on this page http://www.hdbatik.co.uk/temp/waveletsbookpage.html is a page from a book ('the world according to wavelets' hubbard) i'm reading at the moment. in the text about the four graphs on the page it says: We will consider here the coefficients for times t = 1, 5, 10 and 50. For each such time, the coefficients are the same for the entire bar... in the bottom right graph of the four graphs (and the same graph is repeated at a higher resolution [with some red additions by me] at the bottom of the web page i've linked to) the dots on the verticle lines are labelled "coefficients". as indicated in the bottom graph (and i know it's obvious but i'm just making it clear) the series of dots from one time are not the same. so to me there's a contradition between: "for each such time, the coefficients are the same for the entire bar" and the dots hightlighted by red in the graph at the bottom of the linked to web page -- which are obviously not the same value. contradiction or am i misunderstadning and wrong about a contradiction existing there? according to a dictionary, a coefficient is a value used to multiply something by -- a coefficient is a multiplyer. so i'm thinking/guessing that the misleading part in the above, is the label pointing to each dot saying "coefficient". are those (in particular, highlighted by red) dots in fact the results from multiplying various values by a coefficient, rather than those dots being coefficients themselves? (this last paragraph was a guess). any clarification much appreciated. thanks, ben.
apparent contradiction between coefficient graph and text
Started by ●February 16, 2005
Reply by ●February 16, 20052005-02-16
ben wrote:> > on this page http://www.hdbatik.co.uk/temp/waveletsbookpage.html is a > page from a book ('the world according to wavelets' hubbard) i'm > reading at the moment. in the text about the four graphs on the page it > says: > > We will consider here the coefficients for times t = 1, 5, 10 and 50. > For each such time, the coefficients are the same for the entire bar... > > in the bottom right graph of the four graphs (and the same graph is > repeated at a higher resolution [with some red additions by me] at the > bottom of the web page i've linked to) the dots on the verticle lines > are labelled "coefficients". as indicated in the bottom graph (and i > know it's obvious but i'm just making it clear) the series of dots from > one time are not the same. so to me there's a contradition between: > "for each such time, the coefficients are the same for the entire bar" > and the dots hightlighted by red in the graph at the bottom of the > linked to web page -- which are obviously not the same value. > contradiction or am i misunderstadning and wrong about a contradiction > existing there? > > according to a dictionary, a coefficient is a value used to multiply > something by -- a coefficient is a multiplyer. so i'm thinking/guessing > that the misleading part in the above, is the label pointing to each > dot saying "coefficient". are those (in particular, highlighted by red) > dots in fact the results from multiplying various values by a > coefficient, rather than those dots being coefficients themselves? > (this last paragraph was a guess). > > any clarification much appreciated. > > thanks, ben.Ben, I get a strong sensation of deja vu reading this. Here's what I wrote before: "When a function is subjected to Fourier analysis, the result is of the form A*sin(w) + B*cos(w) + C*sin(2w) + D*cos(2w) + E*sin(3w) + ... The letters A-E... are the coefficients. Since the shape of the curve changes with time, so do the Fourier coefficients." What part of that is obscure, and how can I clarify it? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 16, 20052005-02-16
In article <3pCdnZaBrNULGY7fRVn-sQ@rcn.net>, Jerry Avins <jya@ieee.org> wrote:> ben wrote: > > > > on this page http://www.hdbatik.co.uk/temp/waveletsbookpage.html is a > > page from a book ('the world according to wavelets' hubbard) i'm > > reading at the moment. in the text about the four graphs on the page it > > says: > > > > We will consider here the coefficients for times t = 1, 5, 10 and 50. > > For each such time, the coefficients are the same for the entire bar... > > > > in the bottom right graph of the four graphs (and the same graph is > > repeated at a higher resolution [with some red additions by me] at the > > bottom of the web page i've linked to) the dots on the verticle lines > > are labelled "coefficients". as indicated in the bottom graph (and i > > know it's obvious but i'm just making it clear) the series of dots from > > one time are not the same. so to me there's a contradition between: > > "for each such time, the coefficients are the same for the entire bar" > > and the dots hightlighted by red in the graph at the bottom of the > > linked to web page -- which are obviously not the same value. > > contradiction or am i misunderstadning and wrong about a contradiction > > existing there? > > > > according to a dictionary, a coefficient is a value used to multiply > > something by -- a coefficient is a multiplyer. so i'm thinking/guessing > > that the misleading part in the above, is the label pointing to each > > dot saying "coefficient". are those (in particular, highlighted by red) > > dots in fact the results from multiplying various values by a > > coefficient, rather than those dots being coefficients themselves? > > (this last paragraph was a guess). > > > > any clarification much appreciated. > > > > thanks, ben. > > Ben, > > I get a strong sensation of deja vu reading this. Here's what I wrote > before:sorry i didn't realise that/this was an answer to the above question. i thought it was an answer to what is a coeficient.> > "When a function is subjected to Fourier analysis, the result is of the > form A*sin(w) + B*cos(w) + C*sin(2w) + D*cos(2w) + E*sin(3w) + ... > The letters A-E... are the coefficients. Since the shape of the curve > changes with time, so do the Fourier coefficients." > > What part of that is obscure, and how can I clarify it?i'm pretty confused. are you agreeing with and explaining what the book is saying, or saying something contradictory to"For each such time, the coefficients are the same for the entire bar"? or maybe saying something not directly connected to that? clarification on this might sort it all out for me: the dots pointed to by the splay of arrows labelled "Fourier Coefficients at times 0 , 1, 5, 10, 50" in the bottom right graph: are they representing actual coefficient values? or, are those dots the results from calculations that use, amongst other values, coefficient values (a bit like a curve in a graph is labelled a function when its actually the result of the use of that function)? "For each such time, the coefficients are the same for the entire bar" i'm not sure if that sentence is saying the coefficients of one, single time are the same, or, if the set/collection of various coefficients from one time are the same to the set/collection of coefficients from another time. either way it seems wrong: (in the bottom right graph:) - the black dots for each single time, curve -- that is they bend (so not level -- different). - five arrows for five different coefficients for five different times. that says that the coefficients are different at the five different times. if the black dots are coefficient values themselves (not the results from calculations using coefficients), it seems to me that one or both of the above two points blatantly goes against "For each such time, the coefficients are the same for the entire bar". i mean, i'm not even going into the maths -- i'm just using my eyes and very basic logic and seeing something that seems to contradict. thanks, ben.
Reply by ●February 16, 20052005-02-16
ben wrote: ...> sorry i didn't realise that/this was an answer to the above question. i > thought it was an answer to what is a coeficient.I'm sorry too. I guess I didn't understand your question, and I still don't. My answer is probably worthless. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 17, 20052005-02-17
In article <usSdnRx__sgqa47fRVn-pg@rcn.net>, Jerry Avins <jya@ieee.org> wrote:> ben wrote: > > ... > > > sorry i didn't realise that/this was an answer to the above question. i > > thought it was an answer to what is a coeficient. > > I'm sorry too. I guess I didn't understand your question, and I still > don't. My answer is probably worthless.oh. it's probably not. it's obviously my fault -- not explaining and not understanding. it's basically the bottom right graph of the four (on this page http://www.hdbatik.co.uk/temp/waveletsbookpage.html ), displaying various coefficients. and the text from beneath the graph that says "We will consider here the coefficients for times t = 1, 5, 10 and 50. For each such time, the coefficients are the same for the entire bar". those two things (the graph and the quoted text) seem to be at odds with each other -- contradictory? from the graph, the coefficients don't seem to be the same for each such time for the entire bar -- i can't see any coefficients in the graph that are the same at all. if your answer clarifies or deals with that (which it probably does and i'm just not getting it), sorry to be silly, but i'm not sure if i'm correct in saying there is a contradiction between the graph and the bit of text, or, what seems far more likely, i'm incorrect and misunderstanding the text and/or graph? thanks, ben.
Reply by ●February 17, 20052005-02-17
ben wrote:> In article <usSdnRx__sgqa47fRVn-pg@rcn.net>, Jerry Avins <jya@ieee.org> > wrote: > > >>ben wrote: >> >> ... >> >> >>>sorry i didn't realise that/this was an answer to the above question. i >>>thought it was an answer to what is a coeficient. >> >>I'm sorry too. I guess I didn't understand your question, and I still >>don't. My answer is probably worthless. > > > oh. it's probably not. > > it's obviously my fault -- not explaining and not understanding. > > it's basically the bottom right graph of the four (on this page > http://www.hdbatik.co.uk/temp/waveletsbookpage.html ), displaying > various coefficients. and the text from beneath the graph that says "We > will consider here the coefficients for times t = 1, 5, 10 and 50. For > each such time, the coefficients are the same for the entire bar". > > those two things (the graph and the quoted text) seem to be at odds > with each other -- contradictory? from the graph, the coefficients > don't seem to be the same for each such time for the entire bar -- i > can't see any coefficients in the graph that are the same at all. if > your answer clarifies or deals with that (which it probably does and > i'm just not getting it), sorry to be silly, but i'm not sure if i'm > correct in saying there is a contradiction between the graph and the > bit of text, or, what seems far more likely, i'm incorrect and > misunderstanding the text and/or graph? > > thanks, ben.It turns out that your question is what I thought it was. My answer was correct, but you didn't get it, so it wasn't good enough. I'll try again. Each curve is represented by a Fourier series. (One could also describe the curve with a power series.) The form of the series, whatever the shape of the curve, is the same. A power series will be infinity( ) SUM (a_n * x^n) n = 0 ( ) Now, the x^n is part of every power series, but the a_n are what makes every series unique. Change the curve, and the a_n change. (It's the same with Fourier series, but I didn't want to write it out.) The a_n terms are the coefficients. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 17, 20052005-02-17
In article <BcKdnWRzK77tW4nfRVn-qA@rcn.net>, Jerry Avins <jya@ieee.org> wrote:> ben wrote: > > In article <usSdnRx__sgqa47fRVn-pg@rcn.net>, Jerry Avins <jya@ieee.org> > > wrote: > > > > > >>ben wrote: > >> > >> ... > >> > >> > >>>sorry i didn't realise that/this was an answer to the above question. i > >>>thought it was an answer to what is a coeficient. > >> > >>I'm sorry too. I guess I didn't understand your question, and I still > >>don't. My answer is probably worthless. > > > > > > oh. it's probably not. > > > > it's obviously my fault -- not explaining and not understanding. > > > > it's basically the bottom right graph of the four (on this page > > http://www.hdbatik.co.uk/temp/waveletsbookpage.html ), displaying > > various coefficients. and the text from beneath the graph that says "We > > will consider here the coefficients for times t = 1, 5, 10 and 50. For > > each such time, the coefficients are the same for the entire bar". > > > > those two things (the graph and the quoted text) seem to be at odds > > with each other -- contradictory? from the graph, the coefficients > > don't seem to be the same for each such time for the entire bar -- i > > can't see any coefficients in the graph that are the same at all. if > > your answer clarifies or deals with that (which it probably does and > > i'm just not getting it), sorry to be silly, but i'm not sure if i'm > > correct in saying there is a contradiction between the graph and the > > bit of text, or, what seems far more likely, i'm incorrect and > > misunderstanding the text and/or graph? > > > > thanks, ben. > > It turns out that your question is what I thought it was. My answer was > correct, but you didn't get it, so it wasn't good enough. I'll try again. > > Each curve is represented by a Fourier series. (One could also describe > the curve with a power series.) The form of the series, whatever the > shape of the curve, is the same. A power series will be > > infinity( ) > SUM (a_n * x^n) > n = 0 ( ) > > Now, the x^n is part of every power series, but the a_n are what makes > every series unique. Change the curve, and the a_n change. (It's the > same with Fourier series, but I didn't want to write it out.) The a_n > terms are the coefficients.right so the set of curves that are used to make up the end curve are unchanging, static -- the full spread of curves available for use are always the same throughout. which curves are actually used from the set vary. and it's the coefficients that dictate which curves are used. and as the curves change over time, obviously so do the coefficients that are used to make up the curves because they're tied together -- one dictates the other. so the book's wrong then?! that's the part i'm unsure and struggling with -- i'm still not completely sure, but all info seems to contradict "For each such time, the coefficients are the same for the entire bar". the reason i'm finding it such a problem is because usually, no always, when i start something new to me like this, i pick holes in whatever book/webpage etc i'm using (based on my misunderstandings), and people tell me no you've got the wrong end of the stick, it's actually like this.... that's how i usually learn stuff like this. i'm *still* not sure if i'm making myself look really, really silly now by talking as if the book's incorrect when in actual fact i've still got the wrong end of the stick and it's not incorrect. so the actual question is (just so i can be sure): is the book incorrect in saying "For each such time, the coefficients are the same for the entire bar"? thanks, ben.
Reply by ●February 17, 20052005-02-17
ben wrote:> In article <BcKdnWRzK77tW4nfRVn-qA@rcn.net>, Jerry Avins <jya@ieee.org> > wrote: > > >>ben wrote: >> >>>In article <usSdnRx__sgqa47fRVn-pg@rcn.net>, Jerry Avins <jya@ieee.org> >>>wrote: >>> >>> >>> >>>>ben wrote: >>>> >>>> ... >>>> >>>> >>>> >>>>>sorry i didn't realise that/this was an answer to the above question. i >>>>>thought it was an answer to what is a coeficient. >>>> >>>>I'm sorry too. I guess I didn't understand your question, and I still >>>>don't. My answer is probably worthless. >>> >>> >>>oh. it's probably not. >>> >>>it's obviously my fault -- not explaining and not understanding. >>> >>>it's basically the bottom right graph of the four (on this page >>>http://www.hdbatik.co.uk/temp/waveletsbookpage.html ), displaying >>>various coefficients. and the text from beneath the graph that says "We >>>will consider here the coefficients for times t = 1, 5, 10 and 50. For >>>each such time, the coefficients are the same for the entire bar". >>> >>>those two things (the graph and the quoted text) seem to be at odds >>>with each other -- contradictory? from the graph, the coefficients >>>don't seem to be the same for each such time for the entire bar -- i >>>can't see any coefficients in the graph that are the same at all. if >>>your answer clarifies or deals with that (which it probably does and >>>i'm just not getting it), sorry to be silly, but i'm not sure if i'm >>>correct in saying there is a contradiction between the graph and the >>>bit of text, or, what seems far more likely, i'm incorrect and >>>misunderstanding the text and/or graph? >>> >>>thanks, ben. >> >>It turns out that your question is what I thought it was. My answer was >>correct, but you didn't get it, so it wasn't good enough. I'll try again. >> >>Each curve is represented by a Fourier series. (One could also describe >>the curve with a power series.) The form of the series, whatever the >>shape of the curve, is the same. A power series will be >> >> infinity( ) >> SUM (a_n * x^n) >> n = 0 ( ) >> >>Now, the x^n is part of every power series, but the a_n are what makes >>every series unique. Change the curve, and the a_n change. (It's the >>same with Fourier series, but I didn't want to write it out.) The a_n >>terms are the coefficients. > > > right so the set of curves that are used to make up the end curve are > unchanging, static -- the full spread of curves available for use are > always the same throughout. which curves are actually used from the set > vary. and it's the coefficients that dictate which curves are used. and > as the curves change over time, obviously so do the coefficients that > are used to make up the curves because they're tied together -- one > dictates the other. > > so the book's wrong then?! that's the part i'm unsure and struggling > with -- i'm still not completely sure, but all info seems to contradict > "For each such time, the coefficients are the same for the entire bar". > > the reason i'm finding it such a problem is because usually, no always, > when i start something new to me like this, i pick holes in whatever > book/webpage etc i'm using (based on my misunderstandings), and people > tell me no you've got the wrong end of the stick, it's actually like > this.... that's how i usually learn stuff like this. i'm *still* not > sure if i'm making myself look really, really silly now by talking as > if the book's incorrect when in actual fact i've still got the wrong > end of the stick and it's not incorrect. > > so the actual question is (just so i can be sure): is the book > incorrect in saying "For each such time, the coefficients are the same > for the entire bar"?Wrong or not, I can't say because I can only guess what it means. The coefficients aren't points on a curve; they are numbers that multiply individual elements of the series of sines and cosines (or complex exponentials) that together describe the entire curve at any instant. Jerry P.S. I think the offending sentence is a mental lapse, like the wavy temperature curve at time zero. The intended meaning probably was "For each time shown, the coefficients apply to the entire bar." -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 17, 20052005-02-17
also, forgetting about if the book's incorrect or not for a minute, about the fourier transform generally, from physical space to fourier space, would a reasonable, very simple way of summing up what happens in a fourier transform be: counts of occurances of similar values - so ending up with a set of counts ? that is, in physical space say the value 5 occurs there and over there and there etc, say 20 times in the space you're looking at, then in fourier space the 5 marker/postion carries 20 values worth? how would anyone explain what goes on in a fourier transform to an 8 year old?
Reply by ●February 17, 20052005-02-17
In article <svGdnaUGgsWphYjfRVn-hQ@rcn.net>, Jerry Avins <jya@ieee.org> wrote:> ben wrote: > > In article <BcKdnWRzK77tW4nfRVn-qA@rcn.net>, Jerry Avins <jya@ieee.org> > > wrote: > > > > > >>ben wrote: > >> > >>>In article <usSdnRx__sgqa47fRVn-pg@rcn.net>, Jerry Avins <jya@ieee.org> > >>>wrote: > >>> > >>> > >>> > >>>>ben wrote: > >>>> > >>>> ... > >>>> > >>>> > >>>> > >>>>>sorry i didn't realise that/this was an answer to the above question. i > >>>>>thought it was an answer to what is a coeficient. > >>>> > >>>>I'm sorry too. I guess I didn't understand your question, and I still > >>>>don't. My answer is probably worthless. > >>> > >>> > >>>oh. it's probably not. > >>> > >>>it's obviously my fault -- not explaining and not understanding. > >>> > >>>it's basically the bottom right graph of the four (on this page > >>>http://www.hdbatik.co.uk/temp/waveletsbookpage.html ), displaying > >>>various coefficients. and the text from beneath the graph that says "We > >>>will consider here the coefficients for times t = 1, 5, 10 and 50. For > >>>each such time, the coefficients are the same for the entire bar". > >>> > >>>those two things (the graph and the quoted text) seem to be at odds > >>>with each other -- contradictory? from the graph, the coefficients > >>>don't seem to be the same for each such time for the entire bar -- i > >>>can't see any coefficients in the graph that are the same at all. if > >>>your answer clarifies or deals with that (which it probably does and > >>>i'm just not getting it), sorry to be silly, but i'm not sure if i'm > >>>correct in saying there is a contradiction between the graph and the > >>>bit of text, or, what seems far more likely, i'm incorrect and > >>>misunderstanding the text and/or graph? > >>> > >>>thanks, ben. > >> > >>It turns out that your question is what I thought it was. My answer was > >>correct, but you didn't get it, so it wasn't good enough. I'll try again. > >> > >>Each curve is represented by a Fourier series. (One could also describe > >>the curve with a power series.) The form of the series, whatever the > >>shape of the curve, is the same. A power series will be > >> > >> infinity( ) > >> SUM (a_n * x^n) > >> n = 0 ( ) > >> > >>Now, the x^n is part of every power series, but the a_n are what makes > >>every series unique. Change the curve, and the a_n change. (It's the > >>same with Fourier series, but I didn't want to write it out.) The a_n > >>terms are the coefficients. > > > > > > right so the set of curves that are used to make up the end curve are > > unchanging, static -- the full spread of curves available for use are > > always the same throughout. which curves are actually used from the set > > vary. and it's the coefficients that dictate which curves are used. and > > as the curves change over time, obviously so do the coefficients that > > are used to make up the curves because they're tied together -- one > > dictates the other. > > > > so the book's wrong then?! that's the part i'm unsure and struggling > > with -- i'm still not completely sure, but all info seems to contradict > > "For each such time, the coefficients are the same for the entire bar". > > > > the reason i'm finding it such a problem is because usually, no always, > > when i start something new to me like this, i pick holes in whatever > > book/webpage etc i'm using (based on my misunderstandings), and people > > tell me no you've got the wrong end of the stick, it's actually like > > this.... that's how i usually learn stuff like this. i'm *still* not > > sure if i'm making myself look really, really silly now by talking as > > if the book's incorrect when in actual fact i've still got the wrong > > end of the stick and it's not incorrect. > > > > so the actual question is (just so i can be sure): is the book > > incorrect in saying "For each such time, the coefficients are the same > > for the entire bar"? > > Wrong or not, I can't say because I can only guess what it means. The > coefficients aren't points on a curve; they are numbers that multiply > individual elements of the series of sines and cosinesah, right -- that's what i was trying to get at earlier on asking are the dots actually representing coefficients or not -- i suspected that what you've just said was the case. that explains all my confusion. that's why i was talking about, suggesting the situation of describing a curve on a graph as a function. it's analogously (in a language use way) the same as that. talking about the result of something as the something. so pointing to the dots and calling the coefficients is pretty darn misleading itself. those dots represent calculations that just used the sodding coefficients, they're not the coefficients themselves.> (or complex > exponentials) that together describe the entire curve at any instant. > > Jerry > > P.S. I think the offending sentence is a mental lapse, like the wavy > temperature curve at time zero. The intended meaning probably was "For > each time shown, the coefficients apply to the entire bar."i think there's all sorts of problems/things that misleading on that page. there's another possible one i've noticed, but anyway won't bother with it. thanks for the replies Jerry :) ben.
