Download presentation

Published byJuan Fletcher Modified over 4 years ago

1
**Polyphase FIR Filter Implementation for Communication Systems**

DSP C5000 Chapter 20 Polyphase FIR Filter Implementation for Communication Systems

2
**Multirate Processing 1 of 2**

Multirate processing arises in many fields of digital signal processing: Digital audio: sampling frequency conversion (32 kHz, 44.1kHz, 48kHz), sharp cut-off of FIR filter, … Signal processing for digital communications: symbol rate processing, bit rate processing, sample rate processing, … Speech processing: 3G speech codec (Adaptive Multi Rate), fractionnal pitch estimation, ... … 3G = Third generation of cellular mobile communications.

3
**Multirate Processing 2 of 2**

Involves two actions on the digital signal: Downsampling: resampling downwards the digital signal in the digital domain. Upsampling: resampling upwards the digital signal in the digital domain. M Fe Fe/M Retain one sample over M and discard the M-1 others, every M samples. L Fe LFe Downsampling decreases the sampling rate by discarding samples (decimation). Upsampling adds extra samples (interpolation). Insert L-1 zeros between each sample

4
Downsampling 1 of 2 M x(n) y(m) Folding term

5
**Downsampling 2 of 2 Anti-aliasing Filter Noble identity for decimation**

x(n) y(m) H(z) Fe Fe/M fc : (Fe/M)/2 The anti-aliasing filter removes frequences above the Nyquist frequency for the new sampling rate. M H(zM) M H(z)

6
Upsampling 1 of 2 x(m) y(n) L

7
**Upsampling 2 of 2 Interpolating Filter Noble identity for upsampling L**

x(m) y(n) H(z) LFe Fe fC : (Fe/L)/2 The interpolating filter smoothes out the values that were filled with zeroes. Interpolating filter with unity gain have an Equivalent noise bandwidth of 1/L so it cancels 1/Lth of the signal energy. Thus it needs to have a gain of L to preserve the signal magnitude after interpolation. H(zL) L H(z) L

8
**Polyphase Implementation of FIR Filters Decimation Case 1 of 4**

H(z) M E(zM) Let n=lM+k with

9
**Polyphase Implementation of FIR Filters Decimation Case 2 of 4**

Time Processing load (MAC/s) MTe N M H(z) M E0(zM) E1(zM) EM-1(zM) z-1 Fe Fe/M M-1 filter evaluation over M are discarded. N filter length

10
**Polyphase Implementation of FIR Filters Decimation Case 3 of 4**

Using noble identity M E0(z) E1(z) EM-1(z) z-1 Fe Fe/M Time Processing load (MAC/s) MTe N No more useless computations, but one sampling period over M, CPU is burdned with N MAC/s.

11
**Polyphase Implementation of FIR Filters Decimation Case 4 of 4**

Equivalent commutator model E0(z) Processing load (MAC/s) E1(z) N/M EM-1(z) MTe Time Fe Fe/M Commutator runs at Fe,. At each input sample only one component is computed and accu- mulated with the result of the previous one. The result is output when the last component is reached and accumulator is reset. This spreads the processing load over MTe.

12
**Polyphase Implementation of FIR Filters Interpolation Case 1 of 5**

H(z) R(zL) L Let n=mL+L-1-k with

13
**Polyphase Implementation of FIR Filters Interpolation Case 2 of 5**

H(z) Processing load (MAC/s) N R0(zL) R1(zL) RM-1(zL) z-1 L Te/L Time L-1 multiplications by 0 over L For each filter evaluation. N filter length. Fe LFe

14
**Polyphase Implementation of FIR Filters Interpolation Case 3 of 5**

Using noble identity R0(z) R1(z) RM-1(z) L At each output sampling instant, only one component is non zero z-1 L L Fe LFe

15
**Polyphase Implementation of FIR Filters Interpolation Case 4 of 5**

Equivalent commutator model R0(z) R1(z) RM-1(z) Processing load (MAC/s) N/L Te/L Time Fe LFe For each output sampling instant one polyphase component is computed. When we reach again the first component (M-1) a new input sample is inputed in the delay line of each polyphase component.

16
**Polyphase Implementation of FIR Filters Interpolation Case 5 of 5**

Linear Periodically Varying Time system z-1 z-1 hL-1 h2L-1 h3L-1 z-1 h0 h1 hL-1 hL hL+1 h2L-1 h2L+1 h3L-1 h2L z-1 z-1 h1 hL+1 h2L+1 h0 z-1 hL h2L

17
**Case Study Shaping filters for a QPSK modem :**

Emitter: interpolation case. Receiver: decimation case Efficient Algorithm Implementation : Good ordering of computations, Efficient memory organization and management.

18
**Emitter 1 of 4 QPSK modulator Fb Fs Fe fk**

s(t)=1/2[cos(2pfot).cos(f(Ak,Bk))-sin(2pfot).sin(f(Ak,Bk))] QPSK modulator Cos() RCF DAC Ak fk fk: Phase computation bits Bk Sin() RCF DAC Fb Fs Fe RCF: raised cosine filter DAC: digital to analog converter Bit frequency Symbol frequency Sample frequency

19
**Emitter 2 of 4 Let Fe=16Fs (16 sample / symbol)**

Define a raised cosine filter with: 6 symbols length. Roll_off : 0.5 Matlab command h=RCOSFIR(0.5,3,16,1); Equivalent system 16 H(z) In red: ideal interpolating filter In blue: actual RC filter

20
**Emitter 3 of 4 The 16 Polyphase filters are defined by :**

Filter length is 97, impulse response is padded with 0 to reach 112=7*16 With N=112 and L=16

21
**Emitter 4 of 4 Shuffle coefficients Coefficients Symbols 1st sample**

R=flipud(reshape(h,8,12)); R=round(R*2^15); fid=fopen('coef.inc','wt'); for p=1:8 fprintf(fid,'\t.word\t%d\n,R(p,:)) end fclose(fid); 2nd sample 15th sample When coefficient pointer reaches this address a new symbol will be input at the next output sample period

22
**Emitter (C callable) .sect "coefs2"**

Ncomp .set 16 ;number of polyphase component coefs2 .include "coefpoly2.inc" coefsfin: coefsize .set coefsfin-coefs2 Lfil .set coefsize/Ncomp ;polyphase component length filbufQ .usect "filtre2",Lfil ;data buffer .text _firinit: ST #coefs2,*(adbufQ) ;pointer to current coefs pointer STM #filbufQ,AR2 ;zeroed initial buffer condition RPT #Lfil-1 STL A,*AR2+ RET

23
**_firTxQ:… ;context save**

LD #var,DP STM #coefsize,BK MVDM adbufQ,AR2 ;current coefs pointer STM #1,AR0 STM #filbufQ,AR3 ;symbol buffer STL A,*AR3 ;new sample (guess hold during 16 samples) RPTZ A,#Lfil-1 ;compute one polyphase component MAC *AR2+0%,*AR3+,A MVMD AR2,adbufQ ;save new current coefs pointer SFTA A,-16 SFTA A,-1 ;output of RCF can be greater than 1 ! ;test if delay symbols is needed BC endTxQ,NTC ;jump if not necessary MAR *+AR3(-2) RPT #Lfil-2 DELAY *AR3- endTxQ: … ;context restore RET

24
**Symbol vs Sample Output**

Symbol output Sample output Fe: 16 khz Fs: 1 khz Df : p/4 constant for each symbol f= Fs/8=125 Hz

25
**Receiver 1 of 2 Fe Fb Fs Bit processing Symbol processing ADC RCF ADC**

26
**Receiver 2 of 2 Receiver structure is quite similar, except that:**

Each polyphase component has its own delay tap Each polyphase output has to be accumulated for M polyphase computations and accumulator is outputed every M input sample and reset. E0(z) E1(z) EM-1(z)

27
**Follow on Activities Laboratory 10 for the TMS320C5416 DSK**

Illustrates the effects of decimation and anti-aliasing filters. Laboratory 11 for the TMS320C5416 DSK Illustrates the effects of interpolation and anti-imaging filters. Application 9 for the TMS320C5416 DSK Uses interpolation and decimation to produce sharper cut-offs FIRs than would be obtained otherwise.

28
Reference Digital Signal Processing a Practical Approach by Emmanuel C. Ifeachor and Barrie W. Jervis. Chapter 9. Multirate digital signal processing.

Similar presentations

Presentation is loading. Please wait....

OK

Chapter 14 Finite Impulse Response (FIR) Filters

Chapter 14 Finite Impulse Response (FIR) Filters

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on different types of computer softwares and hardwares Ppt on coalition government definition Ppt on email etiquettes presentation folder Ppt on famous indian entrepreneurs in the us Ppt on marie curie timeline Ppt on edge detection in image processing Ppt on entisols Ppt on sociology of education Ppt on biodegradable and non biodegradable pictures Ppt on accounting standards 1