> Why does the sudden change in the amplitude cause the side lobes appear to > apear when the maginitude response is obtained? > Ex: The magnitude response of the RECTANGULAR WINDOW. > > Again, mathematically this can be proved with the sinc function. > However, I want to know the physical interpretation of the sameWell... in my world, this is like asking "What makes gravity work?" The mathemathical formula gravity is there, it involves some masses, a distance and a universal factor, so one can compute the result of gravitational forces. WHY gravity works? I have no idea. And I don't care. Same thing with sincs and sidelobes. You know that's what pops out of the maths, and you know you have to relate to them. WHY they are there is not really important. Rune
Why Side Lobes appear in magnitude response?
Started by ●September 29, 2004
Reply by ●September 29, 20042004-09-29
Rune Allnor wrote:>>Why does the sudden change in the amplitude cause the side lobes appear to >>apear when the maginitude response is obtained? >>Ex: The magnitude response of the RECTANGULAR WINDOW. >> >>Again, mathematically this can be proved with the sinc function. >>However, I want to know the physical interpretation of the same > > > Well... in my world, this is like asking "What makes gravity work?" > The mathemathical formula gravity is there, it involves some masses, > a distance and a universal factor, so one can compute the result of > gravitational forces. > > WHY gravity works? I have no idea. And I don't care. > > Same thing with sincs and sidelobes. You know that's what pops out > of the maths, and you know you have to relate to them. > > WHY they are there is not really important. > > RuneYou can't do anything to modify gravity. If sampling were as resistant to engineering manipulation as gravity, you wouldn't care about the details of sampling either. The replications are real. A physical processes that is entirely ignorant of mathematics creates them. Mathematics elucidates them. Those who believe that mathematics creates them should call it mathemagics instead. Where is R.B-J. when we need him! Jerry -- ... they proceeded on the sound principle that the magnitude of a lie always contains a certain factor of credibility, ... and that therefor ... they more easily fall victim to a big lie than to a little one ... A. H. �����������������������������������������������������������������������
Reply by ●September 29, 20042004-09-29
Jerry Avins <jya@ieee.org> writes:> [...] > Those > who believe that mathematics creates them should call it mathemagics > instead.I find that statement arrogant, Jerry. I happen to be one who believes mathematics is discovered, not invented, and I believe this distinction is the root of the issue. Allow me to posit this conjecture: God really did form creation by speaking, thus physical reality follows logos, not vice-versa. --Randy -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA randy.yates@sonyericsson.com, 919-472-1124
Reply by ●September 29, 20042004-09-29
Randy Yates wrote:> Jerry Avins <jya@ieee.org> writes: > >>[...] >>Those >>who believe that mathematics creates them should call it mathemagics >>instead. > > > I find that statement arrogant, Jerry. I happen to be one who believes > mathematics is discovered, not invented, and I believe this > distinction is the root of the issue. > > Allow me to posit this conjecture: God really did form creation by speaking, > thus physical reality follows logos, not vice-versa. > > > --RandyPosit whatever you like. Mathematics being discovered is an interesting idea. To me it is in the class of ideas that includes the notion that there can be no noise without a hearer. Those ideas are tenable and logically self consistent, but they demand that some simple statements be couched in awkward locutions. Integration by parts was invented, not discovered. Mathematical truths -- like others -- may be discovered, but if we agree that all of mathematics is discovered, then we must also agree that integration by parts, indeed any mathematical technique, is not mathematics and must have another name. As I wrote, that's a tenable view, but one that forces those who hold it away from simplicity and directness. Mathematics may inform us that the replications must be there, but it doesn't create them. To put it arrogantly, chopping the signal creates them. Jerry -- ... they proceeded on the sound principle that the magnitude of a lie always contains a certain factor of credibility, ... and that therefor ... they more easily fall victim to a big lie than to a little one ... A. H. �����������������������������������������������������������������������
Reply by ●September 29, 20042004-09-29
Jerry Avins wrote:> Randy Yates wrote:(snip)>> I happen to be one who believes >> mathematics is discovered, not invented, and I believe this >> distinction is the root of the issue.(snip)> Integration by parts was invented, not > discovered. Mathematical truths -- like others -- may be discovered, but > if we agree that all of mathematics is discovered, then we must also > agree that integration by parts, indeed any mathematical technique, is > not mathematics and must have another name. As I wrote, that's a > tenable view, but one that forces those who hold it away from simplicity > and directness.> Mathematics may inform us that the replications must be there, but it > doesn't create them. To put it arrogantly, chopping the signal creates > them.Hydrogen atoms, among others, can solve differential equations, as that is how the electron knows where to go. (The solution to the Schrodinger equation.) Following your distinction, the mathematics, say the solution to an integral is discovered. The methods for finding that solution, (or finding it faster) such as integration by parts, are invented. Now, this reminds me of a solution to an electrostatics problem that I saw once. The problem should have been done in polar coordinates, but the student used rectangular coordinates. When he (or she) couldn't do the integral, trig substitution was used resulting in the same equation as if the original was done in polar coordinates. Now, the physical solution to an equation is the same independent of the coordinate system, but the representation will be different. Coordinate systems are invented, but solutions to differential equations are discovered. -- glen
Reply by ●September 29, 20042004-09-29
glen herrmannsfeldt wrote:> > > Jerry Avins wrote: > >> Randy Yates wrote: > > (snip) > >>> I happen to be one who believes >>> mathematics is discovered, not invented, and I believe this >>> distinction is the root of the issue. > > (snip) > >> Integration by parts was invented, not >> discovered. Mathematical truths -- like others -- may be discovered, but >> if we agree that all of mathematics is discovered, then we must also >> agree that integration by parts, indeed any mathematical technique, is >> not mathematics and must have another name. As I wrote, that's a >> tenable view, but one that forces those who hold it away from simplicity >> and directness. > > >> Mathematics may inform us that the replications must be there, but it >> doesn't create them. To put it arrogantly, chopping the signal creates >> them. > > > Hydrogen atoms, among others, can solve differential equations, > as that is how the electron knows where to go. > (The solution to the Schrodinger equation.) > > Following your distinction, the mathematics, say the solution > to an integral is discovered. The methods for finding that solution, > (or finding it faster) such as integration by parts, are invented. > > Now, this reminds me of a solution to an electrostatics problem that > I saw once. The problem should have been done in polar coordinates, > but the student used rectangular coordinates. When he (or she) > couldn't do the integral, trig substitution was used resulting in > the same equation as if the original was done in polar coordinates. > > Now, the physical solution to an equation is the same independent of > the coordinate system, but the representation will be different. > Coordinate systems are invented, but solutions to differential > equations are discovered. > > -- glenI can buy that. It's not only neat, but it's the way I think about things. But if I maintained that mathematics consists only of the discovered parts, I would tie myself up in knots. Lots of things solve differential equations. That's what made analog computers practical. Jerry -- ... they proceeded on the sound principle that the magnitude of a lie always contains a certain factor of credibility, ... and that therefor ... they more easily fall victim to a big lie than to a little one ... A. H. �����������������������������������������������������������������������
Reply by ●September 29, 20042004-09-29
Jerry Avins <jya@ieee.org> writes:> [...] > Mathematics may inform us that the replications must be there, but it > doesn't create them.A sure sign that we've exited fruitful terrirtory - proof by assertion. -- % Randy Yates % "Midnight, on the water... %% Fuquay-Varina, NC % I saw... the ocean's daughter." %%% 919-577-9882 % 'Can't Get It Out Of My Head' %%%% <yates@ieee.org> % *El Dorado*, Electric Light Orchestra http://home.earthlink.net/~yatescr
Reply by ●September 29, 20042004-09-29
Randy Yates wrote:> Jerry Avins <jya@ieee.org> writes: > >>[...] >>Mathematics may inform us that the replications must be there, but it >>doesn't create them. > > > A sure sign that we've exited fruitful terrirtory - proof by assertion.Assertion, not proof, was my intention. One can no more prove this point than disprove it. About points of view, one can only assert. I, mine; you, yours. Go with my blessing. (And how's that for arrogance? I can arrogate with the best!) :-) Jerry -- ... they proceeded on the sound principle that the magnitude of a lie always contains a certain factor of credibility, ... and that therefor ... they more easily fall victim to a big lie than to a little one ... A. H. �����������������������������������������������������������������������
Reply by ●September 30, 20042004-09-30
Randy Yates wrote:> Allow me to posit this conjecture: God really did form creation by > speaking, thus physical reality follows logos, not vice-versa.I like that, and I agree. But the consequence is not, that physical reality follows mathematics. Instead, mathematics is a vehicule to transport insight in either physical reality or in the process which happens when a special logo/word is spoken, or anything between. As long as mathematics deals with physical reality (symptoms), it's nature is describing, and it's after the symptoms. As soon as it leaves this territory and digs into the laws behind, it's more and more becoming philosophical and/or religious. And, at the same time it may become prophetic, even describing things which haven't yet been discovered or not even created. But still, there's the logo or the fundamental law of creation, which goes before. And mathematics has to stay behind. Bernhard
Reply by ●September 30, 20042004-09-30
Jerry Avins <jya@ieee.org> wrote in message news:<cjetds$jd6$1@bob.news.rcn.net>...> Rune Allnor wrote: > > >>Why does the sudden change in the amplitude cause the side lobes appear to > >>apear when the maginitude response is obtained? > >>Ex: The magnitude response of the RECTANGULAR WINDOW. > >> > >>Again, mathematically this can be proved with the sinc function. > >>However, I want to know the physical interpretation of the same > > > > > > Well... in my world, this is like asking "What makes gravity work?" > > The mathemathical formula gravity is there, it involves some masses, > > a distance and a universal factor, so one can compute the result of > > gravitational forces. > > > > WHY gravity works? I have no idea. And I don't care. > > > > Same thing with sincs and sidelobes. You know that's what pops out > > of the maths, and you know you have to relate to them. > > > > WHY they are there is not really important. > > > > Rune > > You can't do anything to modify gravity.So what? It helps to understand (i.e. be able to predict) what will happen in a gravitational field. The law of gravity predicts that a rock will fall back to the ground when I throw it. The law of gravity predicts that a rocket that takes off from the earth's surface can only bring 1% (or whatever the number is) of its mass as payload, if one wants it to escape the earth's gravity field. The law of gravity predict that one can use planet's gravitational fields to 'sling-shot' space probes into outer space. The laws of gravity also predict what will happen if we somehow can travel to a different 'gravitational setting', like travelling to the moon or into a dense cloud of asteroids. To me, that's 'modifying gravity' good as any. The laws of mathemathical physics predict what is going to happen in various situations, they don't explain *why* things happen. The law of gravity does not explain *why* the earth 'knows' it is under the gravitational influence of the sun: Is there an exchange of gravitons between the two? If not, what else causes the interaction? I have no idea, and I don't care, as long as the laws of gravity predict what's going on with sufficient accuracy.> If sampling were as resistant > to engineering manipulation as gravity, you wouldn't care about the > details of sampling either.The theory of sampling predicts what is goind go happen, when you transform signals between the analog and digital domains. You know the rules, it's up to you to avoid the pitfalls (e.g. see to that there is a prior anti-alias filter) or exploit the loopholes (e.g. sub-band sampling). The only difference between gravity and sampling, is that it is easier to re-design an electronic cirquit than it is travel go to the moon.> The replications are real. A physical processes that is entirely > ignorant of mathematics creates them.I could agree with you. Except for I don't believe in anthropomorph physical processes (I've looked up 'anropomorph' in the dictionary since the last time I used the word...)> Mathematics elucidates them.Well, physics is so densely intertwined with mathemathics that I somehow become sceptical of physical phenomena that can not (or at least their basic principles) be explained in terms of maths. Now, that's a one-way relation. I don't expect each and every mathemathical feature and phenomenon to have a physical interpretation.> Those > who believe that mathematics creates them should call it mathemagics > instead.'Mathemagics'... that's a useful word. I did contemplate the interaction between maths and physics once or twice, during my work with my thesis. My starting point, was seismic waves that travelled in the seafloor. Those were very physical, I once attended a similar experiment on land, where they used dynamite as sources. We hard the 'bang' when the carges went off, and the land fill we stood on made a very real 'thump' that we felt through our feet, a couple of seconds later. Those 'thumps' were the waves we were analyzing. The waves got digitized by seismometers. Noise comes in, reduced bandwidth,.... the numebers become crude representations of the waves we felt. We put these numbers into a generic mathemathcal routine, which had nothing whatsoever to do with physics, and set up a set of equations from the numbers. The solution of the equations involved eigenvalues, which can only be approximated. This approcimate vector that was the solution of a plain, completely abstarct equation was not used directly, it was regarded as a polynomial which *roots* were interesting. so we computed the roots with a standard (though approximate) routine and expressed them on polar form. Leave the results of these excercises alone for a minute, and have a look at the physical model we had for the waves: It was highly idealized, it was based on that the underground conisted of perfectly homogeneous, horizontal layers with perfectly smooth surfaces and constant parameters within the layers. A completely unrealistic set of assumptions. But we used it. We used a very idelized, approximate method to compute wave-field parameters from this idealized model. The one 'physical' aspect the model actually included, was the effects of cylindrical spreading, i.e. that the volume density of the energy 'dilutes' as the cylindrical wave propagates far from the source. We discarded that effect. We made our comutations as if no such dilution took place. At this stage, we went back to the solutions of our equations, and compared them to the output of the model. Everything matched up. When we took input parameters, to the extent we knew them, that were typical for the area we worked in, and put them into the highly idealized and approximately computations of the models, the results matched that popped out of the crude, generic maths we applied to the data, even after having discareded the one physical effect included in themodel, that the waves could be expected to clearly show. I never really knew why that happened. I have never been able to perform an appropriate blind-test of these types of results and compare them to ground-truth data. Simply because no alternative methods of measurements exist. But in each and every case, I have been able to make predictions based on the results of this kind of analysis, and these predictions tend to be confirmed. So as of yet, I'll accept that circumstancial evidence suggest that these methods work. That's really 'mathemagic', what I am concerned. I make no claims of being a 'mathemagician', though. I am only amused that the results of all these more or less ad hoc, idelaized ideas and approximate methods actually link up to the physical observations at all.> Where is R.B-J. when we need him!That's a good point. I haven't seen any posts from him for months. Rune
