ; (Allowable Aliasing When Down Sampling)

( ) 1 ( )

(1 ) / 22 (1 ) / 22

1 ( ) (Ops/Output);

(1 ) 22 (I

S

S

S

f f

M

f A dB A dB N

f M M

N A dB N

M M

α

α α

α

Δ = −

= =− −

=−

Rate:

Substitute in Filter Length at Input Sample Rate :

Dividing both sides by M

(Ops)

nput/Output) ( Input)

N

M =

N-Tap

Lowpass

Filter

M-to-1

f f f s s sM

x(n) y(n) y(nM)

f /Ms-f /Ms 0

Δf= (1-α)f /Ms

2BW = f /Mα s

f

........

Efficient Filtering WhenSample Rate is LargeCompared to Bandwidth


9/49

Bad Mismatch: Sample Rate LargeCompared to Bandwidth

200 Hz

80 dB

0.1 dB

200 Hz

20 kHz

f

-6 dB/Octa ve

365 Tap

FIR Filter

20 kHz Input

Sam p le Rate20 kHz Output

Sample Rate

Nyquist Rate for Filter is 200 Hz+200Hz = 400 Hz or fs/50

Long Filters, High Sample Rate: Expensive!

-200 -150 -100 -50 0 50 100 150 200-0.2

0

0.2

0.4

0.6

0.8

1

365 Tap Protype Low Pass Filter

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-100

-80

-60

-40

-20

0

Spectrum

Frequency (kHz)

L o g

M a g n

i t u

d e (

d B )

-0.2 -0.1 0 0.1 0.2-0.2

-0.1

0

0.1

0.2Spectrum: Zoom to P ass-Band Ripple

Frequency (kHz) L o g

M a g n

i t u d e

( d B )

Sample Rate: 20.0 kHz

Pass Band: 0.0-to-0.1 kHzStop Band: 0.4-to-10 kHzStop Band Atten: 80 dB


10/49

Filter to Extract Low BandwidthSecondary Signal

Primary Signa l

Second ary SignalLow BW

Primary Signa l

-10,000 10,000100 300-300 -100

0

f

Reduce Sample Rate at Input to Filter:Very Efficient Implementation!

… … …

φ0

φ1

φ2

φ49

φ48

50-to-1

365 Tap s

20 kHz

20 kHz

400 Hz

400 Hz

Polyphase

Low Pa ss Filter

8-taps

8-tap

20 kHz 400 Hz

Coefficient

Bank

Select

Path

Weights


11/49

Down Sample to Reduce Sample RateProportional to Bandwidth Reduction and

Up Sample to Preserve Input Sample Rate.

… … … … … …

φ0 φ0

φ1 φ1

φ2 φ2

φ49 φ49

φ48 φ48

50-to-1 1-to-50

365 Tap s 365 Tap s

20 kHz 20 kHz

20 kHz 20 kHz

400 Hz

400 Hz

Polyphase

Low Pa ss Filte r Polyphase

Low Pass Filte r

8-taps 8-taps

Efficient Polyphase Filter

8-tap 8-tap

20 kHz 20 kHz400 Hz

Coefficient

Bank

Coefficient

BankSelect Selec t

365 TapFIR Filte r

20 kHz Inp ut

Sample Rate20 kHz Output Sa m ple Ra te


12/49

Two Processes in Boxes: How can you

tell which is which from outside box?

365-TapLowpass

Filter

20kHz

20kHz

20kHz

400 Hz20kHz

8-Tap Filter

8-Tap Filter

Coefficient

BankCoefficient

Bank

State Mac hineSelec tSelec t

White Box

White Box

365-ops/input

16-ops/input

(The Wet Finger Test)

Clean-Up Filter BetweenPolyphase Resampling Filters

Coefficient

BankCoefficient

BankSelect Selec t

20 kHz400 Hz 400 Hz

20 kHz

8-tap 16-tap 8-tap

f

-200 200100-100

0

Clean-up

Filter

Filter BankResponse


13/49

Commercial FM Signal Structure

X 2 X 2 Pilot

19-kHz

19-kHz

76-kHz38-kHz

LL+ R

Composite Stereo

L-RR

-

SCA

0 1915 23 100

f(kHz)

Sam ple Rate : 200

Transition BW 4 kHz

Attenuation 60 dB

38 7653

Pilot

Pilot Filter

L+ RL-R SCA SCA

L-R

Stereo FM Receiver

X 2 X 2PilotFilter

19-kHz 76-kHz

38-kHz

2L

Composite Stereo

2R

-SCA

Low

Pass

Low

Pass

Low

Pass

The Difficult One

to Implement


14/49

Extracting Pilot Signal From

Composite Stereo FM Signal

FIR

Filter

140 Tap s

DLY

19 kHz Pilot

38kHz Pilot

019

2315 38 53f

pilot

L+ R L-R L-R

100

=>

Sf atten(dB) 200 60

N = = = 136.6 140df 22 4 22

Polyphase Pilot Extraction

H (Z)H (Z )

Low Pass

Filter

H (Z)H (Z)

H (Z )H (Z)

H (Z )H (Z )

00

11

22

99

. .

. . .

.

. .

. .

. .

x(n)p(n)

y(nM,1) p(nM,1)

e 1010

2π2π

e 1010

j 0k 0

2π2π

e 1010 j 2

2π2π

e10

10 j 92π 2π

200 kHz

Comp osite Stere o

(Real)

200 kHz

Up Sam pled

and Translated

38-kHz Pilot

(comp lex)

200 kHz

Double Frequency

38-kHz Pilot

(Rea l)

2 0 kHz

Aliased toBaseband

Pilot

(Complex)

20 kHz

Aliased to Baseba nd

Filtere d Pilot

(Complex)

20 kHz

Frequency

Doubled Aliased

Baseband Pilot

(Real)

2

2

2

2

2 2

j 1

cos( )

cos( )2

cos( )4

cos(18 )


15/49

Prototype Filter with Multiple StopBands and Don’t-Care Bands

-15 -10 -5 0 5 10 15-0.2

0

0.2

0.4

0.6

0.8

1

Impulse Response, 10-to-1 Downsample Prototyple Low Pass Filter

Time Samples

A m p l i t u d e

-100 -80 -60 -40 -20 0 20 40 60 80 100-80

-60

-40

-20

0

Frequency (kHz)

L o g - M a g

n i t u d e ( d B )

Batman Filter

Input and Output Spectra from

Nyquist Zone 1 in 10 Stage Polyphase Filter

0 5 10 15 20 25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

Input Spectrum: Pilot at 19 kHz

Frequency (kHz)

M a g n i t u d e

Nyquist Zone Centered at 20 kHz

Input Polyphase Filter Frequency Responsein First Nyquist Zone

-10 -8 -6 -4 -2 0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

1st Nyquist Zone Polyphase Output Spectrum: Pilot at -1 kHz

Frequency (kHz)

M a g n i t u d e

Frequency Response of Baseband Clean-up Filter


16/49

Extracted and Processed AliasedPilot Signal

-10 -8 -6 -4 -2 0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

Low-pass Output Spectrum: Pilot at -1 kHz

Frequency (kHz)

M a g n i t u d e

-10 -8 -6 -4 -2 0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

Doubler Output Spectrum: Pilot at -2 kHz

Frequency (kHz)

M a g n i t u d e

Pilot Aliased into Nyquist Zone-2 in 10-Stage Polyphase Up Sampler

0 5 10 15 20 25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

2nd Polyphase Output Spectrum: Pilot at 38 kHz

Frequency (kHz)

M a g n i t u d e

0 5 10 15 20 25 30 35 40 45 50

-1

-0.5

0

0.5

1

Time Series: Pilot and Double Frequency Pilot

Time Samples

A m p l i t u d e


17/49

InterpolatorsAnd Interpolation

Applications Fixed Up-Sampler Interpolators

Fixed Down-Sample Filters

Reduced Cost Filtering When Large Ratio ofSample Rate to Bandwidth

Timing Recovery Re-Sampling of Time Series

Timing Recovery Re-Sampling of Matched

Filter Clock Domain Alignment


18/49

Spectrum of Interpolator andPeriodic Spectrum of

Zero-Packed Shaping Filter

-30 -20 -10 0 10 20 30-80

-60

-40

-20

0

Spectrum of Shaping Filter and 1-to-32 Interpolating Filter

Normalized Frequency

G a i n ( d B )

-8 -6 -4 -2 0 2 4 6 8-80

-60

-40

-20

0

Zoom to Spectrum


G a i n ( d B )

Spectrum of 1-to-32 InterpolatedShaping Filter

-30 -20 -10 0 10 20 30-80

-60

-40

-20

0

Spectrum of Interpolated Shaping Filter


G a i n ( d B )

-8 -6 -4 -2 0 2 4 6 8-80

-60

-40

-20

0

Zoom to Spectrum


G a i n ( d B )


19/49

Polyphase Partition of M-PathResampling Filter

H (Z )

H (Z )

H (Z )

H (Z )

0

1

2

M-1

x(n) y(m)

N/M= 4

. . . .

. . . .

Efficient Hardware Implementationof 1-to-M Polyphase Interpolator

N/M= 4

H (Z )r

. .

. .

. .

x(n) y(m )

h(0+ nM)

h(1+ nM)

h(2+ nM)

h(M-1+ nM)


20/49

Interpolation Options

Initial Sa m ple G rid,Unit distanc e

Between Sam ples

Sam e Rate Samp le Grid,

Unit Distanc e Between Sam ples

Highe r Rate Sam ple Grid, Less Tha n Unit Distanc e Between Sam ples

Lowe r Rate Sam ple Grid,More Than Unit Distanc e Between Sam ples

Interpolated Sample PositionsInitial Sa mple Positions

M-Path, 1-to-M/Q Interpolator

H (Z )

H (Z )

H (Z )

H (Z )

0

1

2

M-1

x(n)y(m )

N/M= 4

. . . .

. . . . Q:1

Q:11:Mx(n) y(m)

H(Z)

Polyphase Filter


21/49

5/3, Rational Ratio Re-Sampling

3-to-1

phs(0)

phs(1)

phs(2)

phs(3)

phs(4)

x(n)

y (m)= x(n+ k/5)5

y(m)= x(n+ 3k/5)

n n+ 1 n+ 2 n+ 3

0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4

x x x x xx x x xx x x x

In Out

n 0,3n+ 1 1,4n+ 2 2

K(m+1)=[k(m)+3] modulo(5)

Rational Ratio Interpolation.Example; up 8, down 3

n+ 1

m+ 1 m+ 3

m+ 6

n+ 2

m+ 2 m+ 4

m+ 7

m+ 5

m+ 8

n+ 3

n

m

Input Samp les and ava ilable

1-to-8 Interpolated Sam ples

3-to-8 Interpolated Sa m ples (up 8, down 3)


22/49

Interpolation To Time Position BetweenAvailable Interpolation Points

(Arbitrary Ratio Interpolation)

n n+ 1

Desired Sample

Position n+ k/M+ Δ

Desired Sample Value

Availab le Sample Value

Nearest Available Sample Position n+ k/M

InputSample

Error

Zero Order Hold Model ofNearest (Left) Neighbor Interpolation

n n+ 1

Desired Sample Position n+ k/M+ Δ

Error

Interpolated Sample Values

Zero-Order-Hold

Analog Levels

Δ


23/49

Spectrum of Up-Sampled Signal atInput and Output of Virtual DAC

BW= 1

BW= 1

0

0

N

N

f

f

2N

2N

Output Sam ple Rate

Output Sam ple Rate

DAC Response

Frequency Response of DACat First Spectral Null

NN-0.5 N+0.5

f

DAC ResponseH( f )= -Δ Δf 1N

1 1 1 1 | ( ) | : | ( ) | : 2

2 2 2

( 1) 7 2 , 8( ), 2 128

When signal is already 4-times oversampled

Need 32 stage up-sampler to suppress spectral artifact

s

to -

b H f f H

N N N

b N Say b bits N

−Δ = Δ = <

−> = > =

48 dB


24/49

Shaping Filter: Time and FrequencyResponse, Four Times Over Sampled

-5 0 5 10 15 20 25 30 35 40 45 50-0.1

0

0.1

0.2

0.3time response of shaping filter

time

a m p l i t u d e

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-60

-40

-20

0

spectral response of shaping filter

frequency

l o g m a g

n i t u d e

Time and Frequency Response of32/6.4 Left Neighbor Interpolator

0 50 100 150 200 250

-0.01

0

0.01

0.02

0.03

0.04

0.05

-10 -8 -6 -4 -2 0 2 4 6 8 10-80

-60

-40

-20

0


25/49

Time and Frequency Response of 32/6.37Left Neighbor Interpolator

0 50 100 150 200 250

-0.01

0

0.01

0.02

0.03

0.04

0.05

-10 -8 -6 -4 -2 0 2 4 6 8 10-80

-60

-40

-20

0

Prototype Interpolator Length for 8-bit data, initially Over Sampled by 2.

f

f

0

0

2

2

-2

-2

-0.5

-0.5

0.5

0.5

1.5

1.5

-1.5

-1.5

-4

-4

4

4

Δf= 1

Δf= 1

DCDCDC DC

To Obtain 128 Over Sample, M=64, N=(128/1)(66/22)=384N/M=6: Need 64 6-tap filters in Polyphase Interpolator


26/49

Prototype Interpolator Length for 8-

bit data, initially Over Sampled by 4.

f

f

0 8-8

-8

-0.5 0.5 3.5

3.5

-1.5

-3.5

-4

-4

4

4 8

Δf= 3

Δf= 3

DCDC

DCDC

0-0.5 0.5

To Obtain 128 Over Sample, M=32, N=(128/3)(66/22)=128N/M=4: Need 32 4-tap filters in Polyphase Interpolator

Address Control:Modulo Accumulator

. . .

Mod(M) Int(--)Z-1

d-acc

acc(m)

-

k(m)

δ(m)

Filter x(n) y(m)

Polyph ase

Weights

n n+ 1 n+ 2

Input

Sam ples

Output

Sam ples

0 1 2 3 4 5 6 9 8 9 0 1 2 3 4 5 6 9 0 1 2........ ....

TINTOUT

Input Time index ”n”Polyphase inde x ”k”

= =Fractional Offset: d-acc

- Out In

In Out

T f d acc M M

T f

On Overflow,Insert New Input

Fractional Part(For later use)


27/49

Two Neighbor,Linear Slope Interpolator

n

n+ 1

Desired Samp le

Position k+ Δ

DesiredSampleValue

InterpolatedSamp le Value

Left Available InterpolationSample Position

Left Available InterpolatedSamp le Value

Right Available InterpolationSamp le Position

Right Available InterpolatedSample Value

InputSample value

InputSam ple value

Linear Interpolator

n+ k/Mn+ (k+ 1)/M

Δ

Equivalent Interpolating Kernel

k-1 k+ 2Δ

TRI(k)TRI(k+ 1)

k k+ 1

x(k)

x(k+ )Δ

x(k)

x(k+ 1)

x(k+ 1)

M M M M


28/49

Spectrum of Up-Sampled Signal at

Input and Output of Virtual LinearInterpolator

BW= 1

BW= 1

0

0

N

N

f

f

2N

2N

Output Sample Rate

Output Samp le Rate

Triangle Spec tral

Response

RepeatedSpectral Zeros

Frequency Response at FirstSpectral Null of Linear Interpolator

NN-0.5 N+ 0.5

f

Triangle

Response

H( f)=Δ Δf 1N

[ ]2

2 2 211 1 1 / 2 | ( ) | : | ( ) | : 2 : 2

2 2 2( / 2 1) 7

2 , 16( ), 2 128

When signal is already 4-times ov

1

2

b b H f f H

N N N

b N Say b bits N

N

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ − −Δ = Δ = < = > =

ersampled

Need 32 stage up-sampler to suppress spectral artifacts by -96 dB


29/49

Estimate y(n+k/M) & y(n+k/M)

With 3 Arms of Polyphase Filter

PHS-(k-2)

PHS-(k)

PHS-(k-1)

PHS-(k+ 1)

PHS-(k+ 2)

y(n+ k/M)

y(n)

- y(n+ k/M) .

.

Estimate y(n+k/M) & y(n+k/M)With 2 Polyphase Filters

PolyphaseDerivativeMatched

Filter

Polyphase

Matched

Filter

y(n+ k/M)

y(n)

y(n+ k/M) .

.

.

.

.

.

.

.

.

k

k

.


30/49

y(n+k/M) & y(n+k/M) With 2Efficient Polyphase Filters

1-Stage Filter

1-Stage Filter

y(n+ k/M)

y(n+ k/M)y(n)

.

PolyphaseMatched Filter Coefficients

Polyphase DerivativeMatched Filter

Coefficients

CoefficientSelec tion

.

Interpolation with Polyphase Low-pass

Filter and Polyphase Derivative Filterfor Local Slope Correction

Mod(M) Int(--)Z-1

d-acc

acc(m)

-

k(m)

k(m)

δ(m)

δ

Filter

Filter

x(n)x(n)

x(n)

y(n+ k/M)y(n+ k/M+ /M) =δ

y(n+ k/M)+ y(n+k/M)δ

y(n+ k/M)

h (n)k

dh (n)k

.

.

Derivative Polyphase Filter

dh=conv(h,[1 0 -1]*M/2

dh=dh(2:length(dh)-1);


31/49

Input Shaping Filter at4-Samples per Symbol

Spectra of 64/10.49 Interpolated Signal

0 200 400 600 800 1000 1200

-0.2

0

0.2

0.4

0.6

0.8

1

Interpolated Shaping Filter

-20 -15 -10 -5 0 5 10 15 20-120

-100

-80

-60

-40

-20

0

Frequency Response

Normalized Frequency (f/f sym

)

L o g m a g n

i t u

d e

( d B

)


32/49

Signal Conditioning and Processing

Spectral Centers 1.7 MHz SeparationChannel BW: 1.7 MHzChannels Span ≈ 30 MHz (≈ 17 Channels)

24-Channel Channelizer: 24*1.7=40.8MHz12-to-1 Down Sample in ChannelizerOutput Sample Rate; 3.4 MHz/Channel

160 MHz

ADC Half Band Filter

Half Band Filter

Interpolate Filter

DDSDDS

PhaseAccumulator

160MHz

81.6MHz

40.8MHz

40.8MHz

163.2 MHz

3.4MHz

3.4MHz

3.4MHz

22 22

2

2

24-PathPolyphase Filter

24-PNT FFT

Interp Bank

. . .

1 6 C h a n n e l s

C i r c u

l a r B u

f f e r

12-to-1

Wide Dynamic Range Resampler


33/49

Spectra from 24-channel Channelizerat 3.4 MHz Sample Rate

-1.5 -1 -0.5 0 0.5 1 1.5

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1. 5 - 1 - 0.5 0 0. 5 1 1.5

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1.5 -1 -0. 5 0 0.5 1 1. 5

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1.5 -1 -0.5 0 0.5 1 1.5

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1.5 -1 -0.5 0 0.5 1 1. 5-150

-100

-50

0

-1 0 1-150

-100

-50

0

-1 0 1-150

-100

-50

0

-1 0 1-150

-100

-50

0

-1.5 -1 -0. 5 0 0.5 1 1. 5

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

-1 0 1

-150

-100

-50

0

Time Series from 24-channelChannelizer at 3.4 MHz Sample Rate

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2

0 50 100 150 200-2

0

2


34/49

Equipment Bay: 192-Stereo FM Modulators

Conversation with Client! How big a room will we need to house the DSP

version of this Transceiver?

Answer: I think it will fit on one chip.

Response: Don’t be Absurd, You Can’t Pack aRoom into a Single Chip!

Results: 48-Analog Devices Blackfin Processorsto Demodulate 192 MP3 Stereo Channels.

1 Virtex V-4 for 192 Digital Stereo FMModulators and 256 Channel Channelizer @ 293kHz Bandwidth per channel. (60% of Chip)


35/49

Prototype Analog Stereo FM Modulator

dbxEncode

d bxEncode

50- secPre-emph

μ

75- secPre-emp h

μ

50- secPre-emph

μ

LPF14 kHz

LPF14 kHz

LPF7.5 kHz

BPF15-50 kHz

BPF60-90 kHz

VCO32 kHz

VCO80 kHz

−100 . .

−40 . .

3.2 MHz

3.2 MHz

Left

Right

SCA

L+ R

L - R IFOutput

DSP Based Stereo FM Modulator

db x

Encod er

db xEncod er

LPF

14-kHz

LPF14-kHz

LPF

14-kHz

BPF

35-kHz

BPF30-kHz

DDSFM-MOD

&

Up-Converter

DDS FM-MOD &

Up-Converter

50-usec

Pre-emph

50-usecPre-emph

75-usec

Pre-emph

48-to-293

Arbitrary

Re-Sam ple

48-to-293

Arb itraryRe-Sam ple

48-to-293

Arb itrary

Re-Sam ple

Gain

Gain

Gain

Gain

IIR

IIR

K ACC

K ACC

IIR IIR

IIR

IIRIIR

IIRSCA

Left

Right

(L+ R)

(L-R)

32 kHz

32 kHz

CORDIC

CORDIC

Satellite Cloc k Dom ain Transceiver Cloc k Doma in


36/49

256 Channel Channelizer for 50-MHz

Digital IF Sampled at 225.024 MHz

Radix-2 Butterfly of two 128-Point FFT’s

2 5 6 C h a n n e

l s 1 : 2

U p

_ S a m p

l e r

2 5 6 C h a n n e

l s A d d e r

OddSamp les

EvenSamples

1 2 8 P o i n t F F T

1 2 8 P o i n t F F T

1 2 8 P a t h P o

l y p

h a s e

F i l t e r

1 1 - T a p s

P e r

P a

t h

1 2 8

P a t h P o

l y p

h a s e

F i l t e r

1 1 - T a p s

P e r

P a

t h

H a l f

B a n

d P h a s e

S h i f t

1-to-3Up-Samp le

DDS

Quantize DAC

50 MHz

225.024 Mhz

225.024 Mhz

75.008 Mhz


37/49


38/49

New Directionsin

Channelized Receivers


39/49

M-Channel Channelizer

Resampled M-Path Narrowband Filter

with Rotators Replaced by M-Point IFFT

Armstrong to Tuned RF with AliasDown Conversion to Polyphase Receiver

DigitalBand-Pass

M-to-1

H(Ze )-jθ k

DigitalLow-Pass

M-to-1

H(Z)

e-j θkn

Rather than selecting center frequency at input and reducesample rate at output, we reverse the order, reduce samplerate at input and select center frequency at output. Weperform arithmetic operations at low output raterather than at high input rate!

M-Path Digital

Polyphase

M-to-1

H(Z)r

e-j 2π

Mrk


40/49

Channelizer Parameters

Center frequencies, hence channel spacing, andthe number of paths in filter partitiondefined by length M of IFFT.

Channel bandwidth and spectral characteristics,in-band ripple, out-of band attenuation,and transition BW defined by prototypelow-pass filter in polyphase partition.

Channelizer output sample rate determined byinput commutator span of P inputs per M-point IFFT output.

Three Parameters are independent and adjustable.

Two Channelizer BW Options

f

f

Crossover

BW

Channel BWTransition BW

Transition BW

Channel Spa c ing

Channel Spa c ing

Channelizer for High Quality Spectrum Analyzer

Channelizer for High Quality FDM Receiver


41/49

Overlapped Channel BW and

Output Sample Rate Options

The Winner!

Fast Channelizer:

Time Series and Spectrum From Same Channelizer

Fast Channelizer:

Spectrum and Time Series from same Channelizer

Variable Bandwidth Filter:

Fast Convolution, Efficient, Low Workload

Multiple Bandwidth Channelizer

Arbitrary Channel Spacing Channelizer

Interesting

Variations

of

Channelizer


42/49

Block Diagram of Parallel Processor SpectralSniffer Steered Digital Drop Receiver

720

Path

8192Path

16-Sets:

Channel

Pha se Rotator

Vectors

8192

Point

IFFT

Poly-

Pha se

Filter

32,768

Point

4-FoldFolded

Window

720 Cha nnel Channelizer

8192 Bin Spec trum Analyzer

Ensemble

Average| |

Log 10

2.

Spectral

Mask &

Channel

Selec t

Channel

Processing

andMultiplexing

f S=90 MHz

f BW=11 kHz

f S =11 kHz

f BW =125 kHz

f S =500

kHz


43/49

16 Digital Drop Receivers, Brute Force

16-Copies of

Same Filter

Low Pass

Low Pass

Low Pass

DDS

DDS

DDS

fs=9 0 MHz

fs= 500 kHz

f = 12 5 kHzBW

f = 125 kHzBW

f = 12 5 kHzBW

fs= 500 kHz

fs= 500 kHz

2

2

2

2

2

2

2

2

2

2

2

2

180:1

180:1

180:1

fc

fc

fc

1440 Tap

1440 Tap

1440 Tap

. . . . . . . . . .

. . . . . . . . . .

1

2

16

Resample in Single Polyphase Filter, useRotators to Extract 16 Specific Aliases

0

179

180

359

360

539

540

719

Sample Data

Buffer

720-path Polypha se

Coefficients

Rotators

Rotators

Rotators

Rotators

720Complex

720

2

720

2 720

2

2

720

. . . . . .

1

2

3

16

fs= 90 MHz

180-to-1

1 4 4 0 T a p s 16-Sets of

Complex Rotators

720 Mult & Addper Output

1 PolyphaseFilter

Down

Samples

And Services

all Channels

46,080 Multiplies

At 500 kHz Rate


44/49

Replace 16-Sets of Rotators withSingle 720 Point IFFT

0

179

180

359

360

539

540

719

Sample Data Buffe r

720-path PolyphaseCoe ffic ients

720PointIFFT

720

2

720

2 720

2

2720

. . . . . .

1

2

3

720

fs= 90 MHz

180-to-1

1 4 4 0 T a p s

A 720 point IFFT,

Prime Factors: 5,8,9

Implemented with

Winograd Transform

Workload is

2,400 Multiplies.

5.2% of workload to

compute 16 Outputs

Three Options for Digital Drop Receiver

720

Path720

Point

IFFT Poly-

Phase

Filter

720 Channel Channelizer

720Path

16-Sets:Channel Phase Rota tor Vec tors

Poly-Phase Filte r

16 Cha nnel Channe lizer

Low Pass

DDS

2 22

fc

1440 Tap

16 Cha nnel Channelizer

16 Sets

5,300 Multiplies at

500 kHz Rate

49,000 Multiplies at

500 kHz Rate

58,000 Multiplies at

500 kHz Rate


45/49

Spectrum Analyzer:Polyphase Partition of Overlapped Window

H ( Z )0

H ( Z )1

H ( Z )2

H ( Z )M-2

H ( Z )M-1

. . . .

. . . .

x(n)

y(nM,0)

y(nM,k)

y(nM,1)

y(nM,2)

y(nM,M-1)

y(nM,M-2)

M-Point

IFFT

8,192 Point IFFT

160,000 Multiplies

Per Transform

At 11-KHz Rate

32,768 Point Window65,000 MultipliesPer Transform At 11-KHz Rate

Window and IFFT193,000 MultipliesPer Transform At 11-KHz Rate

We have accounted for the Two Major Blocks:Spectrum Analyzer and Channelizer!

720

Path

8192

Path

16-Sets:

Channel

Pha se Rotator

Vec tors

8192

Point

IFFT

Poly-

Pha se

Filter

32,768

Point

4-FoldFolded

Window


8192 Bin Spec trum Analyzer

Ensemble

Average| |

Log 10

2.

Spectral

Mask &

Channel Selec t

Channel

Processing

andMultiplexing

f S=90 MHz

f BW=11 kHz

f S =11 kHz

f BW =125 kHz

f S =500 kHz


46/49

Block Diagram of Cascade Channelizer andSpectrum Analyzers

720

Path720

Point

IFFT Poly-

Phase

Filter


180 45-Bin

Spectrum Analyzers

Ensemble

Average| |

Log 10

2.

Spectral

Mask &

Channel Selec t

Channel

Processing

andMultiplexing

Window

Window

Window

Window

IFFT

IFFT

IFFT

IFFT

M-to-2 Down-SampledM-path Polyphase Channelizer0 0

1 1

2 2

3

M/2-1

M-1

M/2

M/2+ 1

M-2M-1

M MM

. . . .

. . . . . . . .

… .

M - P

a t h P o l y p h a s e F i l t e r

M - P

o i n t I F F T

FDM

TDM

M - P

a t h I n p u

t D a t a B u

f f e r

C i r c u

l a r O u

t p u

t B u

f f e r

State Eng ine


47/49

Spectrum and Zoom Detail of Input Test Signal

Course Spectrum and Zoom Detail: Power Output from180 Channelizer Filters


48/49

Time Series from 60 Channels of 180 Path InputChannelizer Simulation

Spectrum from 60 Channels of 180 Path Input Channelizer Simulation


49/49

Power Spectra from Selected Channels

Closing Comments(on this Topic)

Full Channelizers are SurprisinglyEfficient and Inexpensive

Don’t Waste Bandwidth Reduction andSample Rate Reduction Offered byChannelizer

Perform Spectrum Analysis at Output of

Channelizer Rather than at Input Noise Figure Improvement due to

Spectrum Analysis of Decoupled Channels

Documents

Session A3 Part 2 Multirate DSP Wireless 2011