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Motorola
Digital Signal
Processors
Digital Sine-Wave
Synthesis Using the
DSP56001/2
by
Andreas Chrysafis
Digital Signal Processing Division
MOTOROLA
APR 1
Table
of Contents
SECTION 1
SECTION 2
SECTION 3
I
ntroduction
Background
Direct Table Look-Up
3.1 Integer Delta Implementation
3.2 Real Delta Implementation
3.3 Harmonic Distortion
Table Look-Up with Linear Interpolation
4.1 Harmonic Distortion
Computation of Total Harmonic
Distortion (THD)
The Sine Table
1-1
2-1
3-1
3-5
3-10
4-1
4-8
SECTION 4
APPENDIX A
A-1
B-1
Reference-1
APPENDIX B
REFERENCES
MOTOROLA
iii
Illustrations
Figure 3-1
Figure 3-2
Figure 3-3
Figure 3-4
Figure 3-5
Figure 3-6
Figure 3-7
Integer Delta
“SINWGID” Routine
“SINWGID” Memory Map
Real Data Without Interpolation
“SINWGRD” Routine
“SINWGRD” Memory Map
“SINWGRD” Data ALU Programmer’s Model
3-2
3-3
3-3
3-5
3-6
3-7
3-7
Figure 4-1
Figure 4-2
Figure 4-3
Figure 4-4
Figure 4-5
Real Delta Interpolation
“SINWGLI” Flow Diagram
“SINWGLI” Routine
“SINWGLI” Memory Map
“SINWGLI” Data ALU Programmer’s Model
4-2
4-3
4-5
4-6
4-7
Figure A-1
VAX VMS FORTRAN Source Code for THD
Computation
A-5
MOTOROLA
v
List of Tables
Table 2-1
Sine-Wave Table Values
2-1
Table 3-1
Table 3-2
Total Harmonic Distortion — Integer Delta
Total Harmonic Distortion — Real Delta
3-11
3-12
Table 4-1
Total Harmonic Distortion — Real Delta
4-8
Table A-1
Table A-2
Single Precision Accuracy
Double Precision Accuracy
A-4
A-4
Table B-1
The SIne Table
B-1
MOTOROLA
vii
SECTION 1
Introduction
“This document
describes three
table look-up
methods for
sine-wave
generation . . .”
S
ine-wave generators are used in communications
and control applications (1,2). With the introduction of
high-speed high-precision digital signal processors,
stable and low distortion sine waves of any frequency
can be produced digitally using some form of table
look-up with interpolation to reduce distortion (3,4,5).
This document describes three table look-up methods
for sine-wave generation and provides the Total Har-
monic Distortion (THD) performance and Maximum
Synthesizable Frequency (MSF) for each case.
A routine for synthesizing sine waves having frequen-
cies limited to integer multiples of the Fundamental
Table Frequency (FTF) is described in
Section 3.1.
The MSF is highest using this approach. In
Section
3.2
a routine using only direct table look-up for syn-
thesizing sine waves having frequencies which are
fractional multiples of the FTF is described. This ap-
proach can be used to synthesize sine waves with
frequencies which are not integer multiples of the FTF
but they have substantially higher THD. A routine for
synthesizing sine waves using table look-up with in-
terpolation is described in
Section 4.
Sine waves with
frequencies which are not limited to multiples of the
FTF and yet have low THD are possibly using this
s
synthesis approach.
MOTOROLA
1-1

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