On Mar 31, 1:38=A0am, Fred Marshall <fmarshallxremove_th...@acm.org> wrote:> On 3/30/2011 8:48 PM, robert bristow-johnson wrote: > > > there*is* =A0a > > qualitative difference between the real and imaginary axes and it > > isn't just because of the labels. > > r b-j, > > OK. =A0What is it then? =A0I'm interested in how an axis can have > "quality"... and I'm more interested in the answer to the first question > here.there is a perfect symmetry with the imaginary axis. there is nothing you can say about +j that you cannot say about -j. now, how about the real axis? is there anything about +1 that is different than -1? i.e., even if we can flip about the real axis without changing anything, we cannot rotate the complex plane 90 degrees without changing something noticeable. that's for starters. r b-j
Calibrating FFT results, amplitude in to magnitude out
Started by ●March 25, 2011
Reply by ●March 31, 20112011-03-31
Reply by ●March 31, 20112011-03-31
On 3/31/2011 4:31 AM, robert bristow-johnson wrote: ..snip> > i.e., even if we can flip about the real axis without changing > anything, we cannot rotate the complex plane 90 degrees without > changing something noticeable. > > that's for starters. > > r b-jOK. What is the something noticeable? I'm not being intentionally dense here, just want to understand. Fred
Reply by ●March 31, 20112011-03-31
robert bristow-johnson <rbj@audioimagination.com> wrote: (snip)> there is a perfect symmetry with the imaginary axis. there is nothing > you can say about +j that you cannot say about -j. now, how about the > real axis? is there anything about +1 that is different than -1?Using my previous example, with R being real impedance, and L being imaginary, would it not have worked the other way around? Yes changing the axis doesn't change anything, but changing L to -L does change things.> i.e., even if we can flip about the real axis without changing > anything, we cannot rotate the complex plane 90 degrees without > changing something noticeable.-- glen
Reply by ●March 31, 20112011-03-31
On 3/31/2011 1:05 PM, glen herrmannsfeldt wrote:> robert bristow-johnson<rbj@audioimagination.com> wrote: > > (snip) >> there is a perfect symmetry with the imaginary axis. there is nothing >> you can say about +j that you cannot say about -j. now, how about the >> real axis? is there anything about +1 that is different than -1? > > Using my previous example, with R being real impedance, and L > being imaginary, would it not have worked the other way around? > Yes changing the axis doesn't change anything, but changing L to -L > does change things. > >> i.e., even if we can flip about the real axis without changing >> anything, we cannot rotate the complex plane 90 degrees without >> changing something noticeable. > > -- glenI really don't get it guys... Why talk about "L" at all? First, we must be talking about a single frequency. Second, we are talking about the phase difference between voltage and current. Voltage is real-world. Current is real-world. Phase is a temporal measure. "j" only helps with phasor notation regarding the phase of this or that ... All of these are physical quantities that can be observed. So, no ghosts.... What's the point being made with this? Fred
Reply by ●March 31, 20112011-03-31
I know I'm coming in late, but I've been away all day. I haven't read the r= est of the thread yet. Please excuse me if that turns out to be a mistake. On Wednesday, March 30, 2011 11:48:09 PM UTC-4, robert bristow-johnson wrot= e:> On Mar 30, 1:51 pm, Fred Marshall <fmarshallxr...@acm.org> > wrote: > > > > Well, I believe all that. It's just more information about a physical > > reality. You're very clear it's about a phase shift - which is clearly > > a real thing. > > > > I think what you're describing is the *handy notation* that ends up > > using 2-dimensional numbers/vectors .. whatever. We label one dimensio=n> > "real" (unfortunately) and the other dimension "imaginary" > > (unfortunately) and call the combinations of them "complex" which may b=e> > OK but is just another term for "2-dimensional". >=20 > no, it's *not* just another dimension like y is to x. in empty space, > there is no qualitative difference between x, y, and z. there *is* a > qualitative difference between the real and imaginary axes and it > isn't just because of the labels.What is that difference, then? In the s plane, one axis represents frequenc= y and the other, gain. The only reason co call one imaginary has to do with= the way we do the math.> i really think that the labels, "real" and "imaginary" flow from the > description. =20Why is frequency imaginary and gain real, other than sigma and j-omega?> when we measure and describe physical quantity of things > that are real, of time and spatial displacement and mass and energy > and charge, we use real numbers for that quantity. complex and > imaginary numbers come in as a concept or an intellectual > construction. we imagine phasors, but it's a sinusoidal voltage > changing in time.And the Poyinting vector?> On Mar 30, 2:09=A0pm, Jerry Avins <j....@ieee.org> wrote: > > Right on, Fred! Adopting your new terms (for 2D) there is a view worth =noting.>=20 > am i the only once here that thinks that "real" and "imaginary" are > apt names for these kind of numbers? i dunno about "complex", but i > think it's as good as anything else. maybe "total" or "comprehensive" > would be a better term than "complex", but "real" and "imaginary" are, > i think the best descriptive adjectives for the kind of numbers they > are referring to. >=20 > > Combining righteous and upper quantities into a single number makes sen=se only if those quantities are orthogonal.>=20 > so are you suggesting, Jerry, that "real" and "imaginary" are not > orthogonal?No. I tried to write that propagation delay and attenuation are orthogonal,= making the pair a good candidate for being expressed as a single complex n= umber.> is it because you make something more imaginary does, conceptually, > affect how real it is.I don't understand what you're driving at there. Jerry --=20 Engineering is the art of making what you want from things you can get.
Reply by ●March 31, 20112011-03-31
On Mar 31, 1:44=A0pm, Fred Marshall <fmarshallxremove_th...@acm.org> wrote:> On 3/31/2011 4:31 AM, robert bristow-johnson wrote: > ..snip > > > > > i.e., even if we can flip about the real axis without changing > > anything, we cannot rotate the complex plane 90 degrees without > > changing something noticeable. > > > OK. > What is the something noticeable? I'm not being intentionally dense > here, just want to understand.well, start with the complex plane oriented the normal way, take any x on the horizontal real axis and stuff that into an exponential (they're sorta all the same, but let's say the exponential base is e). so we're sending x (which is real) to e^x (which is also real). or try raising any of these real x's to the 0th power. the result remains on the real axis. so now let's turn the complex plane clockwise 90 degrees and pick any number, j*y, on the horizontal imaginary axis. stuff *this* purely imaginary number into the exponential (e^(j*y)) and see if the result remains on the horizontal imaginary axis. does it? even if you chose your base to be on the imaginary axis, so now it's (j*e)^(j*y) it *still* won't remain on the horizontal imaginary axis. and definitely, (j*y)^0 is gonna be 1. r b-j
Reply by ●March 31, 20112011-03-31
Jerry Avins <jya@ieee.org> wrote: (snip)> No. I tried to write that propagation delay and attenuation > are orthogonal, making the pair a good candidate for being > expressed as a single complex number.Yes. In electronics, attenuation (R) is real, where delay (L and C) are imaginary. In optics, attenuation is imaginary, and delay is real. -- glen
Reply by ●March 31, 20112011-03-31
Whatever simplifies the math. Orthogonal either way. Jerry -- Engineering is the art of making what you want from things you can get.
Reply by ●March 31, 20112011-03-31
On 3/31/2011 3:04 PM, robert bristow-johnson wrote:> On Mar 31, 1:44 pm, Fred Marshall<fmarshallxremove_th...@acm.org> > wrote: >> On 3/31/2011 4:31 AM, robert bristow-johnson wrote: >> ..snip >> >> >> >>> i.e., even if we can flip about the real axis without changing >>> anything, we cannot rotate the complex plane 90 degrees without >>> changing something noticeable. >> >> >> OK. >> What is the something noticeable? I'm not being intentionally dense >> here, just want to understand. > > well, start with the complex plane oriented the normal way, take any x > on the horizontal real axis and stuff that into an exponential > (they're sorta all the same, but let's say the exponential base is > e). so we're sending x (which is real) to e^x (which is also real). > > or try raising any of these real x's to the 0th power. the result > remains on the real axis. > > so now let's turn the complex plane clockwise 90 degrees and pick any > number, j*y, on the horizontal imaginary axis. stuff *this* purely > imaginary number into the exponential (e^(j*y)) and see if the result > remains on the horizontal imaginary axis. does it? even if you chose > your base to be on the imaginary axis, so now it's (j*e)^(j*y) it > *still* won't remain on the horizontal imaginary axis. > > and definitely, (j*y)^0 is gonna be 1. > > r b-jHmmmm.... thanks! Well this leads me to a number of thoughts: I found this in my text on Advanced Calculus: "Many mathematical results may be stated more simply, and obtained more readily, by the use of complex quantitites in the intermediate stages, even if the final applications involve real numbers only." and this from a mathematician... not as an argument, just as a point of reference. I think this is the crux of the discussion here. Anyway... I was led to thinking about roots of equations in 3-D or some such thing: What are the roots of (x^4-1)(y^4-1) ? One would say that the imaginary roots of x^4-1 are x=+/- j. So, we're really still talking about x so far. OK but then what are the roots of y^4-1? One would say that the imaginary roots of y^4-1 are y=+/- j. So now were talking about y. Clearly this presents a 4-D situation: x re and im, y re and im. I'm not sure how this is dealt with but it sure isn't plotted, eh? So, what if we have (x^4-1)(y^4-1)(z^4-1) ? The space of roots then takes up 6 dimensions. So, thinking about this I found: http://users.ox.ac.uk/~tweb/00001/#08 Heck, I don't understand much of it and the issue above doesn't just jump out at me! I don't think everything I said earlier was correct but I don't think it was all wrong either. Back to the crux above..... Still pondering... I wonder if above you might have said: (j)^0 is gonna be 1, without the y. Fred
Reply by ●April 1, 20112011-04-01
On Mar 31, 6:44=A0pm, Fred Marshall <fmarshallxremove_th...@acm.org> wrote:> On 3/31/2011 4:31 AM, robert bristow-johnson wrote: > ..snip > > > > > i.e., even if we can flip about the real axis without changing > > anything, we cannot rotate the complex plane 90 degrees without > > changing something noticeable. > > > that's for starters. > > > r b-j > > OK. > What is the something noticeable? I'm not being intentionally dense > here, just want to understand. > > FredThe identity of the algebra is on the real axis, thereby distinguishing it from the imaginary axis. More completely, complex conjugation is an algebra homomorphism. Multiplying by i is not an algebra homomorphism. Therefore, switching real and imaginary parts, which is equvalent to complex conjugation followed by multiplication by i, is not an algebra homomorphism. So x and y axes are not equivalent (this is the definition of equivalence in fact). illywhacker;
