robert bristow-johnson <rbj@audioimagination.com> writes:> On 10/23/12 4:31 AM, manishp wrote: >> >> Yes. I assumed asterisk operator above to be convolution function. >> My mistake indeed ... > > it's the problem with ASCII math (maybe one reason Randy used TeX > script, but then you gotta know what "\cdot" means) > > in my opinion, the naked asterisk is an unfortunate choice for > convolution in the textbooks and other lit. i would have put that > asterisk in a little circle to make it look like is "more" than > multiplication. in ASCII math, i surround it with parenths to make it > look like something else: > > y(t) = h(t) (*) x(t) > > i am now trying to get out of the habit of using * for multiplication > on these pages but sometimes it's unavoidable. > >> >> But coming back to main question. I do understand that sub-carriers are >> orthogonal, but question is in what way this property is useful? >> That is, orthogonality in sub-carriers ... > > you can put different and unrelated information of similar bandwidth > on the two different carriers if they are orthogonal.Exactly. It's why I once asked in (information theory?) class why anyone would use BPSK instead of QPSK - twice the data rate for the same bandwidth. I suppose it's done due to other concerns, e.g., simpler receiver. -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
OFDM
Started by ●October 20, 2012
Reply by ●October 23, 20122012-10-23
Reply by ●October 23, 20122012-10-23
On Tue, 23 Oct 2012 11:12:09 -0400, robert bristow-johnson wrote:> On 10/23/12 4:31 AM, manishp wrote: >> >> Yes. I assumed asterisk operator above to be convolution function. My >> mistake indeed ... > > it's the problem with ASCII math (maybe one reason Randy used TeX > script, but then you gotta know what "\cdot" means) > > in my opinion, the naked asterisk is an unfortunate choice for > convolution in the textbooks and other lit. i would have put that > asterisk in a little circle to make it look like is "more" than > multiplication. in ASCII math, i surround it with parenths to make it > look like something else: > > y(t) = h(t) (*) x(t) > > i am now trying to get out of the habit of using * for multiplication on > these pages but sometimes it's unavoidable.For multiplication I try to use something like (a(t))(b(t)). For convolution, I try to say "convolve". Oh, if we'd all just install TeX interpreters in our heads... -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com
Reply by ●October 23, 20122012-10-23
On Tue, 23 Oct 2012 11:29:33 -0400, Randy Yates wrote:> robert bristow-johnson <rbj@audioimagination.com> writes: > >> On 10/23/12 4:31 AM, manishp wrote: >>> >>> Yes. I assumed asterisk operator above to be convolution function. My >>> mistake indeed ... >> >> it's the problem with ASCII math (maybe one reason Randy used TeX >> script, but then you gotta know what "\cdot" means) >> >> in my opinion, the naked asterisk is an unfortunate choice for >> convolution in the textbooks and other lit. i would have put that >> asterisk in a little circle to make it look like is "more" than >> multiplication. in ASCII math, i surround it with parenths to make it >> look like something else: >> >> y(t) = h(t) (*) x(t) >> >> i am now trying to get out of the habit of using * for multiplication >> on these pages but sometimes it's unavoidable. >> >> >>> But coming back to main question. I do understand that sub-carriers >>> are orthogonal, but question is in what way this property is useful? >>> That is, orthogonality in sub-carriers ... >> >> you can put different and unrelated information of similar bandwidth on >> the two different carriers if they are orthogonal. > > Exactly. It's why I once asked in (information theory?) class why anyone > would use BPSK instead of QPSK - twice the data rate for the same > bandwidth. I suppose it's done due to other concerns, e.g., simpler > receiver.BPSK has a larger distance between decision points (dang, I can't remember the real term). QPSK requires twice the power at the same bandwidth (in essence, it requires the _same_ energy/symbol) to get the same bit error rate. At least, if the caffeine is working yet... And yes, both transmit and receive are simpler with BPSK. -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com
Reply by ●October 23, 20122012-10-23
On Tue, 23 Oct 2012 03:31:46 -0500, manishp wrote:>>Tim Wescott <tim@seemywebsite.com> wrote: >>> On Mon, 22 Oct 2012 09:44:34 -0500, manishp wrote: >> >>>>>Frequency elements a and b are orthogonal if >>>>> >>>>> +infinity >>>>> INTEGRAL(f(a)*f(b))dt=0 >>>>> -infinity >> >>>> Hello Jerry, >> >>>> Since convolution includes intgration already, does the above >>>> equation mean there is a double integration. First due to convolution >>>> and then over the resultant signal. Can you please clarify? >> >>> How did convolution get into this? You were asking about >>> orthogonality > >>> in the frequency domain -- that has no direct relationship to > convolution. >> >>Jerry used *, the symbol for multiply in most computer languages, but >>also similar to the symbol some use for convolution. >> >>-- glen > > Yes. I assumed asterisk operator above to be convolution function. My > mistake indeed ... > > But coming back to main question. I do understand that sub-carriers are > orthogonal, but question is in what way this property is useful? That > is, orthogonality in sub-carriers ...At its most basic, because no sub-carrier interferes with any other. So regardless of what you put in subcarrier n, it doesn't affect the information in subcarrier m so long as n != m. -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com
Reply by ●October 23, 20122012-10-23
Tim Wescott <tim@seemywebsite.com> writes:> On Tue, 23 Oct 2012 11:29:33 -0400, Randy Yates wrote: > >> robert bristow-johnson <rbj@audioimagination.com> writes: >> >>> On 10/23/12 4:31 AM, manishp wrote: >>>> >>>> Yes. I assumed asterisk operator above to be convolution function. My >>>> mistake indeed ... >>> >>> it's the problem with ASCII math (maybe one reason Randy used TeX >>> script, but then you gotta know what "\cdot" means) >>> >>> in my opinion, the naked asterisk is an unfortunate choice for >>> convolution in the textbooks and other lit. i would have put that >>> asterisk in a little circle to make it look like is "more" than >>> multiplication. in ASCII math, i surround it with parenths to make it >>> look like something else: >>> >>> y(t) = h(t) (*) x(t) >>> >>> i am now trying to get out of the habit of using * for multiplication >>> on these pages but sometimes it's unavoidable. >>> >>> >>>> But coming back to main question. I do understand that sub-carriers >>>> are orthogonal, but question is in what way this property is useful? >>>> That is, orthogonality in sub-carriers ... >>> >>> you can put different and unrelated information of similar bandwidth on >>> the two different carriers if they are orthogonal. >> >> Exactly. It's why I once asked in (information theory?) class why anyone >> would use BPSK instead of QPSK - twice the data rate for the same >> bandwidth. I suppose it's done due to other concerns, e.g., simpler >> receiver. > > BPSK has a larger distance between decision points (dang, I can't > remember the real term).yeah, me either - but i know what you mean.> QPSK requires twice the power at the same > bandwidth (in essence, it requires the _same_ energy/symbol) to get the > same bit error rate.Oh yeah. I forgot about that...> At least, if the caffeine is working yet...It is - what octane are you using? I need to upgrade. -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●October 23, 20122012-10-23
On Tue, 23 Oct 2012 11:29:33 -0400, Randy Yates <yates@digitalsignallabs.com> wrote:>robert bristow-johnson <rbj@audioimagination.com> writes: > >> On 10/23/12 4:31 AM, manishp wrote: >>> >>> Yes. I assumed asterisk operator above to be convolution function. >>> My mistake indeed ... >> >> it's the problem with ASCII math (maybe one reason Randy used TeX >> script, but then you gotta know what "\cdot" means) >> >> in my opinion, the naked asterisk is an unfortunate choice for >> convolution in the textbooks and other lit. i would have put that >> asterisk in a little circle to make it look like is "more" than >> multiplication. in ASCII math, i surround it with parenths to make it >> look like something else: >> >> y(t) = h(t) (*) x(t) >> >> i am now trying to get out of the habit of using * for multiplication >> on these pages but sometimes it's unavoidable. >> >>> >>> But coming back to main question. I do understand that sub-carriers are >>> orthogonal, but question is in what way this property is useful? >>> That is, orthogonality in sub-carriers ... >> >> you can put different and unrelated information of similar bandwidth >> on the two different carriers if they are orthogonal. > >Exactly. It's why I once asked in (information theory?) class why anyone >would use BPSK instead of QPSK - twice the data rate for the same >bandwidth. I suppose it's done due to other concerns, e.g., simpler >receiver.There's a 3dB difference in link margin. That's huge. ;) Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●October 23, 20122012-10-23
On 10/23/12 1:48 PM, Tim Wescott wrote:> On Tue, 23 Oct 2012 11:12:09 -0400, robert bristow-johnson wrote: > >> On 10/23/12 4:31 AM, manishp wrote: >>> >>> Yes. I assumed asterisk operator above to be convolution function. My >>> mistake indeed ... >> >> it's the problem with ASCII math (maybe one reason Randy used TeX >> script, but then you gotta know what "\cdot" means) >> >> in my opinion, the naked asterisk is an unfortunate choice for >> convolution in the textbooks and other lit. i would have put that >> asterisk in a little circle to make it look like is "more" than >> multiplication. in ASCII math, i surround it with parenths to make it >> look like something else: >> >> y(t) = h(t) (*) x(t) >> >> i am now trying to get out of the habit of using * for multiplication on >> these pages but sometimes it's unavoidable. > > For multiplication I try to use something like (a(t))(b(t)). For > convolution, I try to say "convolve". > > Oh, if we'd all just install TeX interpreters in our heads... >consider spending some time at Wikipedia either contributing new material to technical pages or standing vigil against errors and crap. then you'll develop a TeX interpreter in your brain. (and they have a page explaining stuff at http://en.wikipedia.org/wiki/Wikipedia:Math . looks like they added a few symbols, \circledast and \triangleq . wish they had those before. the first is what *i* think should be used for convolution and the latter for a defined equality.) -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●October 23, 20122012-10-23
On 10/23/2012 3:02 PM, robert bristow-johnson wrote:> > consider spending some time at Wikipedia either contributing new > material to technical pages or standing vigil against errors and crap. > then you'll develop a TeX interpreter in your brain. (and they have a > page explaining stuff at http://en.wikipedia.org/wiki/Wikipedia:Math . > looks like they added a few symbols, \circledast and \triangleq . wish > they had those before. the first is what *i* think should be used for > convolution and the latter for a defined equality.)And how do these equations get shown on the web page, as a graphic? Rick
