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Filter Design TMS320C54x
Mandy Tsai
Field Application Engineer Customer Application Center Texas Instruments Taiwan Limited
SPRA079 1996
IMPORTANT NOTICE Texas Instruments (TI) reserves right make changes products discontinue semiconductor product service without notice, advises customers obtain latest version relevant information verify, before placing orders, that information being relied current. warrants performance semiconductor products related software specifications applicable time sale accordance with TI's standard warranty. Testing other quality control techniques utilized extent deems necessary support this warranty. Specific testing parameters each device necessarily performed, except those mandated government requirements. Certain applications using semiconductor products involve potential risks death, personal injury, severe property environmental damage ("Critical Applications"). SEMICONDUCTOR PRODUCTS DESIGNED, INTENDED, AUTHORIZED, WARRANTED SUITABLE LIFE-SUPPORT APPLICATIONS, DEVICES SYSTEMS OTHER CRITICAL APPLICATIONS. Inclusion products such applications understood fully risk customer. products such applications requires written approval appropriate officer. Questions concerning potential risk applications should directed through local sales office. order minimize risks associated with customer's applications, adequate design operating safeguards should provided customer minimize inherent procedural hazards. assumes liability applications assistance, customer product design, software performance, infringement patents services described herein. does warrant represent that license, either express implied, granted under patent right, copyright, mask work right, other intellectual property right covering relating combination, machine, process which such semiconductor products services might used.
Copyright 1996, Texas Instruments Incorporated
Contents
Title Page ABSTRACT FILTER DESIGN Efficient Filter Design 'C54x CODE EXPERIMENT Filter Specifications Experiment Results SUMMARY APPENDIX FILTER PROGRAM 'C54x CODE APPENDIX EFFICIENT FILTER PROGRAM 'C54x CODE
List Illustrations
Figure Title Page Direct Form Second-Order Filter Filter Poles Zeros Interchange Canonical Structure Second-Order Filter Canonical Direct Form High-Order Filter Power Integer Conversion
ABSTRACT
Digital filter design plays important role digital signal processor (DSP) field. methods designing digital filter infinite-impulse response (IIR) finite-impulse response (FIR). filter satisfies same specifications filter, filter usually faster requires less memory. filters easy implement with fixed-point DSP. feedback path filter causes calculation overflow. Scaling input data corrects this overflow problem. scaling results small output signal. recover output signal level, last stage hardware design uses operational amplifier boost output signal level. This application report shows eliminate operational amplifier input calculation combining cascaded second-order filters.
FILTER DESIGN
high-order filter design simplifies several second-order filters. equation high-order filter H(z)
H1(z)
4(z)
n(z)
where order filter. Dividing equation several second-order filters gives: k(z)
ba1k zz*1 ab2kzz*1
where k(z) second-order filter Figure shows structure second-order filter. filter provides separate delay buffers input output sequences. This filter structure Direct Form output from filter y(n)
a11y(n a12y(n x(n) b11x(n b12x(n
m(n) x(n)
y(n)
Figure Direct Form Second-Order Filter
second-order filter cascaded sections: zeros poles. Since filters linear systems, sections interchangeable. sections generate same output either order (see Figure Since output delays Figure identical, delays eliminated from filter structure. structure Figure equivalent that Figure while using fewer delay elements define system. This filter structure Direct Form known canonical structure.
d(n) x(n)
y(n)
Figure Filter Poles Zeros Interchange
d(n) x(n)
y(n)
Figure Canonical Structure Second-Order Filter concept eliminating hardware (the delay buffers) from design easy understand, does this translate software? digital filter uses fixed-point DSP, either `C5x `C54x. Data overflow problem limitations 32-bit architecture. feedback path poles filter cause overflow. filter gain (from pole section) increases generates output data overflow. This data value does within bits CPU. prevent overflow problem, input data value scaled down before entering filter system. filter application input data value very small, resulting output without overflow. scaling input causes small output value. programmer follows canonical structure Figure design code, problems emerge: programmer wastes time adjusting input values avoid output overflow system requires additional hardware, operational amplifier, recover level output signal. modified Direct Form structure solves these problems. Figure shows canonical structure Direct Form
Zeros x(n)
Poles
Zeros
Poles
Zeros
Poles
y(n)
Zeros x(n)
Poles
Zeros
Poles
Zeros
Poles
y(n)
Figure Canonical Direct Form High-Order Filter
Efficient Filter Design
filter using Direct Form (see Figure calculates zeros forward path, then poles feedback path. intermittent result m(n) small value zeroes calculation. pole calculation, d(n) Figure provides value larger than m(n). output data, y(n) assumes proper level passing interim value through pole feedback path. This method filter design eliminates overflow concerns. Figure shows high-order filter number cascaded second-order filters. Each second-order uses Direct Form number delay buffers reduced combining poles (a11, a12) second-order filter with zeros (b21, b22) next filter section. This reduction produces canonical direct form. software cascaded sections uses repeat block instruction. overhead software comes from calculations first zero section (b11,b12) last pole portion (an1,an2). output data, y(n), normal level, thus this form eliminates operational amplifier original filter.
`C54x CODE EXPERIMENT
software programs appendixes this report. program Appendix represents original filter; Appendix represents efficient filter design. Both programs `C54x code.
Filter Specifications
low-pass filter meets following frequency standards: cut-off frequency pass band cut-off frequency stop band Figure shows power level input signal converts integers ranging from -16000 16000.
-2.5 Signal Power 32767 16384 -16384 -32768 Integers
Figure Power Integer Conversion
Experiment Results
Table compares filters high-order filter. modified filter achieves same system functionality high-order with second-order design. original filter output signal reduces input signal 100. This results addition operational amplifier hardware system. modified eliminates amp. modified needs scale input signal, extent required original filter design.
Filter Modified Elliptic Symmetric Kaiser Algorithm Elliptic Kaiser Order Filter Input Scaling Output Level 9-Bit Left Shift (1/512) 5-Bit Left Shift (1/32) -16000 16000 (normal) None None -1000 1000 (small) -16000 16000 (normal) -16000 16000 (normal) Program Size (words) Data Size (words) Cycles/Output
Table Comparison Filters
SUMMARY
filter design using modified structure, canonical Direct Form improves upon original filter design ways: scaling input signal eliminates overflow longer necessary, operational amplifier eliminated. modified filter requires scaling input signal provide proper output signal without additional hardware. This input scaling great original filter.
APPENDIX FILTER PROGRAM `C54X CODE
Original pass filter design Language C54x Filter type Elliptic Filter Filter order order (cascade: order order) freq. pass band freq. stop band Designer Mandy Tsai Date Feb,20,1996 second order -----> ------> d(n) ---- -----.
d(n-1)
d(n-2)
.mmregs .def .set .bss .bss .bss .data table .word .word .word .word .word .word .word .word .word
begin, d,3*2 number cascade order section ;delay buffer order ;input buffer ;output buffer
second-order section
-26778 29529 19381 -23184 19381
;A1/2
second-order section
-30497 31131 11363 -20735
;A1/2
.word .sect begin .text SSSSSBX SSBX
11363 "vectors" begin
;define reset vector
;the start program #1111111110100000b,PMST #0010001100000000b,ST1 #0,SWWSR FRCT ;initial PMST ;initial ;zero wait state ;OVM=1 ;FRCT=1 output multiply will left shift automatically
SSBX SSSRPT SINLOOP: SS
#X,AR1 #Y,AR2 #d,AR3 A,#5 A,*AR3+ #2,AR0
;SXM=1
;AR3:d(n),d(n-1),d(n-2) ;initial d(n),d(n-1),d(n-2)=0
;initial constant offset addressing
#d+5,AR3 #table,AR4
;AR3:d(n),d(n-1),d(n-2) ;AR4:coeff filter A2,A1,B2,B1,B0 ;Read data from port save data array. ;the connection between file ;port defined siminit.cmd
PORTR 100H, *AR1
SRPT LOOP:
*AR1,7,A #N-1,BRC ELOOP-1
;scaling input ;calculating sections order
Feedback path Forward path *AR4+,*AR3-,A *AR4+,*AR3,A ;d(n-2)*B2 ;d(n-2)*B2+d(n-1)*B1 ;d(n-2)=d(n-1) ;d(n-2)*B2+d(n-1)*B1+d(n)*B0 ;d(n-1)=d(n) *AR4+,*AR3-,A *AR4,*AR3,A *AR4+,*AR3-,A A,*AR3+0 ;d(n) input+d(n-2)*A2+d(n-1)*A1 ;input+d(n-2)*A2 ;input+d(n-2)*A2+d(n-1)*A1
DELAY *AR3- DELAY ELOOP: PORTW A,*AR2 *AR2, 200h INLOOP *AR4+,*AR3,A *AR3-
;write result file ;calculating next output
APPENDIX EFFICIENT FILTER PROGRAM `C54X CODE
pass filter design Language C54x Filter type Elliptic Filter Filter order order (cascade: order order order) canonical direct from
freq. pass band freq. stop band Designer Mandy Tsai Date Feb,20,1996 .mmregs .def .set Q_FACT .bss .bss .bss .data *Q31 format table .word .word .word .word .word .word .word .word .word .word .sect begin .text SSS
begin, .set d,3*2 32768 length filter
SECOND-ORDER SECTION
19381 -23184 19381 -26778 29529
;A1/2
SECOND-ORDER SECTION
11363 -20735 11363 -30497 31131 "vectors" begin
;A1/2 ;define reset vector
;the start program #1111111110100000b,PMST #0010001100000000b,ST1 #0,SWWSR ;initial PMST ;initial ;zero wait state
SSBX SSBX
FRCT ;FRCT=1 output multiply will left shift
automatically SSBX SRPTZ SINLOOP: SSMPY DELAY DELAY PORTR SRPTB LOOP: DELAY DELAY ELOOP: DELAY PORTW *AR4+,*AR3-,A *AR4,*AR3,A *AR4+,*AR3,A *AR3 A,*AR3 *AR3, 200h ;write result file, word instruction INLOOP *AR4+,*AR3-,A *AR4,*AR3,A *AR4+,*AR3-,A A,*AR3+0 *AR4+,*AR3-,A *AR4+,*AR3,A *AR3- *AR4+,*AR3,A *AR3- ;A=A+d(n)*b0 ;save d(n) ;A=d(n-2)*b2 ;A=A+d(n-1)*b1 A+d(n-2)*(-a2) A+d(n-1)*(-a1) #d+7,AR3 #table,AR4 *AR4+,*AR3-,A *AR4+,*AR3,A *AR3- *AR4+,*AR3,A *AR3 100H,*AR3 *AR3,B B,11,*AR3- #N-2,BRC ELOOP-1 ;left shift scale input ;A=A+d(n)*b0 ;AR1:d(n),d(n-1),d(n-2) ;AR2:coeff filter -a2,-a1,b2,b1,b0 ;A=d(n-2)*b2 ;A=A+d(n-1)*b1 #d,AR3 A,#7 A,*AR3+ #2,AR0 ;AR3:d(n),d(n-1),d(n-2) ;initial d(n),d(n-1),d(n-2)=0
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