On 8/26/2011 2:43 PM, robert bristow-johnson wrote:> On 8/26/11 2:34 PM, Jerry Avins wrote: >> On 8/26/2011 2:07 PM, dbd wrote: >>> On Aug 26, 8:05 am, dvsarwate<dvsarw...@yahoo.com> wrote: >>>> >>>> Wouldn't that be the second harmonic? or has >>>> audio terminology changed from earlier times? >>>> Jerry? >>>> >>> >>> Oh No! The dreaded "Do we start counting [from] zero or one?" topic >>> again! >> >> Oh No indeed! "First harmonic" is synonymous with "fundamental". (The >> zeroth harmonic is DC.) If Raeldor meant "the first harmonic not in the >> original", that would also be correct. >> > > it's more like counting from one or from two. there are some folks > (usually musicians) that count the "first overtone" as being what we > call the second harmonic.Which shows again that "overtone" and "harmonic" aren't synonyms. Jerry -- Engineering is the art of making what you want from things you can get.
FFT and Sine Waves Question
Started by ●August 26, 2011
Reply by ●August 26, 20112011-08-26
Reply by ●August 27, 20112011-08-27
On 8/26/11 10:58 PM, Jerry Avins wrote:> On 8/26/2011 2:43 PM, robert bristow-johnson wrote: >> On 8/26/11 2:34 PM, Jerry Avins wrote: >>> On 8/26/2011 2:07 PM, dbd wrote: >>>> On Aug 26, 8:05 am, dvsarwate<dvsarw...@yahoo.com> wrote: >>>>> >>>>> Wouldn't that be the second harmonic? or has >>>>> audio terminology changed from earlier times? >>>>> Jerry? >>>>> >>>> >>>> Oh No! The dreaded "Do we start counting [from] zero or one?" topic >>>> again! >>> >>> Oh No indeed! "First harmonic" is synonymous with "fundamental". (The >>> zeroth harmonic is DC.) If Raeldor meant "the first harmonic not in the >>> original", that would also be correct. >>> >> >> it's more like counting from one or from two. there are some folks >> (usually musicians) that count the "first overtone" as being what we >> call the second harmonic. > > Which shows again that "overtone" and "harmonic" aren't synonyms. >yup. for multiple reasons. "harmonic" implies an integer multiple of some common fundamental. there are instruments (like bells) that have overtones that are not integer multiples of a common fundamental. unless that fundamental is a contrived frequency that is very, very low. given whatever precision of measurement of frequency, you can always find a greatest-common-factor of all the overtones and then call them "harmonic". -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●August 27, 20112011-08-27
On 8/26/2011 3:43 PM, dvsarwate wrote:> On Aug 26, 1:34 pm, Jerry Avins<j...@ieee.org> wrote: > >> >> Raeldor: The lowest distortion produce being at 2 KHz shows that the >> distortion is asymmetric. Symmetric distortion implies the presence of >> only odd harmonics, 1st, 3rd, 5th, etc. >> > > OK, now I am confused even further. If the input is x(t) > and the output is x(t) + 0.002[x(t)]^2, I would have thought > that the *distortion* would be called symmetric in the sense > that 0.002x^2 is an even function. But when x(t) = cos(wt), > the output is > > cos(wt) + 0.002 cos^2(wt) = 0.002 + cos(wt) + 0.002 cos(2wt), > > that is, the *distortion* was creating only the zeroth > harmonic and the second harmonic! But this is in direct > contradiction to Jerry's assertion that symmetric distortion > creates only odd harmonics. So, somewhere I must be > misunderstanding or maybe miscounting. Or did Jerry mean > to write that symmetric distortion creates only odd overtones > in the sense of rb-j's statement that musicians call the > second harmonic the first overtone?1. Consider a cosine so deeply clipped that it is indistinguishable from a square wave. I bet you know the spectrum by heart, so I won't repeat it here. 2. Why are push-pull amplifiers standard for low-distortion applications? 3. Is a graph of cos(wt) + D*cos^2(wt) symmetric? How about a graph of cos(wt) + D*cos^3(wt)? (Choose D large enough to be seen.) Jerry -- Engineering is the art of making what you want from things you can get.
Reply by ●August 27, 20112011-08-27
On 8/26/11 2:07 PM, dbd wrote:> On Aug 26, 8:05 am, dvsarwate<dvsarw...@yahoo.com> wrote: >> On Aug 26, 9:25 am, Raeldor<rael...@gmail.com> wrote: >> >> >> >>>>> I was doing some experimenting and was wondering if someone could >>>>> explain my results. I have a pure sine wave at 1000hz generated into >>>>> a wave file. >>> Yes, the first harmonic was definitely at 2000hz. >> >> Wouldn't that be the second harmonic? or has >> audio terminology changed from earlier times? >> Jerry? >> > > Oh No! The dreaded "Do we start counting with zero or one?" topic > again! >of course that's a settled topic. i'm with Dijkstra, quoting: http://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html "Real computer programmers count from 0. Anyone who insists on counting from 1 is either a douchebag or a MATLAB developer." -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●August 27, 20112011-08-27
On Aug 26, 8:16�pm, robert bristow-johnson <r...@audioimagination.com> wrote:> ... > > of course that's a settled topic. �i'm with Dijkstra, quoting: > > �http://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html > > "Real computer programmers count from 0. �Anyone who insists on counting > from 1 is either a douchebag or a MATLAB developer." > > -- > > r b-j � � � � � � � � �r...@audioimagination.com > > "Imagination is more important than knowledge."Robert You are becoming so advanced! You have progressed to your lying about quotations and your name calling even before everyone else has finished choosing sides! Dale B. Dalrymple
Reply by ●August 27, 20112011-08-27
On 8/27/11 1:59 AM, dbd wrote:> On Aug 26, 8:16 pm, robert bristow-johnson<r...@audioimagination.com> > wrote: >> ... >> >> of course that's a settled topic. i'm with Dijkstra, quoting: >> >> http://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html >> >> "Real computer programmers count from 0. Anyone who insists on counting >> from 1 is either a douchebag or a MATLAB developer." >> > > Robert > > You are becoming so advanced! You have progressed to your lying about > quotationshow would you know, Dale? did you read the Dijkstra reference from beginning to end? -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●August 27, 20112011-08-27
On 27/08/2011 15:45, robert bristow-johnson wrote:> On 8/27/11 1:59 AM, dbd wrote: >> On Aug 26, 8:16 pm, robert bristow-johnson<r...@audioimagination.com> >> wrote: >>> ... >>> >>> of course that's a settled topic. i'm with Dijkstra, quoting: >>> >>> http://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html >>> >>> "Real computer programmers count from 0. Anyone who insists on counting >>> from 1 is either a douchebag or a MATLAB developer." >>> >> >> Robert >> >> You are becoming so advanced! You have progressed to your lying about >> quotations > > how would you know, Dale? did you read the Dijkstra reference from > beginning to end? >The whole subject turns on the disjunct between ordinal and cardinal numbers. Sure, for computing, zero is the proper starting point, if only to make full and disinterested use of all the available integers in a given container. However, we also have every-day language to deal with, and in the case of harmonics, partials, etc, we think ordinally - "first", "second". A winner "comes first" in some competition, not "zeroth". I doubt anyone want to win "zeroth prize". And who would want to be hailed as "nullus inter pares"? Similarly, the fundamental is the first harmonic, among possibly many (where "harmonic" may be understood as "mode of vibration"). OK, if you want, the "zeroth harmonic" is DC, but that will always be somewhat contrived in language. Presented with a basket of ten apples, we count the apples to give the answer ten (and, no doubt, counted from one to ten inclusive), not eleven to include the basket itself, which is content-agnostic, just as DC is harmonic-agnostic. Everyday speech is almost exclusively ordinal in character, while cardinal counting from zero remains the best programmatic use of the available range of a number, etc etc etc. So programmers will continue counting from zero, hoping the zeroth apple will be available to consume, while all other carbon-based lifeforms, including musicians fretting about harmonics, will continue happily counting from one. Richard Dobson
Reply by ●August 27, 20112011-08-27
On 8/27/2011 12:09 PM, Richard Dobson wrote: ...> Similarly, the fundamental is the first harmonic, among possibly many > (where "harmonic" may be understood as "mode of vibration"). OK, if you > want, the "zeroth harmonic" is DC, but that will always be somewhat > contrived in language. Presented with a basket of ten apples, we count > the apples to give the answer ten (and, no doubt, counted from one to > ten inclusive), not eleven to include the basket itself, which is > content-agnostic, just as DC is harmonic-agnostic. Everyday speech is > almost exclusively ordinal in character, while cardinal counting from > zero remains the best programmatic use of the available range of a > number, etc etc etc. So programmers will continue counting from zero, > hoping the zeroth apple will be available to consume, while all other > carbon-based lifeforms, including musicians fretting about harmonics, > will continue happily counting from one.Calling DC the zeroth harmonic makes good mathematical sense. Symmetric distortion produces only odd harmonics, normally including the first. Asymmetric distortion produces also even harmonics, normally including the zeroth, an offset. For me, it also makes esthetic sense. Jerry -- Engineering is the art of making what you want from things you can get.
Reply by ●August 27, 20112011-08-27
On 8/26/2011 8:16 PM, robert bristow-johnson wrote:> On 8/26/11 2:07 PM, dbd wrote: >> On Aug 26, 8:05 am, dvsarwate<dvsarw...@yahoo.com> wrote: >>> On Aug 26, 9:25 am, Raeldor<rael...@gmail.com> wrote:>> Oh No! The dreaded "Do we start counting with zero or one?" topic >> again! >> > > of course that's a settled topic. i'm with Dijkstra, quoting: > > http://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html > > "Real computer programmers count from 0. Anyone who insists on counting > from 1 is either a douchebag or a MATLAB developer." >Well the douchebag idea seems harsh and I don't *insist* but then I am a MATLAB developer. :-) Also, a Fortran programmer. To be agreeable, it's always seemed to me that it's indeed nice if indices were to match up to something physical like index 0 corresponding to time=0 for example. But, it's not particularly nice for indices to not suggest the length of arrays directly. Otherwise starting with ZERO one has to remember or carry around in one's head that: - the number of elements in an array is N+1 where N is the highest index. Do this all the time with subnets. - the number of intervals in an array (the implied extent of an array) is N unless we're talking about periodic thingys and then it's N+1 again. And if we start indexing at ONE then one has to carry around in one's head that: - the number of elements in an array is N where N is the highest index. Nice and easy. - the number of intervals in an array is N-1 unless we're talking about periodic thingys and then it's N again..... also pretty easy for me anyway. But not a hell of a big difference either way, eh? What does it mean to "count from zero" anyway. To recite Zero, One, Two ... etc.?? Try this: Label a set of 5 rocks Zero, One, Two, Three, Four and then say "See? There are five rocks and the biggest label is Four of course"? How convenient .. NOT. Oh! But this is about computer programmers and not children counting rocks on their fingers. Well, they can start with a closed fist when there's no count and you can call that zero if you want .... but, notice, there is "no count" yet. ;-) Maybe for computer programmers like Dijkstra it means INDEX starting at zero and not COUNTING starting at zero ... even though a COUNTER (not a human) likes to often start at zero (like the closed fist) ... because then maybe that means we have to preload our registers with "-1" so the first count is zero? So, counting is one thing and indexing another. Otherwise we'd always be starting with a count of 1 "thing" represented by a "0". But that's not what you mean when you say "start counting at zero" is it? What you mean is: I'm going to start with my counter at ZERO and then count up from there .. the "count" starting at ONE event. Until then, there is nothing counted. This is a language problem as much as anything. Rather than being annoyed by the reality that both conventions and perspectives do exist, I think it's a lot better to just deal with it. Fred
Reply by ●August 27, 20112011-08-27
.On Aug 27, 7:45�am, robert bristow-johnson <r...@audioimagination.com> wrote:> On 8/27/11 1:59 AM, dbd wrote: > > > > > On Aug 26, 8:16 pm, robert bristow-johnson<r...@audioimagination.com> > > wrote: > >> ... > > >> of course that's a settled topic. �i'm with Dijkstra, quoting: > > >> �http://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html > > >> "Real computer programmers count from 0. �Anyone who insists on counting > >> from 1 is either a douchebag or a MATLAB developer." > > > Robert >.> > You are becoming so advanced! You have progressed to your lying about .> > quotations .> . .> how would you know, Dale? �did you read the Dijkstra reference from .> beginning to end?>... > r b-j � � � � � � � � �r...@audioimagination.com >I read the posted reference and even the handwritten version: http://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF Are you quoting out of context and lying about it again? The archive search function finds no mention of Matlab either. Why would I need to read the archive from beginning to end? Dale B. Dalrymple
