Steve Underwood wrote:> Randy Yates wrote: > > Steve Underwood writes: > > >> 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. > > > In the US, when and where I grew up (Panama City, FL, high school class > > of 1976), the "fast-track" math program went like this: > > > � Grade � Course > > � ----- � ------ > > � 8 � � � Algebra I > > � 9 � � � Geometry > > � 10 � � �Algebra II > > � 11 � � �Trigonometry and Analytical Geometry > > � 12 � � �Math Analysis (pretty much Calc I) > > > At 12, I was in the 6th grade. You had "basic trig and algebra" in 5th > > grade or earlier? > > That appears to mean > > � � Age � � �Course > � �----- � � ------ > � � �14 � � �Algebra I > � � �15 � � �Geometry > � � �16 � � �Algebra II > � � �17 � � �Trigonometry and Analytical Geometry > � � �18 � � �Math Analysis (pretty much Calc I) > > Surely something is wrong with that time line. In the UK we move (moved) > from primary school to high school at 11. In the first year at high > school we did quite a bit of basic algebra and trig. I followed what the > UK called a modern maths course, which involved a lot of logic, set > theory and so on. That caused us to meet calculus later than in the > traditional maths courses, and made a lot of people complain about > modern maths. We'd still done some basic calculus at 16, though.I went to a high school in South Africa. I really don't remember much from the maths or the science classes (I was a complete zero in those subjects, quickly dropping from higher to standard grade in maths and physics simultaneously - my talent lay with languages). I remember doing some geometry, but I'm pretty sure we didn't have any trigonometry or, god forbid, calculus. If we did, it passed me by completely. I finished high school with 17. The first time I saw "j" or some calculus was in my second year taking a Bachelors in EE (age, let me count, ... uh ... , oh my: 22). Regards, Andor
Possibly unrelated questions
Started by ●February 15, 2008
Reply by ●February 16, 20082008-02-16
Reply by ●February 16, 20082008-02-16
On Sat, 16 Feb 2008 07:50:20 -0800 (PST), Rune Allnor <allnor@tele.ntnu.no> wrote:>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. > >RuneHi Rune, I bought that book some time ago based solely on the list of authors. Wow, what a "dream team" of DSP pioneers!!! (That list of names on a DSP book is equivalent to having a book about acting in the movies written by Spencer Tracy, Humphrey Bogart, John Wayne, Jimmy Stewart, Paul Newman, and Robert De Niro.) As for the book, it covers a *VERY* wide range of DSP topics and it contains very many useful "snippets" of DSP theory, and a huge collection of very interesting (and educational) DSP problems for the reader to solve. The book is not for beginners though, because the maths is fairly "heavy". But for someone who is somewhat accustomed to the algebra of DSP equations, the book should pose no severe problems. It seems to me that it would take about a year to go through the book and experiment, using MATLAB, with roughly %80 of the material in the book. In any case, I think that book is certainly a super valuable book. (Assuming, of course, that you have the Sig Proc toolbox routines for MATLAB.) [-Rick-]
Reply by ●February 16, 20082008-02-16
Steve Underwood <steveu@dis.org> writes:> Randy Yates wrote: >> Steve Underwood <steveu@dis.org> writes: >> >>> 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. >> >> In the US, when and where I grew up (Panama City, FL, high school class >> of 1976), the "fast-track" math program went like this: >> >> Grade Course >> ----- ------ >> 8 Algebra I >> 9 Geometry >> 10 Algebra II >> 11 Trigonometry and Analytical Geometry >> 12 Math Analysis (pretty much Calc I) >> >> At 12, I was in the 6th grade. You had "basic trig and algebra" in 5th >> grade or earlier? > > That appears to mean > > Age Course > ----- ------ > 14 Algebra I > 15 Geometry > 16 Algebra II > 17 Trigonometry and Analytical Geometry > 18 Math Analysis (pretty much Calc I)It depends on whether you consider these ages the starting ages or ending ages. I started 8th grade at 13 and finished at 14. Also, many students graduated at 17 and not 18. Between these two factors, the ages above could be two years too high. But even so, you seem to have (had) a curriculum that was well advanced of ours. I definitely think advancing sooner is better. To go back even further, best I can recall, the early math went like this: Grade Math ----- ------ 1 simple addition (one and two digits) 2 complex addition and subtraction 3 multiplication 4 division 5-7 negative numbers, percentages, fractions, factoring Do you have 12 grades in the UK? What age do you start 1st? We usually start first grade at age 5 or 6. That could be sped up a bit, in my opinion, and the material around 5th-7th grades could be compressed. -- % Randy Yates % "Watching all the days go by... %% Fuquay-Varina, NC % Who are you and who am I?" %%% 919-577-9882 % 'Mission (A World Record)', %%%% <yates@ieee.org> % *A New World Record*, ELO http://www.digitalsignallabs.com
Reply by ●February 16, 20082008-02-16
On 17 Feb, 01:06, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote:> On Sat, 16 Feb 2008 07:50:20 -0800 (PST), Rune Allnor > <all...@tele.ntnu.no> wrote: > >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....> The book is not for beginners though, because the > maths is fairly "heavy". �But for someone who is > somewhat accustomed to the algebra of DSP equations, > the book should pose no severe problems.Well, I agree that it might be a challenge for the beginner. As a collection of exercises for a college or university DSP program it would be invaluable, after a couple of small modifications. Rune
Reply by ●February 16, 20082008-02-16
On 16 Feb, 22:15, Andor <andor.bari...@gmail.com> wrote:> Steve Underwood wrote: > > Randy Yates wrote: > > > Steve Underwood writes: > > > >> 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. > > > > In the US, when and where I grew up (Panama City, FL, high school class > > > of 1976), the "fast-track" math program went like this: > > > > � Grade � Course > > > � ----- � ------ > > > � 8 � � � Algebra I > > > � 9 � � � Geometry > > > � 10 � � �Algebra II > > > � 11 � � �Trigonometry and Analytical Geometry > > > � 12 � � �Math Analysis (pretty much Calc I) > > > > At 12, I was in the 6th grade. You had "basic trig and algebra" in 5th > > > grade or earlier? > > > That appears to mean > > > � � Age � � �Course > > � �----- � � ------ > > � � �14 � � �Algebra I > > � � �15 � � �Geometry > > � � �16 � � �Algebra II > > � � �17 � � �Trigonometry and Analytical Geometry > > � � �18 � � �Math Analysis (pretty much Calc I) > > > Surely something is wrong with that time line. In the UK we move (moved) > > from primary school to high school at 11. In the first year at high > > school we did quite a bit of basic algebra and trig. I followed what the > > UK called a modern maths course, which involved a lot of logic, set > > theory and so on. That caused us to meet calculus later than in the > > traditional maths courses, and made a lot of people complain about > > modern maths. We'd still done some basic calculus at 16, though. > > I went to a high school in South Africa. I really don't remember much > from the maths or the science classes (I was a complete zero in those > subjects, quickly dropping from higher to standard grade in maths and > physics simultaneously - my talent lay with languages). I remember > doing some geometry, but I'm pretty sure we didn't have any > trigonometry or, god forbid, calculus. If we did, it passed me by > completely. I finished high school with 17. The first time I saw "j" > or some calculus was in my second year taking a Bachelors in EE (age, > let me count, ... uh ... , oh my: 22).Eh... don't know the proper English terms for the schools I took, but I learned basic vector algebra at 17, basic function analysis and algebra (exponentials and logarithms) at age 18, then one year pause for military service, the first linear algebra and complex numbers around age 20-21... The two things I can remember as standing out, was first when I understood some key aspect of statistics (around age 20). I was very excited about having cracked that nut, and sat in the canteen and explained my newfound insight for a classmate I knew struggled with the same material. I can remember seeing his face change from eagerness to polite disinterest as I explained. When I reviewed my explanation to find out why (I knew he was as eager as myself to get into this), I realized that I had used the exact same words and phrases -- verbatim -- as in the textbook. What had changed was that they were no longer incomprehensable phrases, I understood what they meant. The other episode was a friend of mine, who had to take one year over again at college, who expressed a fascination for linear algebra. I had taken the same class -- did fairly well at the exams, too -- but had been very happy to see the end of the compulsary linear algebra stuff. When this guy came and talked fondly of linear algebra, I realized there must have been something there I hadn't discovered (and yes, being made aware of this by somebody whose academic track record was less than impressive played a major part in my renewed interest). When I later went to university (started there at age 23) I took a voluntary linear algebra class just to find out what this was all about (and, of course, restore my pride). After that there was no turning back. I have ever since gone to great lengths to describe whatever I was doing in terms of linear algebra. Rune
Reply by ●February 16, 20082008-02-16
Rune Allnor wrote:> 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.There's no question of math's importance. Actually, all the math we need boils down to algebra and maybe trig. higher math is like -- no, it is -- a collection of high-level languages that reduce a lot of details to single -- therefore simple-- abstraction. I can't imagine doing Waves and Fields without vector analysis. It took a genius like Maxwell to do that. I can imagine doing physics (mechanics) without vector analysis (it's usually taught that way) but vector analysis simplifies and enlightens the subject more than most people realize. Del cross V is all very nice; cross products and dot products have marvelously intuitive meanings when you know them well enough to get cozy. Still, is curl a fundamental property of fluids, akin to mass and viscosity? Math is a tool. It's hard to do any job without proper tools* The question I raised is whether the tool represents reality or only method. Jerry _______________________________________ * But I once saw a man raise a beautiful cup from a lump of silver, using only a tree stump, some stones, an open fire, and a deer antler. -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 17, 20082008-02-17
Jerry Avins wrote: (snip)> 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.Some of the time I agree. I was watching the usual car commercial where the (aliased) wheels are turning slowly backwards and realized that sometimes negative frequencies do exist. -- glen
Reply by ●February 17, 20082008-02-17
glen herrmannsfeldt wrote:> Jerry Avins wrote: > (snip) > >> 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. > > > Some of the time I agree. > > I was watching the usual car commercial where the (aliased) wheels > are turning slowly backwards and realized that sometimes negative > frequencies do exist. > > -- glen >Never thought of stroboscopic effects in terms of sampling theory. Are wheels going "backwards" and stop/slow motion effects generally really an aliasing effect or artifact of not meeting a Nyquist related criterion?
Reply by ●February 17, 20082008-02-17
On 17 Feb, 12:33, Richard Owlett <rowl...@atlascomm.net> wrote:> glen herrmannsfeldt wrote:> > I was watching the usual car commercial where the (aliased) wheels > > are turning slowly backwards and realized that sometimes negative > > frequencies do exist. > > > -- glen > > Never thought of stroboscopic effects in terms of sampling theory. Are > wheels going "backwards" and stop/slow motion effects generally really > an aliasing effect or artifact of not meeting a Nyquist related criterion?Sort of. The human visual system can only take in so much information per time, that's why we tend to see movies as 'flickering' when there are less than 15 or so frames per second. In spatial sampling (like in antennas and arrays arrays) one discrepancy is between forward and backward propagation; another is between Direction of Arrival. But don't take the analogy too far; in time domain it suffices to note that one can not use the data unless Nyquist's criterion is met. Rune
Reply by ●February 17, 20082008-02-17
"Richard Owlett" <rowlett@atlascomm.net> wrote in message news:13rg6q7a1esbs64@news.supernews.com...> glen herrmannsfeldt wrote:>> I was watching the usual car >> commercial where the (aliased) wheels >> are turning slowly backwards and >> realized that sometimes negative >> frequencies do exist. >> > Never thought of stroboscopic effects in terms of sampling > theory. Are wheels going "backwards" and stop/slow > motion effects generally really an aliasing effect or > artifact of not > meeting a Nyquist related criterion? >I slightly disagree with Rune's answer, "sort of". Assuming your question is posed to need a Yes/No answer, I think the answer is "absolutely". In other words, the flash of a strobe (or the wink of the camera) is "sampling", regardless of what the eye does later with the stream of images. It gets really interesting when a frames of film are re-sampled for the TV frame rate. Note: your question could also be interpreted to require an answer of "aliasing effect" vs. "artifact of not meeting a Nyquist related criterion". I would point out that these two are the same thing, so a Yes vs. No answer is appropriate.
