On 12/27/12 10:17 PM, rickman wrote:> On 12/27/2012 5:13 PM, robert bristow-johnson wrote: >> On 12/27/12 4:56 PM, rickman wrote: >>> On 12/26/2012 6:14 PM, robert bristow-johnson wrote: >>>> On 12/25/12 10:15 PM, rickman wrote: >>>>> I believe that... for everyone else. I have no way to distinguish >>>>> whether you are conscious or a very well programmed automaton. But I >>>>> know I am conscious. I think, therefore I am conscious. >>>> >>>> so you are a being with consciousness and feelings but everyone else >>>> are >>>> sophisticated automatons? are you the only such being? >>>> >>>> i dunno what this would be called, but could we apply a sorta >>>> "Copernican principle" but replace "the Earth" with "oneself"? >>> >>> You miss my point. I can only confirm my consciousness. I can't >>> distinguish you from a very well designed automaton. >>> >> >> i think i hit your point spot on and you missed mine. care to explore >> that a bit? > > I'm a little confused. I already said, "I have no way to distinguish > whether you are conscious or a very well programmed automaton."you said that, and i'm trying to get you to think about how convincing that position is.> So you > may have consciousness or not, how does one distinguish if someone else > has consciousness? I know of no test for this.well, you've tested it on yourself (because you can reach yourself with your test, while you cannot reach others with this same test). so let's say it's EE lab and your lab station has a 15 volt DC supply and you hook a resistor with yellow, violet, and red stripes (4.7 K) and you measure a little over 3 mA flowing through that resistor. then you glance over to the neighboring lab station and they have an identical looking DC supply turned on and an identical looking yellow-violet-red resistor. and you can't reach over there with your milli-ammeter. but what current would you expect to be flowing in that setup that you're unable to measure directly?> One poster seems to be suggesting that I might be a computer simulation > that thinks I have consciousness and you seem to be saying I have no > reason to believe I am special so I should assume all beings who appear > to have consciousness do because I do. Clearly there is no way to tell.we can't tell anything for sure. but from what you perceive, what is the most reasonable thing to surmise. that you're an independently conscious being and everyone else (that walk on two feet and appear to see with two eyes and have other perceived similarities to you) are automatons? i find that reasoning curious.> Are you part of my simulation or am I part of yours?well maybe Copernicus might ask are other stars and astronomical objects expanding away from us or are we, among many other objects, expanding. so if none of us is particularly special and you perceive that you're not an automaton, what is the consistent conclusion from that? -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
discrete fourier series and transform
Started by ●December 23, 2012
Reply by ●December 29, 20122012-12-29
Reply by ●December 29, 20122012-12-29
On 12/28/12 6:51 PM, rickman wrote:> > Yes, you are right. It is so easy to mix up the two issues. The sampling > limits the bandwidth.no. the sampling does *not* limit the bandwidth. sampling with perfect reconstruction *requires* (as a condition) limits to the bandwidth. but what the sampling does itself (say your sample rate is Fs) is cause your spectrum to be repeatedly shifted by a shift equal to all integer multiples of Fs and those shifted results overlapped and added up. that's what sampling does. it causes your spectrum to become periodic. and how it gets periodic is from this shift, overlap and add thing. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●December 30, 20122012-12-30
On 12/28/2012 11:50 PM, robert bristow-johnson wrote:> On 12/27/12 10:17 PM, rickman wrote: >> >> I'm a little confused. I already said, "I have no way to distinguish >> whether you are conscious or a very well programmed automaton." > > you said that, and i'm trying to get you to think about how convincing > that position is. > >> So you >> may have consciousness or not, how does one distinguish if someone else >> has consciousness? I know of no test for this. > > well, you've tested it on yourself (because you can reach yourself with > your test, while you cannot reach others with this same test). > > so let's say it's EE lab and your lab station has a 15 volt DC supply > and you hook a resistor with yellow, violet, and red stripes (4.7 K) and > you measure a little over 3 mA flowing through that resistor. then you > glance over to the neighboring lab station and they have an identical > looking DC supply turned on and an identical looking yellow-violet-red > resistor. and you can't reach over there with your milli-ammeter. but > what current would you expect to be flowing in that setup that you're > unable to measure directly?I'm not able to conduct the same test on your consciousness as I can on my own. I can't see the meter on your device only what you tell me.>> One poster seems to be suggesting that I might be a computer simulation >> that thinks I have consciousness and you seem to be saying I have no >> reason to believe I am special so I should assume all beings who appear >> to have consciousness do because I do. Clearly there is no way to tell. > > we can't tell anything for sure. but from what you perceive, what is the > most reasonable thing to surmise. that you're an independently conscious > being and everyone else (that walk on two feet and appear to see with > two eyes and have other perceived similarities to you) are automatons? i > find that reasoning curious.That's just what I would expect an automaton to say.>> Are you part of my simulation or am I part of yours? > > well maybe Copernicus might ask are other stars and astronomical objects > expanding away from us or are we, among many other objects, expanding. > > so if none of us is particularly special and you perceive that you're > not an automaton, what is the consistent conclusion from that?That is not direct evidence. It just an opinion based on very little. Do you follow Isaac Asimov's "Three Laws of Robotics"? Rick
Reply by ●December 30, 20122012-12-30
On 12/29/2012 1:19 AM, robert bristow-johnson wrote:> On 12/28/12 6:51 PM, rickman wrote: >> >> Yes, you are right. It is so easy to mix up the two issues. The sampling >> limits the bandwidth. > > no. the sampling does *not* limit the bandwidth. sampling with perfect > reconstruction *requires* (as a condition) limits to the bandwidth. but > what the sampling does itself (say your sample rate is Fs) is cause your > spectrum to be repeatedly shifted by a shift equal to all integer > multiples of Fs and those shifted results overlapped and added up. > that's what sampling does. it causes your spectrum to become periodic. > and how it gets periodic is from this shift, overlap and add thing. > >Ok, that's a little pedantic. I'm thinking in practical terms. The *useful* bandwidth becomes limited by the sample rate. If you can find useful ways to allow overlapping, shifted frequencies, then more power to you. For most that is pretty far out there. Rick
Reply by ●December 30, 20122012-12-30
On Sun, 30 Dec 2012 01:08:24 -0500, rickman <gnuarm@gmail.com> wrote:>On 12/28/2012 11:50 PM, robert bristow-johnson wrote: >> On 12/27/12 10:17 PM, rickman wrote: >>> >>> I'm a little confused. I already said, "I have no way to distinguish >>> whether you are conscious or a very well programmed automaton." >> >> you said that, and i'm trying to get you to think about how convincing >> that position is. >> >>> So you >>> may have consciousness or not, how does one distinguish if someone else >>> has consciousness? I know of no test for this. >> >> well, you've tested it on yourself (because you can reach yourself with >> your test, while you cannot reach others with this same test). >> >> so let's say it's EE lab and your lab station has a 15 volt DC supply >> and you hook a resistor with yellow, violet, and red stripes (4.7 K) and >> you measure a little over 3 mA flowing through that resistor. then you >> glance over to the neighboring lab station and they have an identical >> looking DC supply turned on and an identical looking yellow-violet-red >> resistor. and you can't reach over there with your milli-ammeter. but >> what current would you expect to be flowing in that setup that you're >> unable to measure directly? > >I'm not able to conduct the same test on your consciousness as I can on >my own. I can't see the meter on your device only what you tell me.Any test you do on yourself is a self-test and will get the result that you're programmed to get. A self-test can't determine anything it's not programmed to determine.>>> One poster seems to be suggesting that I might be a computer simulation >>> that thinks I have consciousness and you seem to be saying I have no >>> reason to believe I am special so I should assume all beings who appear >>> to have consciousness do because I do. Clearly there is no way to tell. >> >> we can't tell anything for sure. but from what you perceive, what is the >> most reasonable thing to surmise. that you're an independently conscious >> being and everyone else (that walk on two feet and appear to see with >> two eyes and have other perceived similarities to you) are automatons? i >> find that reasoning curious. > >That's just what I would expect an automaton to say. > > >>> Are you part of my simulation or am I part of yours? >> >> well maybe Copernicus might ask are other stars and astronomical objects >> expanding away from us or are we, among many other objects, expanding. >> >> so if none of us is particularly special and you perceive that you're >> not an automaton, what is the consistent conclusion from that? > >That is not direct evidence. It just an opinion based on very little. > >Do you follow Isaac Asimov's "Three Laws of Robotics"? > >RickEric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●December 30, 20122012-12-30
On 12/30/12 1:13 AM, rickman wrote:> On 12/29/2012 1:19 AM, robert bristow-johnson wrote: >> On 12/28/12 6:51 PM, rickman wrote: >>> >>> Yes, you are right. It is so easy to mix up the two issues. The sampling >>> limits the bandwidth. >> >> no. the sampling does *not* limit the bandwidth. sampling with perfect >> reconstruction *requires* (as a condition) limits to the bandwidth. but >> what the sampling does itself (say your sample rate is Fs) is cause your >> spectrum to be repeatedly shifted by a shift equal to all integer >> multiples of Fs and those shifted results overlapped and added up. >> that's what sampling does. it causes your spectrum to become periodic. >> and how it gets periodic is from this shift, overlap and add thing. >> >> > > Ok, that's a little pedantic.it's fundamental. that's fer sure. i am not sure where "fundamental" leaves off and "pedantic" begins.> I'm thinking in practical terms. The > *useful* bandwidth becomes limited by the sample rate.yah, it's pretty hard to have useful bandwidth that's aliased. once you add two numbers together and then you only know the sum, it's pretty hard to know what the two numbers were from the sum.> If you can find > useful ways to allow overlapping, shifted frequencies, then more power > to you. For most that is pretty far out there.i find this fact useful to understand what is really happening (and being a periodicity Nazi, then to inflict this understanding upon everyone else). the basic fact that (unless my Nazi superiors object to naked dirac delta functions) the sampling function is also a Fourier series: +inf +inf T SUM{ delta(t - kT) } = SUM{ e^(j 2 pi n/T t) } k=-inf n=-inf that means, whether you bandlimit the pre-sampled signal or not, that turning this from a continuous-time signal, x(t), to a discrete-time signal, x[n], causes the spectrum of the signal to be periodic with period (in the frequency domain) of 1/T. there is no avoiding that. in this dispute with the periodicity deniers, i am simply applying the very same reasoning when the continuous (but periodic) spectrum coming out of the DTFT is, itself, sampled. that necessarily causes the time-domain signal (which was discrete, but not periodic before) to be made into a periodic signal by the same, repeated shift-and-overlap-add operation. again, there is no avoiding that. the periodicity deniers will be subjugated to the DFT Periodicity Reich whether they like it or not. i am just the messenger. or, they can just give into the Dark Side and accept the fact that the DFT maps one discrete and periodic sequence of period N to another discrete and periodic sequence of the same period in an invertible manner. but that would be the same as saying that the DFT is the same as the Discrete Fourier Series. call that pedantic, but it's curious when something so fundamental on one hand is so controversial on the other. that is a sorta cognitive dissonance. (denial ain't just a river in Egypt.) -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●December 30, 20122012-12-30
On 12/30/12 1:08 AM, rickman wrote:> On 12/28/2012 11:50 PM, robert bristow-johnson wrote: >> On 12/27/12 10:17 PM, rickman wrote: >>> >>> I'm a little confused. I already said, "I have no way to distinguish >>> whether you are conscious or a very well programmed automaton." >> >> you said that, and i'm trying to get you to think about how convincing >> that position is. >> >>> So you >>> may have consciousness or not, how does one distinguish if someone else >>> has consciousness? I know of no test for this. >> >> well, you've tested it on yourself (because you can reach yourself with >> your test, while you cannot reach others with this same test). >> >> so let's say it's EE lab and your lab station has a 15 volt DC supply >> and you hook a resistor with yellow, violet, and red stripes (4.7K) and >> you measure a little over 3 mA flowing through that resistor. then you >> glance over to the neighboring lab station and they have an identical >> looking DC supply turned on and an identical looking yellow-violet-red >> resistor. and you can't reach over there with your milli-ammeter. but >> what current would you expect to be flowing in that setup that you're >> unable to measure directly? > > I'm not able to conduct the same test on your consciousness as I can on > my own. I can't see the meter on your device only what you tell me.no, you see that my power supply appears to be exactly the same model as yours. and you see that yours is a fixed 15 volt supply. and you see that the resistor connected to my terminals have yellow, violent, and red stripes, just like the resistor connected to your terminals. so if your meter tells you that there are 3 mA flowing in your resistor and then the Nazi drill instructor comes in, points to your neighbor's lab station (i guess that's my lab station), and demands that you tell him if there is enough information to know approximately what the current is (in my 4.7K resistor) and what that approximate current would be, and the Nazi drill instructor tells you that if your answer is wrong, you'll be taken out into the courtyard and shot, what will you say? that you don't know? maybe the firing squad is just a figure of imagination. you can't tell if it's real. see, Rickman, you need to apply as tough critical thinking to your own position as you think you're applying to the others.> >>> One poster seems to be suggesting that I might be a computer simulation >>> that thinks I have consciousness and you seem to be saying I have no >>> reason to believe I am special so I should assume all beings who appear >>> to have consciousness do because I do. Clearly there is no way to tell. >> >> we can't tell anything for sure. but from what you perceive, what is the >> most reasonable thing to surmise. that you're an independently conscious >> being and everyone else (that walk on two feet and appear to see with >> two eyes and have other perceived similarities to you) are automatons? i >> find that reasoning curious. > > That's just what I would expect an automaton to say.and that's what I would expect the other automaton (who is deluded into thinking it's special) to say. you have to turn the whole critical skepticism around toward yourself. apply the same critical thinking to yourself that you apply toward the "others" that you think are just stimulus and not real.> >>> Are you part of my simulation or am I part of yours? >> >> well maybe Copernicus might ask are other stars and astronomical objects >> expanding away from us or are we, among many other objects, expanding. >> >> so if none of us is particularly special and you perceive that you're >> not an automaton, what is the consistent conclusion from that? > > That is not direct evidence.so was the case for Copernicus. but what is the *most* reasonable thing to believe? that we are at the center of the universe when there is no astronomical evidence that we are anywhere special? is that the reasonable conclusion?> It just an opinion based on very little.no it's not. none of us have direct evidence. and the fact that you *think* you have consciousness is not evidence***. you could be an automaton that *thinks* it has consciousness. this is the point that Daniel Dennett makes *** Now, some of us, believe that experiential evidence accounts for more than Dennett would grant. but if you are willing to accept "I think therefore I am" as evidence that you are a being, where are you willing to stop with the evidence you "perceive" (using your word) with your senses? unless you think you're living in some kinda Truman Show (did you see that movie), you have to account for what your senses tell you. if you say that you have no proof that what your senses *apparently* convey to you (because they might not be real), then your problem is much deeper. if you are at that philosophical position, you have no way of knowing you're not an automaton programmed with the illusion of consciousness. but if you get past that sorta sophism, it's pretty hard to conclude that these other biological beings that look sorta like you look (head, eyes, two arms, two legs) and interact with you in a predictable manner that might be how you might interact with others, if you get to that point and conclude that the biological being that seems to encase your consciousness is qualitatively so much different than the others that you can't even verify to yourself that they also have consciousness, i think you need to start thinking like Copernicus.> Do you follow Isaac Asimov's "Three Laws of Robotics"?the only science fiction i consume are in movies. from 2001 to Alien to Star Wars. i'm practically illiterate. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●December 30, 20122012-12-30
Eric, i just saw this. On 12/23/12 4:15 PM, Eric Jacobsen wrote:> > I either don't have or can't find my copy of Oppenheim and Willsky, > but in other texts from Oppenheim, e.g., Digitial Signal Processing > and Discrete Time Signal Processing, periodic input sequences are used > for the analysis, but it is not stated (anywhere that I can find) > that this is necessary.from my 1989 edition (this supports what you're saying, Eric): ch.section 8.0, p 514: "Although several points of view can be taken toward the derivation and interpretation of the DFT reprsentations of a finite-duration sequence, we have chosen to base our presentation on the relationship between periodic sequences and finite-length sequences." and then O&S just leave the alternative behind in the dust. on the side of the road. it's almost as if this opening sentence was cursory. for reasons of being polite or political. continuing... "We will bein by consider tihe Fourier series representation of periodic sequences. We accomplish this by constructing a periodic sequence for which each period is identical to the finite-length sequence. As we will see, the Fourier series representation of the periodic sequence corresponds to the DFT of the finite-length sequence. Thus our approach is to define the Fourier series representation for the periodic sequence and to study the properties of such representation. Then we repeat essentially the same derivations assuming that the sequence to be represented is a finite-length sequence. This approach to the DFT emphasizes the fundamental *inherent* periodicity of the DFT representation and ensures that thes periodicity is not overlooked in applications of the DFT." chapter.section 8.6, p. 532: "In recasting Eqs. (8.11) and (8.12) [the DFS analysis and synthesis definitions] in the form of Eqs. (8.61) and (8.62) [the DFT analysis and synthesis definitions] for finite-length sequences, we have not eliminated the *inherent* periodicity. Was with the DFS, the DFT X[k] is equal to samples of the periodic Fourier transform X(e^jw), and if Eq. (8.62) is evalutated for values of n outside the interval 0 <= n <= N-1, the result will not be zero but rather a periodic extension of x[n]. The *inherent* periodicity is *always* present. Sometimes it causes us difficulty and sometimes we can exploit it, but to totally ignore it is to invite trouble."> In Discrete Time Signal Processing the > analysis of the DFT is described using an approach that does not > require any assumption of periodicity in the input.really? doesn't the text say exactly the opposite? Eric, you and i both coming outa the Dakotas, we were probably both exposed to religious fundamentalists who "proof texted scripture" at each other. i am sorta incredulous that i'm doing that with O&S (and it *is* funny how some books become "bibles") or something that's math. to me, it just seems that math is too uncontroversial to have these kinda disparate conclusions. i dunno.> I built on that > approach in this article to amplify the point: > > http://www.dsprelated.com/showarticle/175.php > > As Randy stated a common distinction between the DFS and DFT is that > the DFS model assumes a periodic input, but the Wikipedia entry (which > I agree with) states otherwise: > > http://en.wikipedia.org/wiki/Discrete_Fourier_series > > Likewise, a Berkeley article starts with an assumption of periodicity, > but then also calls the same treatment the Discrete-Time Fourier > Series, which some people hold as distinct from the DFS: > > http://ptolemy.eecs.berkeley.edu/eecs20/week8/dfs.html >i thought it was odd that this says that "you do the DFS with the FFT". (well, i guess that's a paraphrase.) whether it's the DFT or the DFS that we do with the FFT, what is the difference? the FFT is a fast realization of what? i cannot see a single mathematical difference between what the DFT is and what the DFS is as far as you would *use* either. this DFT thing looks, walks, and quacks like this DFS thing. without a single *functional* difference (or *operational* difference), what is the single salient and uncontrived difference? i just don't get it and i really don't think there is anything to get.> I could go on in showing various definitions or descriptions that > differ in significant ways,<sigh> maybe Dale is right. i'm just a fascist.> but I think you get the idea. So > confusion on the topic is understandable. If this is for a class, > use whatever definition your Prof. or Department prefers. Otherwise, > in my experience it is a good idea to clarify with a source what their > definition is to avoid confusion in a particular context. Depending > on the source or context the DFS may or may not be equivalent to the > DFT. > > > > > > Eric Jacobsen > Anchor Hill Communications > http://www.anchorhill.com-- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●December 31, 20122012-12-31
On 12/23/12 8:00 AM, manishp wrote:> > Can you explain what is discrete fourier series vis-a-vis discrete fourier > transform? >okay Manish, i'm thinking about this a little more since i replied last week. if you think of the DFT as sampling the DTFT of x[n] at N equally-spaced points (or if you think of the Z transform of the same sequence, x[n], and you're sampling it around the unit circle at N equally-spaced points), when you sample that (to get X[k]), you are throwing away the information (in X(e^jw)) of what was between the sampling points. there's an infinite amount of information between the samples X(e^(j*2*pi*k/N) that you're tossing away in sampling it. the consequence is that in the other domain, x[n], you are throwing away all of the information outside of the interval 0 <= n < N. there is also an infinite amount of information of x[n] that you are throwing away outside of that interval. now here is the salient difference i have with these other guys: when you lose that information, you end up replacing it with other information that may be true or false. i won't argue with these guys about whether it's true or false - whatever it is that you say is x[n] outside of 0 <= n < N. but what i'll say is that it is this replacement information is not zero. not with the DFT. this replacement information that goes into the same slots of information you had before applying the DFT, that replacement information is the periodic extension of x[n]. this is always the case and for saying that, they (at least one person) calls me a fascist. that's okay, i might be. i think i'm only observing the goose-steppers out in the street and telling everybody else that the fascists have taken over. this would be a paraphrase of Stephen Colbert: "The DFT has a periodic bias." -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●December 31, 20122012-12-31
On Sun, 30 Dec 2012 22:43:21 -0500, robert bristow-johnson <rbj@audioimagination.com> wrote:>Eric, i just saw this. > >On 12/23/12 4:15 PM, Eric Jacobsen wrote: >> >> I either don't have or can't find my copy of Oppenheim and Willsky, >> but in other texts from Oppenheim, e.g., Digitial Signal Processing >> and Discrete Time Signal Processing, periodic input sequences are used >> for the analysis, but it is not stated (anywhere that I can find) >> that this is necessary. > >from my 1989 edition (this supports what you're saying, Eric): > > >ch.section 8.0, p 514: "Although several points of view can be taken >toward the derivation and interpretation of the DFT reprsentations of a >finite-duration sequence, we have chosen to base our presentation on the >relationship between periodic sequences and finite-length sequences." > >and then O&S just leave the alternative behind in the dust. on the side >of the road. it's almost as if this opening sentence was cursory. for >reasons of being polite or political. continuing... > >"We will bein by consider tihe Fourier series representation of periodic >sequences. We accomplish this by constructing a periodic sequence for >which each period is identical to the finite-length sequence. As we >will see, the Fourier series representation of the periodic sequence >corresponds to the DFT of the finite-length sequence. Thus our approach >is to define the Fourier series representation for the periodic sequence >and to study the properties of such representation. Then we repeat >essentially the same derivations assuming that the sequence to be >represented is a finite-length sequence. This approach to the DFT >emphasizes the fundamental *inherent* periodicity of the DFT >representation and ensures that thes periodicity is not overlooked in >applications of the DFT." > >chapter.section 8.6, p. 532: "In recasting Eqs. (8.11) and (8.12) [the >DFS analysis and synthesis definitions] in the form of Eqs. (8.61) and >(8.62) [the DFT analysis and synthesis definitions] for finite-length >sequences, we have not eliminated the *inherent* periodicity. Was with >the DFS, the DFT X[k] is equal to samples of the periodic Fourier >transform X(e^jw), and if Eq. (8.62) is evalutated for values of n >outside the interval 0 <= n <= N-1, the result will not be zero but >rather a periodic extension of x[n]. The *inherent* periodicity is >*always* present. Sometimes it causes us difficulty and sometimes we >can exploit it, but to totally ignore it is to invite trouble." > > >> In Discrete Time Signal Processing the >> analysis of the DFT is described using an approach that does not >> require any assumption of periodicity in the input. > >really? doesn't the text say exactly the opposite? Eric, you and i >both coming outa the Dakotas, we were probably both exposed to religious >fundamentalists who "proof texted scripture" at each other. i am sorta >incredulous that i'm doing that with O&S (and it *is* funny how some >books become "bibles") or something that's math. to me, it just seems >that math is too uncontroversial to have these kinda disparate >conclusions. i dunno. > >> I built on that >> approach in this article to amplify the point: >> >> http://www.dsprelated.com/showarticle/175.php >> >> As Randy stated a common distinction between the DFS and DFT is that >> the DFS model assumes a periodic input, but the Wikipedia entry (which >> I agree with) states otherwise: >> >> http://en.wikipedia.org/wiki/Discrete_Fourier_series >> >> Likewise, a Berkeley article starts with an assumption of periodicity, >> but then also calls the same treatment the Discrete-Time Fourier >> Series, which some people hold as distinct from the DFS: >> >> http://ptolemy.eecs.berkeley.edu/eecs20/week8/dfs.html >> > >i thought it was odd that this says that "you do the DFS with the FFT". > (well, i guess that's a paraphrase.) > >whether it's the DFT or the DFS that we do with the FFT, what is the >difference? the FFT is a fast realization of what? i cannot see a >single mathematical difference between what the DFT is and what the DFS >is as far as you would *use* either. this DFT thing looks, walks, and >quacks like this DFS thing. without a single *functional* difference >(or *operational* difference), what is the single salient and >uncontrived difference? > >i just don't get it and i really don't think there is anything to get. > >> I could go on in showing various definitions or descriptions that >> differ in significant ways, > ><sigh> > >maybe Dale is right. i'm just a fascist.The discussions and arguments have all already been made, and it is clear your mind is set and won't be changed. I see no reason to revisit it.> >> but I think you get the idea. So >> confusion on the topic is understandable. If this is for a class, >> use whatever definition your Prof. or Department prefers. Otherwise, >> in my experience it is a good idea to clarify with a source what their >> definition is to avoid confusion in a particular context. Depending >> on the source or context the DFS may or may not be equivalent to the >> DFT. >> >> >> >> >> >> Eric Jacobsen >> Anchor Hill Communications >> http://www.anchorhill.com > > >-- > >r b-j rbj@audioimagination.com > >"Imagination is more important than knowledge." > >Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
