SteveSmith wrote:> Hi Richard, > One of your comments gave me a little laugh-- > > "I don't have too much problem with complex notation and its advantages > per se." > > In contrast, I have a terrible problem with complex notation. I'd even go > so far at to call it the "scourge of DSP." Let me stand on my soap box a > bit. > > There is no question that complex numbers are elegant and enable some > techniques that could not be achieved otherwise. A good example of this > is the FFT. They also provide a compact and efficient way of handling the > mathematics of DSP. So don't get me wrong; complex notation is a powerful > and useful method. > > However, the vast majority of practical DSP techniques gain no benefit at > all from using complex numbers. This includes the big three: > Convolution, Spectral Analysis, and Basic Filtering. My mission over the > years has been to show that 99% of useful DSP methods can be understood > without needing to resort to complex notation. In my mind, complex > methods should be viewed as an advanced subject; a second tier of > education. For instance, this is how I structured my book. Out of 33 > chapters, I don't use complex numbers until the last four. If interested, > see www.DSPguide.com. Try starting with Chapter 14. This isn't to > downplay other references-- for instance, Rick Lyons book' is really > outstanding. I just wanted to give you an alternative approach that may > mesh better with your background. > > Why is this so personal to me? I came through a conventional Ph.D. > program in EE with emphasis on DSP. My primary mentor was Tom Stockham, a > pioneer in the field and an outstanding instructor. And I did well-- > nothing but "A"s. Then I hit industry with quite a shock. I could do > integrals like crazy, but couldn't design even the most basic filters. > The primary reason I wrote my book was to teach myself useful DSP > techniques-- what I should have learned in college, but didn't because > they were too busy teaching me complex math. > > Soap box speech over. Good luck! > > Regards, > SteveHumm, keep downloading chapters, maybe should buy the book ;)
Possibly unrelated questions
Started by ●February 15, 2008
Reply by ●February 16, 20082008-02-16
Reply by ●February 16, 20082008-02-16
On the topic of "What I never learned in school", in another newsgroup I was pointed to http://www.sjsu.edu/faculty/watkins/sphere.htm . The author, Thayer Watkins, says: "This lack of recent texts on spherical geometry and trigonometry is puzzling because the use of computers should shift the emphasis from numerical computation to theory. This page is an attempt to present derivations of important results from spherical geometry and trigonometry." In fact, I was first asked why I didn't use an readily available canned solution before being referred to that page.
Reply by ●February 16, 20082008-02-16
On 16 Feb, 14:41, Richard Owlett <rowl...@atlascomm.net> wrote:> On the topic of "What I never learned in school", in another newsgroup I > was pointed tohttp://www.sjsu.edu/faculty/watkins/sphere.htm. > > The author, Thayer Watkins, says: > "This lack of recent texts on spherical geometry and trigonometry is > puzzling because the use of computers should shift the emphasis from > numerical computation to theory. This page is an attempt to present > derivations of important results from spherical geometry and trigonometry." > > In fact, I was first asked why I didn't use an readily available canned > solution before being referred to that page.This Watkins guy is wrong. Using computers doesn't shift emphasis towards theory, it sifts emphasis towards nothing at all. Students no longer ask 'how can I acieve this result', they ask 'what function in matlab [or whatever SW package] should I use to...'. Rune
Reply by ●February 16, 20082008-02-16
On 15 Feb, 21:16, "SteveSmith" <Steve.Smi...@SpectrumSDI.com> wrote:>�Then I hit industry with quite a shock. �I could do > integrals like crazy, but couldn't design even the most basic filters. > The primary reason I wrote my book was to teach myself useful DSP > techniques-- what I should have learned in college, but didn't because > they were too busy teaching me complex math.I would like to hear your opinions on McClellan, Burrus, Oppenheim, Parks, Schafer & Schuessler: "Computer-based excercises for Signal Processing Using Matlab 5", Pearson Education, 1998. The book contains lots of nifty excercises, ranging from basics to advanced applications. I have three main objections against the book: 1) It is based on students having the matlab Signal Processing Toolbox available. I would prefer to include a number of excercises where the students implement their own filter design algorithms, spectrum estimators etc. 2) The title mentions Matlab version 5 explicitly. Lots of the stuff still works with Matlab 7; had the authors had students implement the basic functionality, this would be a timeless classic. 3) It has not (to my knowledge) been updated since it was published. Rune
Reply by ●February 16, 20082008-02-16
Rune Allnor wrote:> On 16 Feb, 14:41, Richard Owlett <rowl...@atlascomm.net> wrote: > >>On the topic of "What I never learned in school", in another newsgroup I >>was pointed tohttp://www.sjsu.edu/faculty/watkins/sphere.htm. >> >>The author, Thayer Watkins, says: >>"This lack of recent texts on spherical geometry and trigonometry is >>puzzling because the use of computers should shift the emphasis from >>numerical computation to theory. This page is an attempt to present >>derivations of important results from spherical geometry and trigonometry." >> >>In fact, I was first asked why I didn't use an readily available canned >>solution before being referred to that page. > > > This Watkins guy is wrong. Using computers doesn't shift > emphasis towards theory, it sifts emphasis towards nothing > at all. Students no longer ask 'how can I acieve this > result', they ask 'what function in matlab [or whatever > SW package] should I use to...'. > > RuneReread the quote. He said *should* not does. You are agreeing. Perhaps I should have quoted more context.
Reply by ●February 16, 20082008-02-16
Rick Lyons wrote:> On Fri, 15 Feb 2008 14:16:22 -0600, "SteveSmith" > <Steve.Smith1@SpectrumSDI.com> wrote: > >> Hi Richard, >> One of your comments gave me a little laugh-- >> >> "I don't have too much problem with complex notation and its advantages >> per se." >> >> In contrast, I have a terrible problem with complex notation. I'd even go >> so far at to call it the "scourge of DSP." Let me stand on my soap box a >> bit. >> >> There is no question that complex numbers are elegant and enable some >> techniques that could not be achieved otherwise. A good example of this >> is the FFT. They also provide a compact and efficient way of handling the >> mathematics of DSP. So don't get me wrong; complex notation is a powerful >> and useful method. >> >> However, the vast majority of practical DSP techniques gain no benefit at >> all from using complex numbers. This includes the big three: >> Convolution, Spectral Analysis, and Basic Filtering. My mission over the >> years has been to show that 99% of useful DSP methods can be understood >> without needing to resort to complex notation. In my mind, complex >> methods should be viewed as an advanced subject; a second tier of >> education. For instance, this is how I structured my book. Out of 33 >> chapters, I don't use complex numbers until the last four. If interested, >> see www.DSPguide.com. Try starting with Chapter 14. This isn't to >> downplay other references-- for instance, Rick Lyons book' is really >> outstanding. I just wanted to give you an alternative approach that may >> mesh better with your background. >> >> Why is this so personal to me? I came through a conventional Ph.D. >> program in EE with emphasis on DSP. My primary mentor was Tom Stockham, a >> pioneer in the field and an outstanding instructor. And I did well-- >> nothing but "A"s. Then I hit industry with quite a shock. I could do >> integrals like crazy, but couldn't design even the most basic filters. >> The primary reason I wrote my book was to teach myself useful DSP >> techniques-- what I should have learned in college, but didn't because >> they were too busy teaching me complex math. >> >> Soap box speech over. Good luck! >> >> Regards, >> Steve > > Hi Steve, > your post was fun to read. > Your thoughts on complex notation certainly made > me recall my education and my working career > after graduation. I worked as a EE for over > twenty years and I can't recall having to think > about complex notation in my daily working life. > > Upon my graduation with my EE degree I assumed > complex notation (and "convolution", as well) > were merely concepts created by professors to > make my life, as a student, as miserable > as possible. > > It wasn't until I became interested in DSP that > I began to try to understand what in the heck > does that "j-operator" mean. That time period > was frustrating for me because the j-operator > seemed (at that time) to have *NO* physical > meaning. For example, I couldn't go to Radio > Shack and buy a "j-operator" and solder it on > a printed circuit board. Anyway, now I have > what I think is a fairly good idea of how > and why the j-operator is useful in describing > and processing sinusoidal signals. > > You mentioned your shock when you entered the > "working world". Ha ha. I agree completely. > When I entered the working world I was able > to perform partial fraction expansions > but I was *UNABLE*, in any meaningful way, to > use an oscilloscope, a spectrum analyzer, > or a logic state analyzer! When I graduated > I thought I was pretty "hot stuff". Little > did I know that as a new graduate engineer I was, > as Australians would say, about as useless as > a hat full of busted a__holes. :-) > > Steve, you studied under Thomas Stockham huh? Neat! > I never met Stockham (and never will because he passed > away not long ago) but I've read that he was > famous for: > > * proposing (popularizing?) the process of > "fast convolution" (filtering by way of > freq-domain multiplication) > > * developing the "butterfly structure" descriptions > of various FFT algorithms > > * being the leader in the invention of the > compact disk (CD). > > Steve, did Stockham ever talk about his work > trying to "analyze" the infamous Nixon Watergate > audio tapes? > > [-Rick-]There are a number of very smart people posting in this news group, yet most complain about complex numbers. I've come to realise that my own schooling was a little unusual by global standards. We studied complex numbers at about 12 years of age, not long after basic trig and algebra, and before we had touched any calculus. I grew up thinking of complex numbers as completely natural - more natural than anything non-complex. Maybe the unusual order of our maths syllabus was the better one. Steve
Reply by ●February 16, 20082008-02-16
Eric Jacobsen wrote:> On Fri, 15 Feb 2008 21:00:35 -0500, Jerry Avins <jya@ieee.org> wrote: > >> Thank you for that speech. I've said in the past that all of electronics >> can be done without imaginary numbers. (Maxwell wrote his Treatise using >> sets of three integral equations and trigonometry to develop his famous >> equations.) The mathematics is simplified by complex algebra (I use it >> when others use trig) but it introduces artifacts such as negative >> frequencies. Some of the young whippersnappers here firmly believe that >> complex quantities and negative frequencies are fundamental, inherent in >> the nature of the universe. Some even hold that a single wire loop can >> carry a complex signal. >> >> I'm relieved to have someone to join me on my occasional soap box. >> >> Jerry > > It ain't just the young whippersnappers...I'll be happy to take up > that side of the argument again any time. ;) > > It does take a little bit of standing on one's head and holding the > mirror just right, tho...There's no question that complex algebra is simpler than -- and therefore illuminates -- trigonometry. Trigonometry is (was?) an optional one-semester course in the New York City high-school curriculum. A young friend who hadn't taken the course wanted to test out by taking the Regents exam* two weeks away. I taught him the entire syllabus, identities and all, with time to spare by building on his prior acquaintance with complex algebra. (He aced the test.) The question is whether imaginary numbers and negative frequencies are inherent qualities of the real world, or whether they are scaffolding for the simplified mathematics that we use to describe it. I hold to the latter alternative. Jerry _________________________________________ * Regents exams are (were?) statewide standard tests required for credit in some courses in public high schools. A larger number were required for graduation, so students could chose which ones to skip. Private-school students needed some also in order to qualify for state scholarships. -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 16, 20082008-02-16
Rune Allnor wrote:> On 16 Feb, 03:00, Jerry Avins <j...@ieee.org> wrote: >> SteveSmith wrote: > >>> The primary reason I wrote my book was to teach myself useful DSP >>> techniques-- what I should have learned in college, but didn't because >>> they were too busy teaching me complex math. >>> Soap box speech over. Good luck! >> Thank you for that speech. I've said in the past that all of electronics >> can be done without imaginary numbers. (Maxwell wrote his Treatise using >> sets of three integral equations and trigonometry to develop his famous >> equations.) The mathematics is simplified by complex algebra (I use it >> when others use trig) but it introduces artifacts such as negative >> frequencies. > > Well, I have to take the oposite view: The usual DSP education > programs do not teach enough maths.No you don't. You misread what I intended to say. Read my response to Eric J. ...> So any soap-box speaches on maths should be directed > against those who fail to learn kids and students the > required maths.That's a different topic, and one I would approach in a different way. I agree that math is fundamental to understanding many things and is insufficiently taught. Notice that most universities teach math in the Liberal Arts Department. Math is indeed one of the liberal arts. Integral calculus should be a prerequisite for any bachelor's degree. Your superior's important lack was not knowledge of math, but a lack of understanding (or an unwillingness to admit) that math was important to their decision. Few managers are as competent in all fields as some of their subordinates are in some. Wise managers defer in those cases. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 16, 20082008-02-16
On 16 Feb, 18:13, Jerry Avins <j...@ieee.org> wrote:> Your superior's important lack was not knowledge of math, but a lack of > understanding (or an unwillingness to admit) that math was important to > their decision. Few managers are as competent in all fields as some of > their subordinates are in some. Wise managers defer in those cases.I have mentioned that incident several times before: One reason why I could not communicate with those people was that I went beyond the 'usual' or 'accepted' interpretations of the problem; another was that I could not express the solution in terms of an equivalent RLC cirquit. Those are the sort of 'physical' constraints that become more and more important as DSP becomes more mature. I believe advocates of the 'physical' approach to DSP think DSP is an alternative implementation of RLC cirquits and nothing more. My view, on the other hand, is that DSP is about applied maths and needs to be approached on its own terms. If one can detatch oneself from intuition and 'physics' as far as possible, one stands a better chance to find useful solutions. In that setting, a claim like 'complex numbers are not needed for practical DSP' is tantamount to sabotage. I would go for Rick's approach to complex numbers, 'here is what you need to know about complex numbers, presented as gently as possible' every time. Rune
Reply by ●February 16, 20082008-02-16
On 16 Feb, 17:48, Steve Underwood <ste...@dis.org> wrote:> There are a number of very smart people posting in this news group, yet > most complain about complex numbers.Complex numbers, Dirac's Delta, continuous functions vs discrete sequences... there are few threads here these days that avoid getting sidetracked by basic stuff I used to take for granted was well understood by everyone.> I've come to realise that my own > schooling was a little unusual by global standards. We studied complex > numbers at about 12 years of age, not long after basic trig and algebra, > and before we had touched any calculus. I grew up thinking of complex > numbers as completely natural - more natural than anything non-complex. > Maybe the unusual order of our maths syllabus was the better one.I think so. Or maybe your maths teachers were unusually skilled. Rune
