How Do I Learn DSP?
What follows is one person's response to the perennial question "How
do I learn DSP?" It was written by Dale
Grover, with input from folks including Rick Lyons, Randy Yates, and
Grant Griffin, though their participation is not an endorsement of every
opinion expressed herethey're just good guys. A disclaimer:
I am a coauthor of one of the books mentioned.
1/10/07
Introduction: What do you want to know?
What do you know now?
The three necessary elements
1. Books
Nontraditional
Online
Tutorials
Classics
2. Software
Octave, Matlab,
& relatives
DSPspecific
Symbolic
General
purpose
3. Hardware
Formal courses
A brief overview of DSP topics
About this document
What Do You Want to Know? What Do You
Know Now?
The best way to learn digital signal processing (DSP) depends on your goals
and background. Why is this?

DSP includes many different topics, such as:

digital filters

analysis of signals and systems (especially in terms of frequency)

synthesis of signals

detection of signals and estimation of signal and system parameters

data compression

and on and on ...

DSP is the intersection of a number of different areas of study:

mathematics

electrical engineering

signals and systems

analog circuit theory

computer architecture, (and more)

probability and statistics

computer programming

and others

Implementing DSP, especially in realtime, is generally treated separately
from the theory, so much so it can seem like a field entirely separate
from DSP.
In the pastin fact, until a few years agoDSP was taught (and books
were written) almost exclusively for people with an electrical engineering
background. If that's your background, you have plenty of options
in learning about DSP, and the resources noted in this document will give
you plenty of choices. But if you don't have an electrical engineering
background, there are now some books (and courses) that can bring you up
to speed on basic DSP topics, and even on implementation issues.
More about these options in a moment, when we discuss books.
There are some folksmyself includedwho claim that we should treat
DSP in a similar way with how statistics is taught. Instead of claiming
that every person who wants to know a little about statistics has to learn
Everything There Is To Know about statistics, there are instead statistics
courses for humanities majors, engineers, mathematics majors, and so on.
Why? Because statistics is useful in many fields, and a useful subset
of statistics can be taught to and used by folks even if they haven't studied
all the theory behind statistics. In much the same way (actually,
in a very deep sense), DSP has these same characteristics. DSP is,
of course, useful, and indeed most anyone can learn the basics of DSPand
successfully apply these tools in their field. This document outlines
some resources and approaches to do just that.
Like statistics, there are trade offs between the size of the toolbox
(and your skill in using those tools) and the amount of study and background
required. At one extreme, you can end up with just the stepbystep "recipe"
without any need to understand what's going on. At the other extreme, you
can reach the point where you can select techniques from a wide array of
possibilities, or even create your own, though this will require a good
background in mathematics and so on. Your interests and backgrounds
will be different from everyone else, and there is no single path to "DSP
enlightenment"or even "DSP familiarity."
Two (or Three) Necessary Elements
Any approach to learning DSP outside a formal classroom setting will eventually
involve some combination of books, DSP/math
software, and
DSP hardware, since each can
offer insight and motivation into DSP.

Books (and related resources) will provide both theoretical
and practical knowledge; they "drive" the learning process.

Software will let you gain experience and refine
your understanding of the theory. Other software will help in the
design process, and even in the implementation process (if there is one).

Hardware lets you implement DSP in realtime (if
necessary).
We discuss each in the sections that follow. We also mention some
formal
learning situations. It is our hope that this document can provide
you a framework for determining an appropriate path, and useful tools,
for you to learn more about DSP.
Books
"Nontraditional"
DSP texts are now available that address a range of backgrounds and goals.
As we mentioned above, until recently, DSP texts assumed you had a "traditional"
electrical engineering background. However, there are now some books and
courses that take a subset of DSP techniques and present it in a way that
is accessible to people without this background. For example:
(See the comp.dsp FAQ
and/or dspGuru.com
for bibliographic information.)
These books are aimed, for example, at scientists, engineers, computer
science/programmers, and researchers who want to learn basic DSP for use
in their work. Generally speaking, these books downplay the mathematics,
and emphasize intuitive presentations. (Stein's book, addressed at
computer science students, doesn't shy away from the mathematics and theory,
but like the others doesn't make assumptions about electrical engineering
topics.) Some also emphasize practical implementation issues. Digital
filters and spectral analysis (e.g., the FFTthe fast Fourier transform)
are topics common to all these texts; other topics can include synthesis
of signals, implementation on real hardware, signal detection, etc. Generally
speaking, the core topics common to all these texts are useful in understanding
and using more specialized DSP techniques such as are used, for example,
in creating special music effects.
Online Tutorials
There are several online tutorials availablesee for example the list
of tutorials given at http://www.dspguru.com/info/tutor/other.htm.
Not every tutorial starts with the same assumptions, however. So, just
as with books, don't despair if your interests and background are not addressed;
just seek alternatives.
There are also books aimed at traditional electrical engineering students
who do not yet have the traditional DSP prerequisites; these are an experiment
in rearranging the order in which topics are taught to electrical engineering
students, rather than targeting a nonengineering audience. (See, for example,
McClellan, Schafer, and Yoder's DSP First.) However, since
the intended students do not have an extensive background, these books
might be useful to other readers as well. Bear in mind that while
the background that is assumed may be similar to the other books, the goals
are different. (In this case, the goals include preparing students
for further electrical engineering coursework, so some additional foundations
are laid.)
Where Will This Leave You?
The "nonEE" books and resources above provide a (mostly) selfcontained,
often "lowmath" path to basic DSP theory, and in some cases, implementation.
However, as you might guess, there are some trade offs for books that take
this route. In particular, for those books that downplay the (mathematical)
theory, some connections can be lost between topics that otherwise are
easily seen. If the basic DSP topics you've learned are sufficient,
then this isn't a big loss. But to tackle more complicated DSP, whether
that's understanding some specialized technique, or striking out on your
own to tackle some new problem, it will be necessary to have a deeper background,
including

mathematics: calculus and differential equations

electrical engineering: analog circuit theory through linear signals
and systems theory, computer architecture

computer programming: basic programming (high level languages) and
assembly language

statistics
Many DSP texts start assuming roughly this type of background, corresponding
to perhaps a third year undergraduate engineering curriculum (see below).
It is entirely reasonable to initially explore DSP using less rigorous
texts (some of which are listed above), but it is difficult to understand
the more advanced DSP theory without the techniques and language of these
background areas. The fact is, most DSP papers, books, presentations,
and even software, will assume a certain familiarity with concepts from
the areas above, and it will be hard going to fill these in "on the fly."
Classics
Some classic (and popular texts) are listed in the comp.dsp
FAQ (see below), which include

Oppenheim and Schafer's DiscreteTime Signal Processing

Proakis and Manolakis' Digital Signal Processing: Principles, Algorithms,
and Applications.
A recent text that covers linear signals & systems through basic signal
processing is Lathi's Signal Processing and Linear Systems (1998),
though there are many, many books on linear signals and systems that should
be accessible to readers who have had calculus, differential equations,
and an introductory electronics course.
The more traditional DSP texts do not necessarily omit practical issues,
and some include applications such as digital audio effects (see Orfanidis'
Introduction
to Signal Processing, for example). However, you should be aware of
the level of mathematical comfort the authors assume, even if the topics
covered are appealing.
"But all I wanted was to do some neat audio effects..."
Does this mean that you'll have to master all of basic DSP theory to understand,
for example, some neat digital audio effect? Not at allbut there
are two caveats. First, depending on the field, these neat algorithms
are often expressed using terminology and mathematics that assumes a traditional
DSP or analog electronics (especially analog filter design) background.
You might have to dig around for explanations that are aimed at folks without
a deep DSP background. (For example, Circuit
Cellar Ink often publishes articles on signal processing that are aimed
at nonDSP folks.) Second, realize that you won't have as much flexibility
in using these techniquesit might be difficult to know how to tweak or
change the algorithm without running afoul of some problems. But
this is true with many tools we use, and it is not an excuse to give up.
In fact, playing with some algorithm you are motivated to use and understand
can give you real life experience with the issues textbooks cover (for
example, how sampling rate affects a signal).
Once the basic DSP background is in place, many applicationspecific
DSP areas are accessible. This includes speech processing (recognition,
synthesis, compression), image processing, music processing (analysis,
synthesis, etc.), all types of biomedical signal processing, and on and
on. All draw upon a common set of tools, but you'll find each field also
has its set of favorite tools, many of which might not be used extensively
in other areas of DSP. (In part, this is may be due to historical
influences, but it is also the case that the signals being processed in
different fields can have strikingly different characteristics that make
them more or less amenable to different DSP techniques. Thus, speech
processing often uses very different techniques than image processing,
though they also share many techniques.) In addition, a number of advanced
DSP techniques (multirate filters, various stochastic techniques, etc.)
have wide application, but are difficult to approach without a solid background
in basic DSP.
If you're getting the impression that folks active in DSP end up with
quite a few books, you're right! No single book can take into account the
wide backgrounds and interests of everyone who needs to use DSP. Not to
mention the many areas within DSP that have their own set of tools and
techniques, like image processing, speech processing, etc. In addition,
not every author places the same importance on every topicso it's not
uncommon to try a couple of books before finding, for example, a particular
algorithm you want discussed in nittygritty detail. Though DSP is many
decades old, some cutting edge techniques might be best found in the professional
journals, trade magazines, or conference proceedings. A good web search
may turn up these more recent publications. The divide, mentioned
earlier, between theory and implementation also means some additional books,
since the overlap is often minimal.
Web Resources
If you're reading this, you've likely come across at least some web resources
for DSP. A good starting place is the comp.dsp FAQ at http://www.bdti.com/faq/dsp_faq.htm.
The FAQ contains a list of popular DSP books, online resources, useful
and classic articles, and a host of other information. You will also find
an interesting mix of people on the comp.dsp newsgroup
with a wealth of experience. However, most basic questions can be answered
in any good DSP book, and more specific questions reserved for the newsgroup.
Another resource is http://www.dspGuru.com,
which contains a number of articles on basic and advanced DSP techniques,
pointers to online tutorials, sources of software, and other information
you might find useful. Another site you may wish to check is http://www.dsprelated.com/.
Software
PCbased software helps in several areas of DSP. First, software
can allow you to experiment with DSP. Second, you can do (generally
speaking, nonrealtime) signal processing on PC's using a variety of software.
Third, PCbased software can be used to generate the realtime software
that will run on a dedicated DSP chip. The same software might do
all three pieces, or just one. But for a person learning DSP, the
ability to experiment is most important, and the one that this section
will emphasize.
Whether you want to acquire a few DSP techniques, or make DSP your main
area of study, it is immensely helpful to have a software environment where
you can experiment with signal processing. This environment should allow
you to create (or at least import) signals such as audio signals and images,
process them using simple mathematical operations, and play or display
(graph) the processed signals and their frequency domain representations.
University students in the US will find little trouble locating relatively
inexpensive but powerful mathematical packages that support DSP very well.
The following are some possible environments. (See the comp.dsp
FAQ for more details.)
Octave, MATLAB, and Relatives
Octave is a very
powerful environment for numerical computation. Programs can be
written in a simple language, but the true strength of Octave is in the
powerful matrix and vector operations, along with an extensive library
of functions including some for signal processing. Plotting is
available using the gnuplot program. Octave is available in
source code, and in binary for Mac OS X, Linux, and Windows.
Octave uses a language that is largely compatible with Matlab
(see below), though offers additional features such as zerobase
indexing. Actively maintained. Installation can be a little
more complicated than commercial packages. Highly recommended.
Mac OS X users may find the High Performance Computing for Mac OS X page of use, as they often provide recently compiled versions of Octave.
MATLAB is a very popular
commercial software
package with strengths in numeric processing of arrays and matrices,
but
also has a number of "toolboxes" including one for DSP. Programs
(script
files) can be written or commands entered interactively, and the
graphics
are very good (including 3d plotting). Supports audio output (and
input?),
but does not do realtime processing. Simulink is an addon
product
that allows you to simulate systems using graphical buildingblocks,
and
there are toolboxes for this product as well that apply to DSP.
For
nonstudents, MATLAB can be extremely expensive. There are many
books that feature MATLAB code (much of which can be ported to Octave
fairly easily).
There are several other software packages, freely available, that are similar
to Octave and MATLAB. These include Scilab and Rlab. See the discussion at http://www.dspguru.com/sw/opendsp/mathclo.htm
for details.
DSPSpecific Software
Many packages are available that are specific to creating and analyzing
digital filters (and in many cases, other more advanced DSP operations).
In some cases, code can be generated automatically, targeting either specific
DSP chips (in assembly or C language), or generic C code. The trade off
is flexibility vs. turnkey operation. As discussed below, the low cost
and high function of generic mathematics packages with DSP support probably
makes them a better value for US students and those interested in learning
more about DSP as a subject, while the DSPspecific packages will require
less learning in order to generate viable digital filters. (Both
comp.dsp
FAQ and dspGuru.com
contain more information.)
MathCAD, Mathematica
Mathematica and MathCAD
are also popular mathematical environments, historically with an emphasis
on symbolic mathematics. However, DSP is possible in both packages, and
to a large extent comments applicable to Octave, MATLAB, and relatives apply to
these packages as well. It is also very handy to have a symbolic
mathematics package to verify derivations and other tasks common in traditional
DSP courses and their precursors. Good to excellent plotting capability
is present in these packages. DSPspecific extensions to Mathematica
are described in the comp.dsp
FAQ.
General Purpose Programming Languages
BASIC, C, Java, and other languages can all be used to design,
demonstrate,
and implement DSP. For learning DSP, however, it is very useful having
good plotting capabilitiesthe simplicity and power of the plotting
routines
in the mathematical packages is hard to beat. (Of course, you can
always export your data and use gnuplot or similar for plotting.)
In addition, the interactive
nature of the mathematical packages is nice to have, as it allows more
of a exploration of the processing than a batchmode environment.
While the design and implementation of many digital filters is fairly
straightforward,
it is very convenient having readymade functions to both design and
implement
DSP operations, as are available in the mathematical packages.
Likewise,
other tools such as wavelets or the FFT are fairly easy to write if
performance
is not an issue, but are very sensitive to coding if speed is very
important.
Numerically intensive operations like the FFT are optimized in the math
packages.
In some cases you may want to create a standalone program that
implements your DSP task. For example, a filter that despeckles
an image using a median filter. In this case a useful strategy is
to prototype the program using Octave, where it is fast and easy to
make changes and see what is going on, and then to write the code using
C, ObjectiveC, or what have you. You can then compare the output
or intermediate results with the Octave code to verify operation, but
you'll end up with a smaller and likely faster program, especially if
you are able to take advantage of operating system calls that implement
DSP operations using vector processing abilities that are now fairly
standard on modern PC's (e.g., PowerPC's AltiVec, Intel's SSE).
Spreadsheets
Spreadsheets can offer both good plotting and simple data manipulation
abilities. However, they are fairly constrained when compared to mathematical
packages, or even general purpose languages (though the interactive nature
of the spreadsheet is a positive). Environments like Octave would likely be much more productive.
Software Used in Texts
A recent trend is for text books to integrate computerbased exercises
and examples. By far the most common software used is MATLAB. While
this
is quite beneficial to the average US engineering student (who not only
may purchase the software relatively inexpensivelyon the order of
$100but
will probably use it for many classes), the high cost of the full
version
of MATLAB is a barrier to the nonstudent reader. As discussed
above, Octave may be a reasonable replacement as the language is quite
similar, however some functions might need to be written.
It should also be noted that if you have a specific processing needsuch
as signal analysis with the FFT, speech compression or synthesis, or processing
audio filesthere are often readymade programs that are freely available.
The source code is not always public, but if the function is sufficient,
this is by far the easiest method to perform very specific DSP jobs. Even
if you do avail yourself of these prepackaged solutions, you will probably
benefit from doing a little additional reading on DSP, to get a basic idea
of what's going on "under the hood" and what limits there are to the processing
that is occurring. The comp.dsp
FAQ lists a number of such programs; a web search on appropriate keywords
would also be productive.
RealTime Hardware
Most DSP algorithms are not very complicated.
It's true. In fact, some of the most
important DSP functions are implemented by a simple repeated
multiplication
and summation operation, and could be written out in a BASIC program
that nearly anyone could understand. However, the speed with which the
algorithms must
operate often requires specialized microprocessors ("DSP chips") in
order
to run in realtime. While DSP chips have many similarities with
generalpurpose
microprocessors, they have an architecture tuned to common DSP
operations,
and the programming of such hardware (sometimes in assembly language)
for maximum
performance is a skill that must be acquired.
The good news is that most major DSP manufacturers (e.g., Motorola,
Texas
Instruments, Analog
Devices, etc.) now provide lowcost evaluation platforms for their
DSP chips. Generally $100$500, these kits typically include the DSP chip
on a board with memory and analog input/output sufficient to do some real
time processing of audio and other low bandwidth signals. Software almost
always includes assemblers, linkers, and simulators. A C compiler is often
available. (The fact that a C compiler can be used does not invalidate
the need for the programmer to understand the architecture of the DSP chip,
though if the application represents a very light load on the processor,
the programmer can postpone detailed study during earlier stages in the
design process.) A major factor in choosing a DSP chip is whether
it employs floating or fixed point math. Fixedpoint chips are generally
much cheaper, but floating point chips are easier to program (since one
does not have to worry about certain effects the fixedpoint math can produce).
These kits are an excellent way to explore the implementation issues
of realtime DSP. However, they are typically not a great way on their
own to learn the theory of DSPthis is best accomplished using the texts
noted above and software environments that allow better debugging, visualization,
quick modification, and less complicated programming environment.
In addition, it should be noted that if the processing needs are not
great, it is possible to do DSP using a generalpurpose microprocessor.
DSP need not require a DSP chip; it is (usually) a series of rather simple
mathematical operations on a set of numbers representing a signal. It is
entirely possible to do DSP using a PC in realtime for many types of signals (such as audio).
Lest the wrong impression be given, it should be noted that many people
will never require their particular digital signal processing occur in real time. For example, their data
might be processed in batches, or be data that has no time component (such
as images). Implementation of DSP on DSP chips is an additional skill,
and one which will be entirely optional to many people who require DSP
in their work.
Formal Training
What if you prefer to learn in a more structured way? Universities and
companies offer a variety of short and/or evening courses on DSP. (See
the comp.dsp FAQ for
one list.) The quality of this training, according to some people who have
attended, can vary from good to bad. Universitybased courses may still
follow tradition and begin their classes with so much mathematics that
the fledgling student may have trouble learning the simplicity and beauty
of DSP. As Rick Lyons likes to say: "DSP training that's too rich in mathematics
is hard for beginners to digest." Note also that many technical conferences
are beginning to provide tutorial signal processing lectures. (DSP World,
ICSPAT, and the Wireless Symposium are examples.)
We should also begin to see more DSP courses offered as part of the
standard course offerings that package DSP up for the nonengineer (recall
"DSP First" mentioned above, and Stein's text for computer science students).
Though this may involve a much larger time commitment than alternatives,
it may be worthwhile in that you would be able to ask questions of the
instructor, and there may be labs with realtime DSP hardware set up and
ready to go, along with the equipment to generate and analyze signals.
Summary
Digital signal processing is not impossible to learn, it doesn't require
a PhD in mathematics, and it really can be useful even if you only ever
learn some basic tools. DSP can be done on almost any hardware and using
almost any softwareit is just a question of how fast you need the processing
done. You can learn DSP using a variety of software, including some excellent free programs. There are now texts
and other resources aimed at the nonengineer, and it has never been easier
to experiment with signal processingeven in real time. So get a book,
download some files, and process some signals.
A 60Second Overview of DSP
Start your clock. Here is very brief overview of some of the basic tools
and concepts in DSP.
Why use DSP?

Software basedcan change behavior by changing software.

Powerfulcan do more things than you can do using analog hardware (though
sometimes not as fast).

Cheapsimilar to microprocessors, you can pack a lot of different functions
into one chip.

Arbitrary precision.

Behavior doesn't change with age.
Digital Signals
Sample the analog signal at some regular interval (fast enough to accurately
describe the signal, with enough resolution to keep the noise level low),
and in doing so convert the signal into a long list of numbers that represent
the amplitude (e.g., voltage) of the signal at these points. This is usually
done with an analogtodigital converter.
Processing Digital Signals
The key to DSP is that instead of using opamps, resistors, and other analog
electronics to process an analog signal, you can use a microprocessor (or
specialized microprocessor, as in a DSP chip) to perform mathematical operations
on that list of numbers (the digital signal) to achieve the same (or better)
effect. For example, this might filter out high frequencies, or translate
the signal into another, more useful form (e.g., using the "FFT"). Optionallythough
usuallyyou can convert the resulting list of numbers back into an analog
signal using a digitaltoanalog converter.
(Digital) Filters
As a generalization, digital filters pass certain frequencies while stopping
others. Taking the average of the last 7 daily temperature readings filters
out temperature changes on a daily level. This is a bona fide digital lowpass
digital filter (of the "FIR"finite impulse responsevariety).
Another simple way of filtering a signal would be to take a weighted combination
of the last average and the current reading, and to use this combination
as a new average. This new average, in combination with the next
reading, is used to compute the next average, and so on. This is another
example of a digital lowpass filter (a type known as "IIR"infinite
impulse
response).
Most basic digital filters are just variations on these two themes.
The hardest part is in specifying the desired behavior of the filters and
determining how to combine past input values and past output values to
get this desired behavior (i.e., determining the weights or coefficients).
Often, you just punch in numbers to a software package to calculate the
relevant coefficients, which you plug into very simple algorithms (a fact
that some texts seem to treat like a state secret!).
Spectral Analysis
What frequencies are present in a signal? That is, if you had a filter
that you could tune to just let a narrow band of frequencies through (kind
of like tuning a radio), at what frequencies would parts of the signal
come through? Or, alternatively, what sine waves (i.e., at what frequency
and with what shift) should be added to create a duplicate of a given signal?
The FFT and other related techniques give a picture of a signal in terms
of frequencysomewhat like the display on an audio equalizer shows the
energy at different frequencies of an audio signal.
This Document
This is not intended as a comprehensive review of DSP, but instead as a
framework for pointing the DSP newcomer to some useful approaches to learning
DSP. If there are issues that you feel should be addressed that would
be helpful to the DSP newcomer, comments are welcomesend them to dgrover@redcedar.com.
The most uptodate version of this document can be found at www.redcedar.com.
Nonprofit distribution of this document is permitted as long as this document
is not altered and this notice remains. Specific permission is granted
www.dspGuru.com and the comp.dsp and comp.speech.* newsgroups and associated
FAQ's to include this document.
MATLAB, Mathematica, dspGuru, MathCAD, and others are registered trademarks.
Copyright 2002, Red Cedar Electronics.