On 10 Jul, 16:25, Jerry Avins <j...@ieee.org> wrote:> Rune Allnor wrote: > > On 10 Jul, 00:31, steve <bungalow_st...@yahoo.com> wrote: > > � �... > > >> But if you talk with an experience analog engineer, someone who > >> excelled in linear algebra class, �he still doesn�t want to hear about > >> dot products or linear transforms or optimum least square > >> approximations, he wants to hear about a �bank of sinc filters� > >> analogy. You have to find an analogy that is consistent with a persons > >> background and build on it. > > > The key phrase you use is 'wants to hear.' Not 'needs to hear' or > > 'benefits from hearing'. I know this is considered by many to be > > controversial, but my view is, and has always been, that analog > > electronics and DSP are separate diciplines that should be > > approached separately, each on its own terms. > > Do you feel it is a general rule that insights learned from one activity > ought not be used to enlighten another, or do you confine the rule to > signal processing?Since analogies is the name of the game: Consider the railroad and road transport systems, trains and cars. Asume one has parctical experience from driving a car, how can one benefit from that experience when learning to drive a train? At the outset, cars and trains do the same thing: Transport people and goods from A to B. They also work in essentially the same way, as both cars and trains are self-propelled vehicles, that contain an onboard power plant, a driver's positions and are operated by drivers. So from the bird's eye perspective it seems that any experience frim driving cars would be of benetfit when learning how to drive trains. On lcoser inspection, however, that might not be the case. I don't know what the driver's prosition in a locomotive looks like, so I won't comment on operating the vehicles; the differences may or may not be important. *Handling* the vehicles is vastly different. The car driver needs to be constantly alert to surrounding traffic, pedestrians, multilane roads, other cars in fornt and behiond of the own vehicle. On a train one has the railroad to deal with, not much dynamics there. If you ever gets close to another train on the same track as yourself outside designated areas, you are in deep trouble. The logistsics of the goods or passengers is also vastly different. Trains can only load or unload in designated statoions, and require a secondary logistics network (buses, cars) to transport passengers in and out of stations. And so on. Even if the overall task is the same and the big picture looks similar for the train and car transport systems, the differences in the details and operation constraints are many enough and important enough that few if any people expect that directly transferring experiences from one application to the other will be immediately useful. It's the same with analog electronics and DSP. The tasks that are addressed are similar, but the details and constraints are vastly different. If people take this ad notam, the learning experience of at least DSP will become significantly less painful. Rune
Can you recommend a good explanation of the proof of the Fourier Transform?
Started by ●July 1, 2008
Reply by ●July 10, 20082008-07-10
Reply by ●July 11, 20082008-07-11
Rune Allnor wrote:> On 10 Jul, 00:31, steve <bungalow_st...@yahoo.com> wrote: >> On Jul 9, 4:18 am, Rune Allnor <all...@tele.ntnu.no> wrote: >> >>> Now c is a vector which expresses x in terms of the >>> basis B. Trivial high-school linear algebra, generalizes >>> straight-forward to the DFT. >>> The inner product is stuff I fisrt encountered at age 16, >>> it is hardly revolutionary, nor controversial. >> I think the issue is the DFT dot product explanation works for you >> because it clicks with your background, not because it is easy or can >> be taught in grade school. > > That explanation works because it is accurate as well as easy. > An EE practitioner is likely to have encountered the dot product > in grade school or college at some point. > >> An FIR filter is just a dot product too, >> and probably that view is very meaningful and insightful to you also. > > It is. > >> But if you talk with an experience analog engineer, someone who >> excelled in linear algebra class, he still doesn�t want to hear about >> dot products or linear transforms or optimum least square >> approximations, he wants to hear about a �bank of sinc filters� >> analogy. You have to find an analogy that is consistent with a persons >> background and build on it. > > The key phrase you use is 'wants to hear.' Not 'needs to hear' or > 'benefits from hearing'. I know this is considered by many to be > controversial, but my view is, and has always been, that analog > electronics and DSP are separate diciplines that should be > approached separately, each on its own terms. > > RuneThe first fast practical Fourier transform machines were purely analogue, working directly in terms of sinc functions. 'Wants to hear' is a perfectly reasonable thing to say here, because its just a different perspective on exactly the same thing. Steve
Reply by ●July 11, 20082008-07-11
Rune Allnor wrote:> On 10 Jul, 00:31, steve <bungalow_st...@yahoo.com> wrote: >> On Jul 9, 4:18 am, Rune Allnor <all...@tele.ntnu.no> wrote: >> >>> Now c is a vector which expresses x in terms of the >>> basis B. Trivial high-school linear algebra, generalizes >>> straight-forward to the DFT. >>> The inner product is stuff I fisrt encountered at age 16, >>> it is hardly revolutionary, nor controversial. >> I think the issue is the DFT dot product explanation works for you >> because it clicks with your background, not because it is easy or can >> be taught in grade school. > > That explanation works because it is accurate as well as easy. > An EE practitioner is likely to have encountered the dot product > in grade school or college at some point. > >> An FIR filter is just a dot product too, >> and probably that view is very meaningful and insightful to you also. > > It is. > >> But if you talk with an experience analog engineer, someone who >> excelled in linear algebra class, he still doesn�t want to hear about >> dot products or linear transforms or optimum least square >> approximations, he wants to hear about a �bank of sinc filters� >> analogy. You have to find an analogy that is consistent with a persons >> background and build on it. > > The key phrase you use is 'wants to hear.' Not 'needs to hear' or > 'benefits from hearing'. I know this is considered by many to be > controversial, but my view is, and has always been, that analog > electronics and DSP are separate diciplines that should be > approached separately, each on its own terms. > > RuneThe first fast practical Fourier transform machines were purely analogue, working directly in terms of sinc functions. 'Wants to hear' is a perfectly reasonable thing to say here, because its just a different perspective on exactly the same thing. Steve
Reply by ●July 11, 20082008-07-11
Rune Allnor wrote:> On 10 Jul, 00:31, steve <bungalow_st...@yahoo.com> wrote: >> On Jul 9, 4:18 am, Rune Allnor <all...@tele.ntnu.no> wrote: >> >>> Now c is a vector which expresses x in terms of the >>> basis B. Trivial high-school linear algebra, generalizes >>> straight-forward to the DFT. >>> The inner product is stuff I fisrt encountered at age 16, >>> it is hardly revolutionary, nor controversial. >> I think the issue is the DFT dot product explanation works for you >> because it clicks with your background, not because it is easy or can >> be taught in grade school. > > That explanation works because it is accurate as well as easy. > An EE practitioner is likely to have encountered the dot product > in grade school or college at some point. > >> An FIR filter is just a dot product too, >> and probably that view is very meaningful and insightful to you also. > > It is. > >> But if you talk with an experience analog engineer, someone who >> excelled in linear algebra class, he still doesn�t want to hear about >> dot products or linear transforms or optimum least square >> approximations, he wants to hear about a �bank of sinc filters� >> analogy. You have to find an analogy that is consistent with a persons >> background and build on it. > > The key phrase you use is 'wants to hear.' Not 'needs to hear' or > 'benefits from hearing'. I know this is considered by many to be > controversial, but my view is, and has always been, that analog > electronics and DSP are separate diciplines that should be > approached separately, each on its own terms. > > RuneThe first fast practical Fourier transform machines were purely analogue, working directly in terms of sinc functions. 'Wants to hear' is a perfectly reasonable thing to say here, because its just a different perspective on exactly the same thing. Steve
Reply by ●July 11, 20082008-07-11
Rune Allnor wrote:> On 10 Jul, 00:31, steve <bungalow_st...@yahoo.com> wrote: >> On Jul 9, 4:18 am, Rune Allnor <all...@tele.ntnu.no> wrote: >> >>> Now c is a vector which expresses x in terms of the >>> basis B. Trivial high-school linear algebra, generalizes >>> straight-forward to the DFT. >>> The inner product is stuff I fisrt encountered at age 16, >>> it is hardly revolutionary, nor controversial. >> I think the issue is the DFT dot product explanation works for you >> because it clicks with your background, not because it is easy or can >> be taught in grade school. > > That explanation works because it is accurate as well as easy. > An EE practitioner is likely to have encountered the dot product > in grade school or college at some point. > >> An FIR filter is just a dot product too, >> and probably that view is very meaningful and insightful to you also. > > It is. > >> But if you talk with an experience analog engineer, someone who >> excelled in linear algebra class, he still doesn�t want to hear about >> dot products or linear transforms or optimum least square >> approximations, he wants to hear about a �bank of sinc filters� >> analogy. You have to find an analogy that is consistent with a persons >> background and build on it. > > The key phrase you use is 'wants to hear.' Not 'needs to hear' or > 'benefits from hearing'. I know this is considered by many to be > controversial, but my view is, and has always been, that analog > electronics and DSP are separate diciplines that should be > approached separately, each on its own terms. > > RuneThe first fast practical Fourier transform machines were purely analogue, working directly in terms of sinc functions. 'Wants to hear' is a perfectly reasonable thing to say here, because its just a different perspective on exactly the same thing. Steve
Reply by ●July 11, 20082008-07-11
Rune Allnor wrote:> On 10 Jul, 00:31, steve <bungalow_st...@yahoo.com> wrote: >> On Jul 9, 4:18 am, Rune Allnor <all...@tele.ntnu.no> wrote: >> >>> Now c is a vector which expresses x in terms of the >>> basis B. Trivial high-school linear algebra, generalizes >>> straight-forward to the DFT. >>> The inner product is stuff I fisrt encountered at age 16, >>> it is hardly revolutionary, nor controversial. >> I think the issue is the DFT dot product explanation works for you >> because it clicks with your background, not because it is easy or can >> be taught in grade school. > > That explanation works because it is accurate as well as easy. > An EE practitioner is likely to have encountered the dot product > in grade school or college at some point. > >> An FIR filter is just a dot product too, >> and probably that view is very meaningful and insightful to you also. > > It is. > >> But if you talk with an experience analog engineer, someone who >> excelled in linear algebra class, he still doesn�t want to hear about >> dot products or linear transforms or optimum least square >> approximations, he wants to hear about a �bank of sinc filters� >> analogy. You have to find an analogy that is consistent with a persons >> background and build on it. > > The key phrase you use is 'wants to hear.' Not 'needs to hear' or > 'benefits from hearing'. I know this is considered by many to be > controversial, but my view is, and has always been, that analog > electronics and DSP are separate diciplines that should be > approached separately, each on its own terms. > > RuneThe first fast practical Fourier transform machines were purely analogue, working directly in terms of sinc functions. 'Wants to hear' is a perfectly reasonable thing to say here, because its just a different perspective on exactly the same thing. Steve
Reply by ●July 11, 20082008-07-11
On 11 Jul, 18:12, Steve Underwood <ste...@dis.org> wrote:> Rune Allnor wrote: > > On 10 Jul, 00:31, steve <bungalow_st...@yahoo.com> wrote:> >> But if you talk with an experience analog engineer, someone who > >> excelled in linear algebra class, �he still doesn�t want to hear about > >> dot products or linear transforms or optimum least square > >> approximations, he wants to hear about a �bank of sinc filters� > >> analogy. You have to find an analogy that is consistent with a persons > >> background and build on it. > > > The key phrase you use is 'wants to hear.' Not 'needs to hear' or > > 'benefits from hearing'. I know this is considered by many to be > > controversial, but my view is, and has always been, that analog > > electronics and DSP are separate diciplines that should be > > approached separately, each on its own terms. > > > Rune > > The first fast practical Fourier transform machines were purely > analogue, working directly in terms of sinc functions. 'Wants to hear' > is a perfectly reasonable thing to say here, because its just a > different perspective on exactly the same thing.The first self-propelled vehicles were steam locomotives. While that fact certainly holds some historical interest, do you think it is useful to explain the workings of present-day cars or trains in terms of steam engines? Rune
Reply by ●July 12, 20082008-07-12
Rune Allnor wrote:> On 10 Jul, 16:25, Jerry Avins <j...@ieee.org> wrote: >> Rune Allnor wrote:...>> Do you feel it is a general rule that insights learned from one activity >> ought not be used to enlighten another, or do you confine the rule to >> signal processing? > > Since analogies is the name of the game: Consider the railroad > and road transport systems, trains and cars. Asume one has parctical > experience from driving a car, how can one benefit from that > experience when learning to drive a train?... I agree that analogy can often be misleading. I don't think that the difference we have about an appropriate way to examine the idea behind a Fourier transform involves analogy at all. I have more in mind my (joint) patent for a field flattener for underwater acoustic images that uses the same principle as an astronomy amateur's field flattener for a small Schmidt camera. The lens used in the Schmidt is convex -- hence converging, while the underwater lens is concave -- hence converging. That's not analogy, but technology transfer. It seems to me that the same sort of transference works for ideas. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 12, 20082008-07-12
On 12 Jul, 21:50, Jerry Avins <j...@ieee.org> wrote:> Rune Allnor wrote: > > On 10 Jul, 16:25, Jerry Avins <j...@ieee.org> wrote: > >> Rune Allnor wrote: > > � �... > > >> Do you feel it is a general rule that insights learned from one activity > >> ought not be used to enlighten another, or do you confine the rule to > >> signal processing? > > > Since analogies is the name of the game: Consider the railroad > > and road transport systems, trains and cars. Asume one has parctical > > experience from driving a car, how can one benefit from that > > experience when learning to drive a train? > > � �... > > I agree that analogy can often be misleading. I don't think that the > difference we have about an appropriate way to examine the idea behind a > Fourier transform involves analogy at all. I have more in mind my > (joint) patent for a field flattener for underwater acoustic images that > uses the same principle as an astronomy amateur's field flattener for a > small Schmidt camera. The lens used in the Schmidt is convex -- hence > converging, while the underwater lens is concave -- hence converging. > That's not analogy, but technology transfer. It seems to me that the > same sort of transference works for ideas.It may or may not. I don't know your underwater imaging system, but I know a little bit about sonars. One of the main reasons for the present chaos in the underwater acoustics community is that very few people understand the dynamics of the ocean. Now, everybody have to start out somewhere, no one become experts in an instant, but the first step in becoming literate is to realize that one needs to learn. The sonar problem is deceptively similar to the radar problem. And that's where > 99% of sonar practitioners loose out; they don't understand the many and huge differences between sonar and radar. For instance, Synthetic Aperture Radar (SAR) has been around since the early '60s. The first papers on Synthetic Aperture Sonar (SAS) were written in the mid '70s. Everything was there. The seminal JASA article on SAS contained, in 1976 or '77, the equations, the algorithms - everything. The only problem was that the speed of sound in water is very slow compared to the speed of light. The relative speed of even the slowest marine vehicle is comparable to a radar platform travelling at 30 - 50 km/s. Not to mention the dynamics of the media. So only around 2000 - 25 years after the SAS papers were published - started rumours to appear about working SAS systems. Having worked offshore for a few seasons, I just can't see the usefulness of SAS systems. There are other far simpler systems around that does 95% of what SAS can do in 30% of the time and at 20% of the cost. Anyway, as I understand it, radars operating in the lower atmosphere experience relative fluctuations in sound speed on the order of 1e-7 to 1e-6. Under water you do well if you manage to measure the sound speed in a volume with three significant digits. The problem is that people who look for analogies don't look for situations where the analogies *break* *down* - at times I wonder if people are at all aware that analogies are just that - analogies and not universal truths. Rune
Reply by ●July 12, 20082008-07-12
Rune Allnor wrote:> On 12 Jul, 21:50, Jerry Avins <j...@ieee.org> wrote: >> Rune Allnor wrote: >>> On 10 Jul, 16:25, Jerry Avins <j...@ieee.org> wrote: >>>> Rune Allnor wrote: >> ... >> >>>> Do you feel it is a general rule that insights learned from one activity >>>> ought not be used to enlighten another, or do you confine the rule to >>>> signal processing? >>> Since analogies is the name of the game: Consider the railroad >>> and road transport systems, trains and cars. Asume one has parctical >>> experience from driving a car, how can one benefit from that >>> experience when learning to drive a train? >> ... >> >> I agree that analogy can often be misleading. I don't think that the >> difference we have about an appropriate way to examine the idea behind a >> Fourier transform involves analogy at all. I have more in mind my >> (joint) patent for a field flattener for underwater acoustic images that >> uses the same principle as an astronomy amateur's field flattener for a >> small Schmidt camera. The lens used in the Schmidt is convex -- hence >> converging, while the underwater lens is concave -- hence converging. >> That's not analogy, but technology transfer. It seems to me that the >> same sort of transference works for ideas. > > It may or may not. I don't know your underwater imaging system, > but I know a little bit about sonars. > > One of the main reasons for the present chaos in the underwater > acoustics community is that very few people understand the dynamics > of the ocean. Now, everybody have to start out somewhere, no one > become experts in an instant, but the first step in becoming literate > is to realize that one needs to learn. > > The sonar problem is deceptively similar to the radar problem. > And that's where > 99% of sonar practitioners loose out; they > don't understand the many and huge differences between sonar and > radar. > > For instance, Synthetic Aperture Radar (SAR) has been around since > the early '60s. The first papers on Synthetic Aperture Sonar (SAS) > were written in the mid '70s. Everything was there. The seminal JASA > article on SAS contained, in 1976 or '77, the equations, the > algorithms - everything. > > The only problem was that the speed of sound in water is very > slow compared to the speed of light. The relative speed of even > the slowest marine vehicle is comparable to a radar platform > travelling at 30 - 50 km/s. Not to mention the dynamics of > the media. So only around 2000 - 25 years after the SAS papers > were published - started rumours to appear about working SAS > systems. Having worked offshore for a few seasons, I just > can't see the usefulness of SAS systems. There are other > far simpler systems around that does 95% of what SAS can do > in 30% of the time and at 20% of the cost. > > Anyway, as I understand it, radars operating in the lower > atmosphere experience relative fluctuations in sound speed on > the order of 1e-7 to 1e-6. Under water you do well if you > manage to measure the sound speed in a volume with three > significant digits. > > The problem is that people who look for analogies don't look > for situations where the analogies *break* *down* - at times > I wonder if people are at all aware that analogies are just > that - analogies and not universal truths.All of that is valid, but I don't see how it relates to inner products vs. evaluating an integral as two valid ways to compute the same constant. Incidentally, my hydroacoustic image flattener was applied to well controlled in-tank conditions that already produced sharp images troubled only by curvature of field. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
