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Archive-name: dsp-faq/part2
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Q2: Algorithms and standards
Q2.1: Where can I get public domain algorithms for general-purpose DSP?
Updated 12/31/96
The following archives contain things such as matrix operations,
FFT's and generally useful things like that, as opposed to
complete applications.
Netlib
Netlib serves some of this software via email. Try mail to
netlib@ORNL.GOV with "send help" in the subject field.
To Obtain:
For Europe:
Internet: netlib@nac.no
EARN/BITNET: netlib%nac.no@norunix.bitnet
X.400: s=netlib; o=nac; c=no;
EUNET/uucp: nac!netlib
For more information:
See Jack J. Dongarra and Eric Grosse, "Distribution of
Mathematical Software Via Electronic Mail," Comm. ACM (1987)
30,403--407.
A similar collection of statistical software is available from
statlib@temper.stat.cmu.edu.
The symbolic algebra system REDUCE is supported by
reduce-netlib@rand.org.
NSWC Library
The Naval Surface Warfare Center has a library of mathematical
Fortran subroutines that may be of use. The NSWC library is a
library of general-purpose Fortran subroutines that provide a
basic computational capability in a variety of mathematical
activities. Emphasis has been placed on the transportability of
the codes. Subroutines are available in the following areas:
Elementary Operations, Geometry, Special Functions, Polynomials,
Vectors, Matrices, Large Dense Systems of Linear Equations, Banded
Matrices, Sparse Matrices, Eigenvalues and Eigenvectors, l1
Solution of Linear Equations, Least-Squares Solution of Linear
Equations, Optimization, Transforms, Approximation of Functions,
Curve Fitting, Surface Fitting, Manifold Fitting, Numerical
Integration, Integral Equations, Ordinary Differential Equations,
Partial Differential Equations
For more information:
NSWC Library of Mathematical Subroutines
Report No.: NSWC TR 90-21, January 1990
by Alfred H. Morris, Jr.
Naval Surface Warfare Center (E43)
Dahlgren, VA 22448-5000
U.S.A.
[Witold Waldman]
IEEE Press book "Programs For Digital Signal Processing"
You can get the Fortran source code from the IEEE Press book
"Programs For Digital Signal Processing." See question 1.3.6.
----------------------------------------------------------------------
Q2.2: What are CELP and LPC? Where can I get the source for CELP and LPC?
Updated 09/10/01
CELP stands for "code excited linear prediction". LPC stands for
"linear predictive coding". They are compression algorithms used
for low bit rate (2400 and 4800 bps) speech coding.
The U.S. DoD's Federal-Standard-1016 based 4800 bps code excited
linear prediction voice coder version 3.2 (CELP 3.2) Fortran and C
simulation source codes are available for worldwide distribution
(on DOS diskettes, but configured to compile on Sun SPARC
stations) from NTIS and DTIC. Example input and processed speech
files are included. A Technical Information Bulletin (TIB),
"Details to Assist in Implementation of Federal Standard 1016
CELP," and the official standard, "Federal Standard 1016,
Telecommunications: Analog to Digital Conversion of Radio Voice by
4,800 bit/second Code Excited Linear Prediction (CELP)," are also
available.
To obtain CELP:
Available through the National Technical Information Service:
NTIS
U.S. Department of Commerce
5285 Port Royal Road
Springfield, VA 22161
USA
(800) 553-6847
FS-1016 CELP 3.2 may also be obtained from
ftp://svr-ftp.eng.cam.ac.uk/pub/comp.speech/coding/celp_3.2a.tar.Z.
LPC-10 (2.4 Kbps) is available from
ftp://svr-ftp.eng.cam.ac.uk/pub/comp.speech/coding/lpc10-1.0.tar.gz.
LPC (4.8 Kbps) can be downloaded in SpeakFreely
http://www.speakfreely.org/, or in HawkVoice
http://www.hawksoft.com/hawkvoice/. HawkVoice includes versions of
OpenLPC, LPC-10, LPC, GSM, and Intel/DVI ADPCM. These versions
have been rewritten to support multiple encoding and decoding
streams, and the interfaces have been standardized. [Phil Frisbie,
Jr., phil@hawksoft.com]
OpenLPC (1.4 and 1.8 Kbps) can be downloaded from
ftp://ftp.futuredynamics.com/OpenLPC/.
MATLAB software for LPC-10 is available from
http://www.eas.asu.edu/~spanias/srtcrs.html. Also, postscript
copies of tutorials of speech coding can be found at
http://www.eas.asu.edu/~spanias/papers.html. [Andreas Spanias,
spanias@asu.edu]
For more information:
* The following articles describe the Federal-Standard-1016 4.8-kbps
CELP coder (it's unnecessary to read more than one):
Campbell, Joseph P. Jr., Thomas E. Tremain and Vanoy C. Welch, The
Federal Standard 1016 4800 bps CELP Voice Coder, Digital Signal
Processing, Academic Press, 1991, Vol. 1, No. 3, p. 145-155.
Campbell, Joseph P. Jr., Thomas E. Tremain and Vanoy C. Welch, The
DoD 4.8 kbps Standard (Proposed Federal Standard 1016), in Advances
in Speech Coding, ed. Atal, Cuperman and Gersho, Kluwer Academic
Publishers, 1991, Chapter 12, p. 121-133.
Campbell, Joseph P. Jr., Thomas E. Tremain and Vanoy C. Welch, The
Proposed Federal Standard 1016 4800 bps Voice Coder: CELP, Speech
Technology Magazine, April/May 1990, p. 58-64.
Additional information on CELP can also be found in the comp.speech
FAQ.
* The voicing classifier used in the enhanced LPC-10 (LPC-10e) is
described in: Campbell, Joseph P., Jr. and T. E. Tremain,
Voiced/Unvoiced Classification of Speech with Applications to the U.S.
Government LPC-10E Algorithm, Proceedings of the IEEE International
Conference on Acoustics, Speech, and Signal Processing, 1986, p.
473-6.
The U. S. Federal Standard 1015 (NATO STANAG 4198) is described in:
Thomas E. Tremain, The Government Standard Linear Predictive Coding
Algorithm: LPC-10, Speech Technology Magazine, April 1982, pp. 40-49.
[Most of the above from Joe Campbell, jpcampb@afterlife.ncsc.mil, with
additions from Dan Frankowski, drankow@winternet.com, and Ed Hall,
edhall@rand.org]
----------------------------------------------------------------------
Q2.3: What is ADPCM? Where can I get source for it?
Updated: 04/03/01
ADPCM stands for Adaptive Differential Pulse Code Modulation. It is a
family of speech compression and decompression algorithms. A common
implementation takes 16-bit linear PCM samples and converts them to 4-bit
samples, yielding a compression rate of 4:1.
To obtain:
There is public domain C code available via anonymous ftp at
ftp://ftp.cwi.nl/pub/audio/adpcm.shar written by Jack Jansen
(email Jack.Jansen@cwi.nl). It is very programmer-friendly. The
ADPCM code used is the Intel/DVI ADPCM code which is being
recommended by the IMA Digital Audio Technical Working Group. It
allows the following calls:
adpcm_coder(short inbuf[], char outbuf[], int nsample,
struct adpcm_state *state);
adpcm_decoder(char inbuf[], short outbuf[], int nsample,
struct adpcm_state *state);
Note that this is NOT a G.722 coder. The ADPCM standard is much
more complicated, probably resulting in better quality sound but
also in much more computational overhead.
Platforms:
The routines have been tested on numerous platforms, and will
easily compress and decompress millions of samples per second on
current hardware.
For more information:
The G.721/722/723 packages are available from ITU at
http://www.itu.ch/.
[From Dan Frankowski, dfrankow@winternet.com; Jack Jansen,
Jack.Jansen@cwi.nl]
----------------------------------------------------------------------
Q2.4: What is GSM? Where can I get source for it?
Updated 4/27/00
GSM (Global System for Mobile Communication) is a standard for
digital cellular telephony used in Europe. GSM also refers to the
speech coder used in GSM telephones, which is what this section of
the FAQ is concerned with.
The Communications and Operating Systems Research Group (KBS) at
the Technische Universitaet Berlin is currently working on a set
of UNIX-based tools for computer-mediated telecooperation that
will be made freely available.
As part of this effort they are publishing an implementation of
the European GSM 06.10 provisional standard for full-rate speech
transcoding, prI-ETS 300 036, which uses RPE/LTP (residual pulse
excitation/long term prediction) coding at 13 kbit/s.
GSM 06.10 compresses frames of 160 13-bit samples (8 kHz sampling
rate, i.e. a frame rate of 50 Hz) into 260 bits; for compatibility
with typical UNIX applications, our implementation turns frames of
160 16-bit linear samples into 33-byte frames (1650 Bytes/s). The
quality of the algorithm is good enough for reliable speaker
recognition; even music often survives transcoding in recognizable
form (given the bandwidth limitations of 8 kHz sampling rate).
The interfaces offered are a front end modeled after compress(1),
and a library API. Compression and decompression run faster than
real time on most SPARCstations. The implementation has been
verified against the ETSI standard test patterns.
Jutta Degener jutta@cs.tu-berlin.de, Carsten Bormann
cabo@cs.tu-berlin.de)
Communications and Operating Systems Research Group, TU Berlin
Fax: +49.30.31425156, Phone: +49.30.31424315
To obtain:
ftp://svr-ftp.eng.cam.ac.uk/pub/comp.speech/coding/gsm-1.0.6.tar.gz.
An alternative site is
ftp://ftp.cwi.nl/pub/audio/gsm-1.0.7.tar.gz. Try also:
http://kbs.cs.tu-berlin.de/~jutta/toast.html.
[From Dan Frankowski, dfrankow@winternet.com; Jutta Degener,
jutta@cs.tu-berlin.de]
----------------------------------------------------------------------
Q2.5: How does pitch perception work, and how do I implement it on my DSP chip?
Updated 04/02/01
Pitch is officially defined as "That attribute of auditory
sensation in terms of which sounds may be ordered on a musical
scale." Several good examples illustrating the subtleties of pitch
perception are included in the "Auditory Demonstrations CD" which
is available from the Acoustical Society of America, Woodbury, NY
10797 for $20.
Books/papers:
A good general reference about the psychology of pitch perception
is the book:
B.C.J. Moore, An Introduction to the Psychology of Hearing,
Academic Press, London, 1997.
This book is available in paperback and makes a good desk
reference.
An algorithm implementation that matches a large body of
psycho-acoustical work, but which is computationally very
intensive, is presented in the paper:
Malcolm Slaney and Richard Lyon, "A Perceptual Pitch Detector,"
Proceedings of the International Conference of Acoustics,
Speech, and Signal Processing, 1990, Albuquerque, New Mexico.
Available for ftp at
ftp://worldserver.com/pub/malcolm/ICASSP90.psc.Z
The definitive papers describing the use of such a perceptual
pitch detector as applied to the classical pitch literature is in:
Ray Meddis and M. J. Hewitt. "Virtual pitch and phase
sensitivity of a computer model of the auditory periphery. "
Journal of the Acoustical Society of America 89 (6 1991):
2866-2682. and 2883-2894.
The current work that argues for a pure spectral method starts
with the work of Goldstein:
J. Goldstein, "An optimum processor theory for the central
formation of the pitch of complex tones," Journal of the
Acoustical Society of America 54, 1496-1516, 1973.
Two approaches are worth considering if something approximating
pitch is appropriate. The people at IRCAM have proposed a harmonic
analysis approach that can be implemented on a DSP:
Boris Doval and Xavier Rodet, "Estimation of Fundamental
Frequency of Musical Sound Signals," Proceedings of the 1991
International Conference on Acoustics, Speech, and Signal
Processing, Toronto, Volume 5, pp. 3657-3660.
The classic paper for time domain (peak picking) pitch algorithms
is:
B. Gold and L. Rabiner, "Parallel processing techniques for
estimating pitch periods of speech in the time domain," Journal
of the Acoustical Society of America, 46, pp 441-448, 1969.
Finally, a word of caution:
Pitch is not single-valued. We can hear a sound and match it to
several different pitches. Imagine the number of instruments in an
orchestra, each with its own pitch. Even a single sound can have
more than one pitch. See for example Demonstration 27 from the ASA
Auditory Demonstrations CD.
[The above from Malcolm Slaney, Interval Research, and John
Lazzaro, U.C. Berkeley.]
Information about independently changing the pitch and speed of a
digital recording can be found at
http://www.dspdimension.com/html/timepitch.html. [Stephan M.
Bernsee, spam@dspdimension.com]Updated!
----------------------------------------------------------------------
Q2.6: What standards exist for digital audio? What is AES/EBU? What is S/PDIF?
Updates 1/8/97
Q2.6.1: Where can I get copies of ITU (formerly CCITT) standards?
Try the ITU (International Telecommunication Union) homepage at
http://www.itu.ch/.
----------------------------------------------------------------------
Q2.6.2: What standards are there for digital audio?
AES/EBU
The "AES/EBU" (Audio Engineering Society / European Broadcast
Union) digital audio standard is probably the most popular digital
audio standard today. Most consumer and professional digital audio
devices (CD players, DAT decks, etc.) that feature digital audio
I/O support AES/EBU.
AES/EBU is a bit-serial communications protocol for transmitting
digital audio data through a single transmission line. It provides
two channels of audio data (up to 24 bits per sample), a method
for communication control and status information ("channel status
bits"), and some error detection capabilities. Clocking
information (i.e., sample rate) is derived from the AES/EBU bit
stream, and is thus controlled by the transmitter. The standard
mandates use of 32 kHz, 44.1 kHz, or 48 kHz sample rates, but some
interfaces can be made to work at other sample rates.
AES/EBU provides both "professional" and "consumer" modes. The big
difference is in the format of the channel status bits mentioned
above. The professional mode bits include alphanumeric channel
origin and destination data, time of day codes, sample number
codes, word length, and other goodies. The consumer mode bits have
much less information, but do include information on copy
protection (naturally). Additionally, the standard provides for
"user data", which is a bit stream containing user-defined (i.e.,
manufacturer-defined) data. According to Tim Channon, "CD user
data is almost raw CD subcode; DAT is StartID and SkipID. In
professional mode, there is an SDLC protocol or, if DAT, it may be
the same as consumer mode."
The physical connection media are commonly used with AES/EBU:
balanced (differential), using two wires and shield in three-wire
microphone cable with XLR connectors; unbalanced (single-ended),
using audio coax cable with RCA jacks; and optical (via fiber
optics).
S/P-DIF
"S/P-DIF" (Sony/Philips Digital Interface Format) typically refers
to AES/EBU operated in consumer mode over unbalanced RCA cable.
Note that S/P-DIF and AES/EBU mean different things depending on
how much of a purist you are in the digital audio world; see the
Finger article below.
References:
Finger, Robert, AES3-199X: The Revised Two Channel Digital Audio
Interface (DRAFT), presented at the 91st Convention of the Audio
Engineering Society, October 4-8, 1991. Reprints: AES, 60 East
42nd St., New York, NY, 10165.
[The above from Phil Lapsley and Tim Channon,
tchannon@black.demon.co.uk]
Painter, E. M., and Spanias, A. S. (1997 and revised 1999). A
Review of Algorithms for Perceptual Coding of Digital Audio
Signals. (PostScript, 3MB)
http://www.eas.asu.edu/~spanias/papers.html
[Andreas Spanias, spanias@asu.edu]
----------------------------------------------------------------------
Q2.7: What is mu-law encoding? Where can I get source for it?
Updated 9/13/99
Mu-law (also "u-law") encoding is a form of logarithmic
quantization or companding. It's based on the observation that
many signals are statistically more likely to be near a low signal
level than a high signal level. Therefore, it makes more sense to
have more quantization points near a low level than a high level.
In a typical mu-law system, linear samples of 14 to 16 bits are
companded to 8 bits. Most telephone quality codecs (including the
Sparcstation's audio codec) use mu-law encoded samples.
Desktop Sparc machines come with routines to convert between
linear and mu-law samples. On a desktop Sparc, see the man page
for audio_ulaw2linear in /usr/demo/SOUND/man.
To obtain:
Craig Reese posted the source of similar routines to comp.dsp in
August '92. These are archived on
ftp://mirriwinni.cse.rmit.edu.au/pub/dsp/misc/.
References:
ITU-T (formerly CCITT) Recommendation G.711 (very difficult to
follow).
Michael Villeret, et. al, A New Digital Technique for
Implementation of Any Continuous PCM Companding Law, IEEE Int.
Conf. on Communications, 1973, vol. 1, pp. 11.12-11.17.
MIL-STD-188-113, Interoperability and Performance Standards for
Analog-to-Digital Conversion Techniques, 17 February 1987.
TI Digital Signal Processing Applications with the TMS320 Family
(TI literature number SPRA012A), pp. 169-198.
[From Joe Campbell; Craig Reese, cfreese@super.org; Sepehr Mehrabanzad,
sepehr@falstaff.dev.cdx.mot.com; Keith Kendall,
KLK3%mimi@magic.itg.ti.com]
----------------------------------------------------------------------
Q2.8: How can I do CD <=> DAT sample rate conversion?
Updated 9/13/99
CD players use a 44.1 kHz sample rate, whereas DAT uses a 48 kHz
sample rate. This means that you must do sample rate conversion
before you can get data from a CD player directly into a DAT deck.
[From Ed Hall, edhall@rand.org:]
For a start, look at Multirate Digital Signal Processing by
Crochiere and Rabiner (see FAQ section 1.1).
Almost any technique for producing good digital low-pass filters
will be adaptable to sample-rate conversion. 44.1:48 and
vice-versa is pretty hairy, though, because the lowest
whole-number ratio is 147:160. To do all that in one go would
require a FIR with thousands of coefficients, of which only
1/147th or 1/160th are used for each sample--the real problem is
memory, not CPU for most DSP chips. You could chain several
interpolators and decimators, as suggested by factoring the ratio
into 3*7*7:2*2*2*2*2*5. This adds complexity, but reduces the
number of coefficients required by a considerable amount.
[From Lou Scheffer:]
Theory of operation: 44.1 and 48 are in the ratio 147/160. To
convert from 44.1 to 48, for example, we (conceptually):
1. interpolate 159 zeros between every input sample. This raises
that data rate to 7.056 MHz. Since it is equivalent to
reconstructing with delta functions, it also creates images
of frequency f at 44.1-f, 44.1+f, 88.2-f, 88.2+f, ...
2. We remove these with an FIR digital filter, leaving a signal
containing only 0-20 KHz information, but still sampled at a
rate of 7.056 MHz.
3. We discard 146 of every 147 output samples. It does not hurt
to do so since we have no content above 24 KHz. In practice,
of course, we never compute the values of the samples we will
throw out.
So we need to design an FIR filter that is flat to 20 KHz, and
down at least X db at 24 KHz. How big does X need to be? You might
think about 100 db, since the max signal size is roughly +-32767,
and the input quantization +- 1/2, so we know the input had a
signal to broadband noise ratio of 98 db at most. However, the
noise in the stopband (20KHz-3.5MHz) is all folded into the
passband by the decimation in step 3, so we need another 22 db
(that's 160 in db) to account for the noise folding. Thus 120 db
rejection yields a broadband noise equal to the original
quantizing noise. If you are a fanatic, you can shoot for 130 db
to make the original quantizing errors dominate, and a 22.05 KHz
cutoff to eliminate even ultrasonic aliasing. You will pay for
your fanaticism with a penance of more taps, however.
To obtain:
There's a free implementation of Julius O. Smith III and someone
else's "bandwidth-limited interpolation" rate conversion
algorithm.
A paper available as
ftp://ccrma-ftp.stanford.edu/pub/DSP/Tutorials/
explains the algorithm. Free source code, as well as an HTML
discussion of the algorithm, is available at
http://ccrma-www.stanford.edu/~jos/resample/. It all works quite
well.
[From Kevin Bradley, kb+@andrew.cmu.edu:]
There is an implementation of polyphase resampling for various
rates as a part of the Sox audio toolkit at
http://home.sprynet.com/~cbagwell/sox.html. See file polyphas.c
for details.
Sox also contains an implementation of bandlimited interpolation
and linear interpolation, and serves as a ready vehicle for module
experimentation.
[From Fritz M. Rothacher, f.rothacher@ieee.org:]
You can add my Ph.D. thesis on sample-rate conversion to the FAQ:
Fritz M. Rothacher, Sample-Rate Conversion: Algorithms and VLSI
Implementation, Ph.D. thesis, Integrated Systems Lab, Swiss
Federal Institute of Technology, ETH Zuerich, 1995, ISBN
3-89191-873-9
It can also be downloaded from my homepage at
http://www.guest.iis.ee.ethz.ch/~rota.
----------------------------------------------------------------------
Q2.9: Wavelets
Updated 6/3/98
Q2.9.1 What are wavelets? Where can I get more information?
In short, wavelets are a way to analyze a signal using base
functions which are localized both in time (as diracs, but unlike
sine waves), and in frequency (as sine waves, but unlike diracs).
They can be used for efficient numerical algorithms and many DSP
or compression applications.
Sources of information on wavelets include:
* a newsletter, "Wavelet Digest". Subscriptions for Wavelet
Digest: E-mail to wavelet@math.scarolina.edu with "subscribe"
as subject. The Wavelet Digest can also be found at
http://www.wavelet.org/.
* http://www.amara.com/current/wavelet.html
----------------------------------------------------------------------
Q2.9.2 What are some good books and papers on wavelets
The best introduction to wavelet transforms is in:
Wavelets and Signal Processing- Oliver Rioul and Martin
Vetterli, IEEE Signal Processing magazine, Oct. 91, pp 14-38
A good introductory book on wavelets:
Randy K. Young, Wavelet Theory and Its Applications, Kluwer
Academic Publishers, ISBN 0-7923-9271-X, 1993.
A more thorough book:
Ali N. Akansu and Richard A. Haddad, Multiresolution Signal
Decomposition Transforms, Subbands, Wavelets Academic Press,
Inc., ISBN 0-12-047140-X
A couple more interesting papers:
Wavelets and Filter banks: Theory and Design, IEEE Transactions
on Signal Processing, Vol. 40, No.9, Sept. 1992, pp 2207-2232
Mac Cody's articles in Dr. Dobb's Journal, April 1992 and April
1993
Paper by Ingrid Daubechies in IEEE Trans. on Info. theory , vol
36. No.5 , Sept 1990 and a book titled " Ten lectures on
Wavelets" deal with the mathematical aspects of the WT.
----------------------------------------------------------------------
Q2.9.3: Where can I get some software for wavelets?
ftp://pascal.math.yale.edu/pub/wavelets/software/
Binaries are available for the following platforms: Sun
Sparcstations running SunOS 4.1 or Solaris 2.3, NeXT machines
running NeXTstep 3.0 or higher, with an X server, Silicon Graphics
machines (IRIS), DEC Alpha AXP running OSF/1 1.2 or higher,
i386/i486 PC compatible with Linux 0.99.
There is also a sample data directory containing interesting
signals.
More information:
http://www.math.yale.edu/users/majid/
[From Fazal Majid majid@math.yale.edu]:
Rice Wavelet Tools
Description:
The Rice Wavelet Toolbox (RWT) is a collection of Matlab M-files
and C MEX-files for 1D and 2D wavelet and filter bank design,
analysis, and processing. The toolbox provides tools for denoising
and interfaces directly with our Matlab code for wavelet domain
hidden Markov models and wavelet regularized deconvolution. Also
included is a simple converter to the data format used by the
official Matlab wavelet toolbox.
The current distribution, Version 2.3 (Dec 1, 2000), has been
streamlined and packaged for different systems, including Solaris,
Linux, and Microsoft Windows. Functions omitted in Version 2.3 can
be found in the Version 2.01 distribution.
To obtain:
See http://www-dsp.rice.edu/software/RWT/.
Send mail to wlet-tools@rice.edu (or ramesh@dsp.rice.edu)
----------------------------------------------------------------------
Q2.10: How do I calculate the coefficients for a Hilbert transformer?
Updated 6/3/98
For all the gory details, I suggest the paper: Andrew Reilly and
Gordon Frazer and Boualem Boashash: Analytic signal
generation---tips and traps, IEEE Transactions on Signal
Processing, no. 11, vol. 42, Nov. 1994, pp. 3241-3245.
For comp.dsp, the gist is:
1. Design a half-bandwidth real low-pass FIR filter using
whatever optimal method you choose, with the principle design
criterion being minimization of the maximum attenuation in
the band f_s/4 to f_s/2.
2. Modulate this by exp(2 pi f_s/4 t), so that now your
stop-band is the negative frequencies, the pass-band is the
positive frequencies, and the roll-off at each end does not
extend into the negative frequency band.
3. either use it as a complex FIR filter, or a pair of I/Q real
filters in whatever FIR implementation you have available.
If your original filter design produced an impulse response with
an even number of taps, then the filtering in 3 will introduce a
spurious half-sample delay (resampling the real signal component),
but that does not matter for many applications, and such filters
have other features to recommend them.
Andrew Reilly [Reilly@zeta.org.au]
----------------------------------------------------------------------
Q2.11: Algorithm implementation: floating-point versus fixed-point
According to the WWWebster Dictionary, an algorithm is "a
procedure for solving a mathematical problem (as of finding the
greatest common divisor) in a finite number of steps that
frequently involves repetition of an operation; broadly: a
step-by-step procedure for solving a problem or accomplishing some
end especially by a computer."
Typical (although by no means the only) operations are those of
addition and multiplication. When expressing the algorithm with
pencil and paper, these operations are commonly taken to be within
an algebraically complete number system such as the integers or
the reals. However, when the time comes to implement the algorithm
on a computer, these "ideal" number systems must be exchanged for
something realizable. The number systems available today on common
processors and digital hardware are broadly categorized as
floating-point and fixed-point.
In a floating-point representation, the total number of bits
available are partitioned into an exponent and mantissa. Generally
speaking, the mantissa stores the "significant digits" of the
value while the exponent scales the significant digits to the
desired magnitude. The action of the exponent is to move, or
"float," the decimal point depending on the magnitude being
represented; thus the term "floating-point."
Because floating-point representations are typically at least 32
bits long (IEEE-754 is a popular standard for 32-bit and 64-bit
floating-point numbers), there exists simultaneously high
precision and high dynamic range. These traits of floating-point
numbers allow most algorithms to be ported directly to
floating-point implementations with little or no change, and this
is the key reason floating-point representations are highly
desirable. The disadvantage of floating-point implementations is
that they require a significant amount of extra hardware over
fixed-point implementations, which translates to higher parts
costs, higher power consumption, slower execution, larger chip
area, or a combination of these.
As the term "fixed-point" implies, fixed-point representations
have the binary point at a fixed location. There are two subsets
of fixed-point implementations: fractional and integer. In a
fractional fixed-point implementation, such as that provided on
the Motorola 56K series of DSPs, the binary point is always
assumed to be to the left of the most-significant digit. In an
integer fixed-point implementation, such as that provided by the
Texas Instruments TMS320C54xx series of DSPs, the binary point is
to the right of the least-significant digit. In either case, the
arithmetic operations implemented in the hardware are essentially
integer, which results in a much simpler arithmetic logic unit in
hardware that allows lower cost, lower power consumption, faster
execution, smaller chip area, or a combination of these, over that
of floating-point implementations.
Fixed-Point Arithmetic: The Basics
In essence, a fixed-point representation is a simple integer
scaled (divided) by a power of two. If we denote an unscaled
integer variable by upper case "X" and the scaled, fixed-point
variable by lower case "x," then x = X/2^b, where b is the number
of digits the binary point is shifted left. For example, if X is a
16-bit, two's complement integer, and b=4, then "X" has values
ranging from -2^(15) to +2^(15)-1 and with minimum step size of 1,
while the scaled value "x" ranges from -2^(11) to +2^(11) -
1/(2^4) with a minimum step size of 1/(2^4).
Note that the value of "b" is not part of the representation. You
won't see it in a register or as part of the data anywhere; it is
a parameter that the algorithm implementer must determine and
maintain.
Fixed-point representations place some very different rules on
operations than their floating-point counterparts. For example,
two variables must be scaled the same in order to be added (or
subtracted). Thus it may be necessary to shift one or the other
operand prior to adding. Another example is that when multiplying
two N-bit values with scale factors b0 and b1, the result is
scaled (b0+b1) and requires 2*N bits in general in order to avoid
overflow and maintain precision.
There are several other rules and considerations for fixed-point
arithmetic that are commonly encountered when implementing
algorithms. For more information, see
http://www.digitalsignallabs.com/papers.htm.
Randy Yates [yates@ieee.org]
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Q3: Programmable DSP chips and their software
Q3.1: What are the available DSP chips and chip architectures?
Updated 05/07/02
The "big four" programmable DSP chip manufacturers are Texas
Instruments, with the TMS320C2000, TMS320C5000, and TMS320C6000
series of chips; Freescale, with the DSP56300, DSP56800, and
MSC8100 (StarCore) series; Agere Systems (formerly Lucent
Technologies), with the DSP16000 series; and Analog Devices, with
the ADSP-2100 and ADSP-21000 ("SHARC") series. A good overview of
programmable DSP chips is published periodically in EDN and
Computer Design magazines.
You may also want to check out Berkeley Design Technology's home
page, which has a number of articles on choosing DSP processors,
as well as a "Pocket Guide to Processors for DSP" in HTML format.
Brief overviews of various DSP processors, cores, and
general-purpose processors can be found at
http://www.bdti.com/procsum/index.htm.
Here's a less ambitious chip breakdown by manufacturer:
Agere Systems (formerly Lucent Technologies):
DSP16xxx:
100 to 170 MHz 16-bit fixed-point DSP. The DSP16000 core features
two multipliers with SIMD-like capabilities, a 20-bit address bus,
a 32-bit address bus, and eight 40-bit accumulators. The chips
feature two serial ports and two timers.
The first-generation processor, the DSP16210, contains a single
DSP16000 core and 120 KB of internal RAM. The second-generation
DSP16410 incorporates two DSP16000 cores and 386 KB of internal
RAM.
Analog Devices:
ADSP-21xx:
10 to 80 MHz 16-bit fixed point DSPs; 40-bit accumulator; 24-bit
instructions. Large number of family members with different
configurations of on-chip memory and serial ports, timers, and
host ports. ADSP-21mspxx members include an on-chip codec.
ADSP-219x:
160 MHz 16-bit fixed point DSPs; 40-bit accumulator; 24-bit
instructions. Based on the ADSP-21xx family, and is is mostly, but
not completely, assembly source-code upward compatible with the
ADSP-21xx Adds new addressing modes and an instruction cache,
expands address space, and lengthens pipeline (six stages compared
to three on the ADSP21xx). Family includes members containing
multiple ADSP-219x cores.
ADSP-21xxx ("SHARC"):
33 to 100 MHz floating-point DSP; Supports 32-bit fixed-point,
IEEE format 32-bit floating-point, and 40-bit floating-point;
40-bit registers plus an 80-bit accumulator that can be divided
into two 32-bit registers and a 16-bit register.
The first-generation SHARC, the ADSP-2106x, features a single data
path, a 32-bit address bus, and 40-bit data bus. Versions are
available with up to 512 KB of on-chip memory, up to six
communication ports, and up to 10 DMA channels.
The second-generation ADSP-2116x has two parallel data paths, a
32-bit address bus, and a 64-bit data bus. Versions are available
with up to 512 KB of on-chip memory; up to six communication
ports, and up to 14 DMA channels.
Analog Devices also sells the AD14000 series, which contain four
ADSP-2106x SHARC processors in a single-chip package.
ADSP-2153x:
200 to 300 MHz 16-bit fixed point DSPs that can execute two MAC
instructions per cycle; based on the ADI/Intel MSA core. Uses a
mix of 16-, 32-, and 64-bit instructions. Features include ability
to operate over a wide range of frequencies and voltages.
Freescale:
DSP563xx:
66 to 160 MHz 24-bit fixed-point DSP; most family members have
24-bit address and data busses. The DSP563xx also features 56-bit
accumulators (2), timers, serial interface, host interface port.
The DSP56307 and DSP56311 contain a filter co-processor. Up to 1
MB of internal RAM.
DSP568xx:
40 MHz 16-bit fixed point DSP; 36-bit accumulators (2), three
internal address buses (two 16-bit, one 19-bit) and one 16-bit
external address bus; three 16-bit internal data buses, one 16-bit
external data bus; serial ports, timers. 4-12 KB of internal RAM.
Most family members include an on-chip A/D.
DSP5685x:
160 MHz 16-bit fixed point DSP based on the DSP568xx. Adds an
exponent detector and two accumulators, extends shifter and the
logic unit to 32 bits, and widens internal address and data buses.
The DSP5685x uses a 1X master clock rate rather than the 2X master
clock rate used by the DSP568xx.
MSC81xx:
The 300 MHz MSC8101 is the first processor based on the StarCore
SC140 core. It contains four parallel ALU units that can execute
up to four MAC operations in a single clock cycle. The MSC8101
uses variable-length instructions. Features include: 512 KB
on-chip RAM; 16 DMA channels; an on-chip filter co-processor; and
interfaces for ATM, Ethernet, E1/T1 and E3/T3, and the PowerPC
bus.
Texas Instruments:
TMS320C2xxx:
20-40 MHz 16-bit fixed-point DSPs oriented toward low-cost control
applications; 16 bit data, 32 bit registers. The family members
have a variety of peripherals, such as A/D converters, 41 I/O
pins, and 16 PWM outputs. A variety of RAM and ROM configurations
are available
TI also sells the TMS320C2x family, an older version of the chip
with fewer features.
TMS320C3x:
33-75 MHz floating point DSPs; 32-bit floating-point, 24-bit
fixed-point data, 40-bit registers; DMA controller; serial ports;
some support for multi-processor arrays. Various ROM and RAM
configurations.
TMS320C54xx:
40 to 160 MHz 16-bit fixed-point DSPs with a large number of
specialized instructions. Many family members; the processors
differ in configuration of on-chip ROM/RAM, serial ports,
autobuffered serial ports, host ports, and time-division
multiplexed ports. On-chip RAM ranges from 10 KB to over 1 MB.
TMS320C55xx:
144 to 200 MHz dual-ALU variant of the TMS320C54xx that can
execute two MAC instructions per cycle. Variable instruction word
width. Features include up to 320 KB internal RAM; 6 DMA channels;
2 serial ports; and 2 timers.
TMS320C62xx:
150-300 MHz 16-bit fixed-point DSP with VLIW (very large
instruction word), load/store architecture; 32 32-bit registers;
very deep pipeline; two multipliers, ALUs, and shifters; cache.
TMS320C64xx:
400-600 MHz 16-bit fixed-point DSP based on the TMS320C62xx. Adds
SIMD support to most execution units, including extensive 8-bit
SIMD support. Also doubles data bandwidth and increases size of
on-chip memory.
TMS320C67xx:
100-167 MHz 32-bit and 64-bit IEEE-754 floating-point DSP with
VLIW (very large instruction word), load/store architecture; 32
32-bit registers; very deep pipeline; two multipliers, ALUs, and
shifters; cache.
----------------------------------------------------------------------
Q3.2: What is the difference between a DSP and a microprocessor?
Updated 04/02/01
The essential difference between a DSP and a microprocessor is
that a DSP processor has features designed to support
high-performance, repetitive, numerically intensive tasks. In
contrast, general-purpose processors or microcontrollers
(GPPs/MCUs for short) are either not specialized for a specific
kind of applications (in the case of general-purpose processors),
or they are designed for control-oriented applications (in the
case of microcontrollers). Features that accelerate performance in
DSP applications include:
* Single-cycle multiply-accumulate capability; high-performance
DSPs often have two multipliers that enable two
multiply-accumulate operations per instruction cycle; some
DSP have four or more multipliers
* Specialized addressing modes, for example, pre- and
post-modification of address pointers, circular addressing,
and bit-reversed addressing
* Most DSPs provide various configurations of on-chip memory
and peripherals tailored for DSP applications. DSPs generally
feature multiple-access memory architectures that enable DSPs
to complete several accesses to memory in a single
instruction cycle
* Specialized execution control. Usually, DSP processors
provide a loop instruction that allows tight loops to be
repeated without spending any instruction cycles for updating
and testing the loop counter or for jumping back to the top
of the loop
* DSP processors are known for their irregular instruction
sets, which generally allow several operations to be encoded
in a single instruction. For example, a processor that uses
32-bit instructions may encode two additions, two
multiplications, and four 16-bit data moves into a single
instruction. In general, DSP processor instruction sets allow
a data move to be performed in parallel with an arithmetic
operation. GPPs/MCUs, in contrast, usually specify a single
operation per instruction
While the above differences traditionally distinguish DSPs from
GPPs/MCUs, in practice it is not important what kind of processor
you choose. What is really important is to choose the processor
that is best suited for your application; if a GPP/MCU is better
suited for your DSP application than a DSP processor, the
processor of choice is the GPP/MCU. It is also worth noting that
the difference between DSPs and GPPs/MCUs is fading: many
GPPs/MCUs now include DSP features, and DSPs are increasingly
adding microcontroller features.
----------------------------------------------------------------------
Q3.3: Software for Analog Devices DSPs
Updated 12/01/2006
Q3.3.1: Where can I get a C compiler for the ADSP-21xx and ADSP-21xxx?
The G21 package collects the free source code for the Analog
Devices GCC-based C compilers for their 21xxx (SHARC) and 21xx
series DSPs. These compilers are all based on GCC version 2.3.3.
Full source code for the compiler, assembler, linker, etc. is
available at http://www.kvaleberg.com/g21.html.
The C compilers are available for the 210x series as well as for
the SHARC. The assemblers and linkers are only available for the
SHARC. The source code is based on what is released under GPL by
ADI, but is adapted for use with Linux and other Unix variants.
[Egil Kvaleberg, egil@kvaleberg.no]
----------------------------------------------------------------------
Q3.3.2: Where can I get tools for the ADSP-21xxx?
SHARC development tools are avaiable for Acorn/BSD, Linux, and
other platforms. The tools include frontend/preprocessor ,
assembler, linker, archiver, a utility to generate ROM images for
eprom burners, and other utilities The supplied assembler is not
part of the gnu archive, but is based on a assembler originaly
written by P. Lantto. Source code and binaries are available at:
http://www.markettos.org.uk/electronics/sharc/.
----------------------------------------------------------------------
Q3.3.3: Where can I get algorithms or libraries for Analog Devices DSPs?
The number for the Analog Devices DSP BBS is (617) 461-4258 (300,
1200, 2400, 9600, 14400 bps), 8N1.
You can also find files on Analog Devices' web site at
http://www.analog.com/processors/index.html, or at their FTP site
at ftp://ftp.analog.com.
[Analog Devices DSP Applications, dsp_applications@analog.com]
----------------------------------------------------------------------
Q3.4: Software for Agere Systems (Formerly Lucent Technologies) DSPs
Agere Systems provides application libraries for their DSPs at
http://www.agere.com/networking/dsps.html.
----------------------------------------------------------------------
Q3.5: Software for Freescale DSPs
Updated 12/01/2006
Freescale provides free software development tools that may be
downloaded from the Freescale Web site at
http://www.freescale.com/webapp/sps/site/prod_summary.jsp?code=MSW3SDK000AA&nodeId=01M983916044937.
Q3.5.1: Where can I get a free assembler for the Freescale DSP56000?
A free assembler for the Freescale DSP56000 exists, thanks to
Quinn Jensen, jensenq@zdomain.com. The current version is 1.2. It
is also available at http://www.zdomain.com/a56.html.
----------------------------------------------------------------------
Q3.5.2: Where can I get a free C compiler for the Freescale DSP56000?
There are two separate compiler sources for the Freescale
DSP56000. One is the port of gcc 1.40 done by Andrew Sterian
(asterian@umich.edu) and the other is a port of gcc 1.37.1 done by
Freescale and returned to the FSF. Andrew's port has bowed to
Freescale's version. Both may be portable to gcc2.x.x with some
effort required. Neither of these comes with an assembler, but you
can get a free DSP56000 assembler elsewhere (see question 3.5.1,
above). The Freescale gcc source is available for FTP from:
ftp://nic.funet.fi/pub/ham/dsp/dsp56k-tools/dsp56k-gcc.tar.Z.
From Andrew Sterian, asterian@umich.edu: "My DSP56K compiler,
while not supported nor as well tested as Freescale's, implements
fixed-point arithmetic rather than floating-point arithmetic. This
may be suitable for some applications. The 5615 compiler also
implements fixed-point arithmetic. To the best of my knowledge,
Freescale does not have a C compiler for the 5615 family, although
alternatives may exist. As of this writing (January 1997) I have
not worked with Freescale DSPs or compiler software for nearly 5
years so questions regarding my compilers may well be met with
"Ummm... I have no idea."
Both compilers were posted to alt.sources so any Usenet site that
archives this newsgroup will have a copy. I have also found the
5616 compiler at
ftp://ftp.funet.fi/pub/ham/dsp/dsp56k-tools/gcc5616.tar.Z.
(http://www.newmicros.com) IsoPod(TM) - based on the DSP56F805.
The assembler generates output suitable for Freescale's free JTAG
flash loader.
Pete Gray has announced the availability of a Small C
cross-compiler (with source) and assembler for the Freescale
DSP56800, available for download from
http://petegray.newmicros.com/ . Targetting a simple DOS-box host,
developed and tested using djgpp (http://www.delorie.com/djgpp/)
and Metrowerks CodeWarrior, in conjunction with NMI's
(http://www.newmicros.com) IsoPod(TM) - based on the DSP56F805.
The assembler generates output suitable for Freescale's free JTAG
flash loader.
Small C language reference available online at
http://www.ddjembedded.com/languages/smallc/
----------------------------------------------------------------------
Q3.5.3 Where can I get a disassembler for the Freescale DSP56000?
Miloslaw Smyk has released an open source (BSD style) 5600x
disassembly library. It is available for download at
https://sourceforge.net/projects/lib5600x [Miloslaw Smyk,
thorgal@wmfh.org.pl]
----------------------------------------------------------------------
Q3.5.4: Where can I get algorithms and libraries for Freescale DSPs?
Freescale provides a software archive that is available via
World-Wide Web from the software page at
http://www.mot.com/SPS/DSP/software/. The archive includes macros
for filters (FIR, IIR, adaptive) and floating-point functions.
[Tim Baggett]
----------------------------------------------------------------------
Q3.5.5: Where can I get NeXT-compatible Freescale DSP56001 code?
Try FTP at ccrma-ftp.stanford.edu. The /pub/ directory contains
free code for the Freescale DSP56001 and the NeXT platform.
[bil@ccrma.Stanford.EDU]
----------------------------------------------------------------------
Q3.5.6: Where can I get emulators for the 68HC11 (6811) processor?
While the 68HC11 is not a DSP processor, emulators are available
for those who might be interested in doing DSP on these
processors:
* New Mexico State University (NMSU) simulator engine,
ftp://crl.nmsu.edu/pub/non-lexical/6811/ (Unix). Simulator
engine with a command-line interface.
* Sim6811,
http://www.cs.nmsu.edu/~pfeiffer/classes/273/notes/sim.html
(Mac). Screen-oriented user interface based on the NMSU
simulator engine (plus bug fixes).
* THRSim11, http://programfiles.com/index.asp?ID=8366 allows
you to edit, assemble, simulate and debug programs for the
68HC11 on Windows 95/98. THRSim11 simulates the CPU, ROM,
RAM, all memory mapped I/O ports, and the on board
peripherals.
----------------------------------------------------------------------
Q3.6: Software for Texas Instruments DSPs
Updated 12/01/2006
Q3.6.1: Where can I get free algorithms or libraries for TI DSPs?
ftp://ftp.funet.fi/pub/ham/dsp/ has some old, apparently public
domain, assembler and related tools from TI for the TMS320
family.
TI has a number of free algorithms available on their website at
http://dspvillage.ti.com/docs/sdstools/sdscommon/showsdsinfo.jhtml?templateId=57&path=templatedata/cm/ccstudio/data/free_tools.
TI's world-wide web site is http://www.ti.com. The TI DSP bulletin
board is mirrored on ftp.ti.com. The TI site is the official one,
but has no user contributed software. [Brad Hards,
bradh@gil.com.au]
{ If anyone knows of any other sources for TI DSP software, please
let us know at comp-dsp-faq@bdti.com. Thanks! }
----------------------------------------------------------------------
Q3.6.2: Where can I get free development tools for TI DSPs?
TI development tools are available for free 30 day evaluation on
the TI website.
Go to
http://focus.ti.com/dsp/docs/dspsupportaut.tsp?sectionId=3&tabId=416&familyId=44&toolTypeId=30.
----------------------------------------------------------------------
Q3.6.3: Where can I get a free C compiler for the TI TMS320C3x/4x?
The GNU binutils 2.11 and later have been ported to the TI
C54xx/IBM C54DSP. Most of the binutils tools are supported,
including the assembler, linker and objdump. The assembler is
source-compatible with the TI assembler. The GNU binutils are
available from http://sources.redhat.com/binutils/ GDB ports for
c25/c5x/c54x are also available.
[Timothy Wall]
Dr. Michael P. Hayes has written a GNU C-based compiler for the
TMS320C30 and TMS320C40 families, available at
http://www.elec.canterbury.ac.nz/c4x. The current version patches
against gcc-2.8.1; support is moving to egcs-1.2. The compiler is
freely redistributable under the terms of the GNU Public License.
Front-ends are also available for C++, Java, Fortran 77, Pascal,
Ada 95, among others.
[Dr. Michael P. Hayes, m.hayes@elec.canterbury.ac.nz]
----------------------------------------------------------------------
Q3.6.4: Where can I get a free assembler for the TI TMS320C3x/4x?
Ted Rossin has written an assembler and linker for the TMS320C30.
In his words, "It is somewhat limited by the fact that it can't
handle expressions but it has worked fine for me over the past few
years. There is no manual because it is a clone of the TI
assembler and linker. However the linker command files use a
different (easier to use) syntax. It runs on HP-UX workstations,
Macs, IBM clones and believe it or not the Atari-ST (because I
developed the code on it)."
[Ted Rossin, rossin@fc.hp.com]
Dr. Michael P. Hayes has written a GNU-based assembler for the
TMS320C30 and TMS320C40 families, available at
http://www.elec.canterbury.ac.nz/c4x. The current version patches
against binutils-2.7. According to Michael Hayes, the assembler
syntax is compatible with the Texas Instruments TMS320C30
assembler, although not all the Texas Instruments directives are
supported. The binutils include a linker (ld), archiver (ar),
disassembler (objdump), and other miscellaneous utilities. The
object format of the assembler is compatible with the COFF format
used by the Texas Instruments assembler. The assembler and other
binary utilities are freely redistributable under the terms of the
GNU Public License.
[Dr. Michael P. Hayes, m.hayes@elec.canterbury.ac.nz]
----------------------------------------------------------------------
Q3.6.5: Where can I get a free simulator for the TI TMS320C3x/4x?
A freely distributable instruction set architecture simulator is
available for the TMS320C30 DSP as part of the Web-Enabled
Simulation framework from UT Austin at
http://signal.ece.utexas.edu/~arifler/wetics/.
We have released all of the source code, as well as prebuilt C30
simulators for Windows '95/NT and Solaris 2.5 architectures.
The C30 simulator is bit-, cycle-, and instruction-accurate. The
behavior of the C30 simulator has been validated against a C30 DSK
board. The C30 simulator correctly reports interlocking and
pipeline flushes, so it provides a convenient way to check C30
programs for these hidden delays. The C30 simulator is based on
the C30 DSK tools by Keith Larson at Texas Instruments.
[Brian Evans, bevans@ece.utexas.edu]
Herman Ten Brugge (haj.ten.brugge@net.hcc.nl) has also written a
GNU debugger (GDB) based simulator for the TMS320C30 and
TMS320C40, available via anonymous FTP at
http://www.elec.canterbury.ac.nz/c4x. This is freely
redistributable under the terms of the GNU Public License.
This simulator allows you to debug your programs without having to
a connect to a real C[34]x target system. It will also profile
your code showing you where the pipeline conflicts are occurring.
You can connect I/O ports to files (or TCP/IP sockets), trigger
interrupts, examine the cache etc. It will detect different
threads of control running and generate a profile summary for each
thread, annotating both the C code and assembler code with the
number of executed cycles.
[Dr. Michael P. Hayes, m.hayes@elec.canterbury.ac.nz]
----------------------------------------------------------------------
Q3.6.6: What is Tick? Where can I get it?
Tick is a TMS320C40 parallel network detection and loader utility.
It is available from:
http://wotug.kent.ac.uk/parallel/vendors/ti/tms320c40/tick/
Supports: Transtech, Hunt, and Traquair boards hosted by DOS,
SunOS, Linux
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