Hi everybody,
I need some help to prove thses statements :
1)Show that white noise has a power-spectral density SNw(f) =
N0=2 knowing that SN(f) is the Fourier transform of the autocorrela-
tion function R(�) = E[N(t+�)N(t)] of the stationary noise process
N(t).
2)Show that the sinc-pulse:
p(t) =sin((pi*t)/T) /((pi*t)/T) T^0.5 is the inverse Fourier transform
of the spectrum
P(f) = T^0.5 for |f| < 1 / (2T)
0 for |f| > 1 / (2T)
3) Show that sinc-pulses are orthonormals
Thanks in advance :)
Need proofs about digital comminucation
Started by ●April 15, 2004
Reply by ●April 15, 20042004-04-15
"ford" <ford_usa_mustang@yahoo.fr> wrote in message news:9fe525a9.0404150420.48a5d0ba@posting.google.com...> Hi everybody, > I need some help to prove thses statements : > > 1)Show that white noise has a power-spectral density SNw(f) = > N0=2 knowing that SN(f) is the Fourier transform of the autocorrela- > tion function R(�) = E[N(t+�)N(t)] of the stationary noise process > N(t). > > 2)Show that the sinc-pulse: > p(t) =sin((pi*t)/T) /((pi*t)/T) T^0.5 is the inverse Fourier transform > of the spectrum > P(f) = T^0.5 for |f| < 1 / (2T) > 0 for |f| > 1 / (2T) > 3) Show that sinc-pulses are orthonormals > > Thanks in advance :)Final exam time already, huh? Good luck to you. You might want to try studying your textbook a little bit before turning in a blank paper...
Reply by ●April 15, 20042004-04-15
ford_usa_mustang@yahoo.fr (ford) writes:> Hi everybody, > I need some help to prove thses statements : > > 1)Show that white noise has a power-spectral density SNw(f) = > N0=2 knowing that SN(f) is the Fourier transform of the autocorrela- > tion function R(�) = E[N(t+�)N(t)] of the stationary noise process > N(t).In my usenet client, I get some funny characters. Try using plain ascii.> 2)Show that the sinc-pulse: > p(t) =sin((pi*t)/T) /((pi*t)/T) T^0.5 is the inverse Fourier transform > of the spectrum > P(f) = T^0.5 for |f| < 1 / (2T) > 0 for |f| > 1 / (2T)You know the equation for the inverse Fourier transform, right? Plug it in and try it.> 3) Show that sinc-pulses are orthonormalsYou know the definition of orthonormal, right? Apply the tests implicit in the definition and see if the sinc function passes. -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA randy.yates@sonyericsson.com, 919-472-1124
Reply by ●April 16, 20042004-04-16
On Thu, 15 Apr 2004 13:12:18 -0400, "James Calivar" <amheiserbush@yahoo.com.au> wrote:>"ford" <ford_usa_mustang@yahoo.fr> wrote in message >news:9fe525a9.0404150420.48a5d0ba@posting.google.com... >> Hi everybody, >> I need some help to prove thses statements : >> >> 1)Show that white noise has a power-spectral density SNw(f) = >> N0=2 knowing that SN(f) is the Fourier transform of the autocorrela- >> tion function R(�) = E[N(t+�)N(t)] of the stationary noise process >> N(t). >> >> 2)Show that the sinc-pulse: >> p(t) =sin((pi*t)/T) /((pi*t)/T) T^0.5 is the inverse Fourier transform >> of the spectrum >> P(f) = T^0.5 for |f| < 1 / (2T) >> 0 for |f| > 1 / (2T) >> 3) Show that sinc-pulses are orthonormals >> >> Thanks in advance :) > >Final exam time already, huh? Good luck to you. You might want to try >studying your textbook a little bit before turning in a blank paper...Yeah, is it just me, or are people getting less creative about disguising classwork here? Some of the recent appearances are pretty obvious... Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org
Reply by ●April 16, 20042004-04-16
On Fri, 16 Apr 2004 03:34:54 GMT, eric.jacobsen@delete.ieee.org (Eric Jacobsen) wrote:>On Thu, 15 Apr 2004 13:12:18 -0400, "James Calivar" ><amheiserbush@yahoo.com.au> wrote: > >>"ford" <ford_usa_mustang@yahoo.fr> wrote in message >>news:9fe525a9.0404150420.48a5d0ba@posting.google.com... >>> Hi everybody, >>> I need some help to prove thses statements : >>> >>> 1)Show that white noise has a power-spectral density SNw(f) = >>> N0=2 knowing that SN(f) is the Fourier transform of the autocorrela- >>> tion function R(�) = E[N(t+�)N(t)] of the stationary noise process >>> N(t). >>> >>> 2)Show that the sinc-pulse: >>> p(t) =sin((pi*t)/T) /((pi*t)/T) T^0.5 is the inverse Fourier transform >>> of the spectrum >>> P(f) = T^0.5 for |f| < 1 / (2T) >>> 0 for |f| > 1 / (2T) >>> 3) Show that sinc-pulses are orthonormals >>> >>> Thanks in advance :) >> >>Final exam time already, huh? Good luck to you. You might want to try >>studying your textbook a little bit before turning in a blank paper... > >Yeah, is it just me, or are people getting less creative about >disguising classwork here? Some of the recent appearances are pretty >obvious...I think the law of large numbers are at work here. I am sure the letters from nigerian princes which want to transfer money to US and give you some portion of it are pretty obviously bogus to you but still they get some people. As the reach of comp.dsp is getting larger, I am sure some people are responding to even the most obvious homework problems.
Reply by ●April 16, 20042004-04-16
Eric Jacobsen wrote:> On Thu, 15 Apr 2004 13:12:18 -0400, "James Calivar" > <amheiserbush@yahoo.com.au> wrote: > > >>"ford" <ford_usa_mustang@yahoo.fr> wrote in message >>news:9fe525a9.0404150420.48a5d0ba@posting.google.com... >> >>>Hi everybody, >>>I need some help to prove thses statements : >>> >>>1)Show that white noise has a power-spectral density SNw(f) = >>>N0=2 knowing that SN(f) is the Fourier transform of the autocorrela- >>>tion function R(�) = E[N(t+�)N(t)] of the stationary noise process >>>N(t). >>> >>>2)Show that the sinc-pulse: >>>p(t) =sin((pi*t)/T) /((pi*t)/T) T^0.5 is the inverse Fourier transform >>>of the spectrum >>>P(f) = T^0.5 for |f| < 1 / (2T) >>> 0 for |f| > 1 / (2T) >>>3) Show that sinc-pulses are orthonormals >>> >>>Thanks in advance :) >> >>Final exam time already, huh? Good luck to you. You might want to try >>studying your textbook a little bit before turning in a blank paper... > > > Yeah, is it just me, or are people getting less creative about > disguising classwork here? Some of the recent appearances are pretty > obvious... > > > Eric Jacobsen > Minister of Algorithms, Intel Corp. > My opinions may not be Intel's opinions. > http://www.ericjacobsen.orgMight I suggest that the only ones we notice are the ones who have no shame? When I interviewed new graduates as job candidates, I would ask them which subjects they liked best or felt they were strongest in, then concentrated on those. I didn't expect encyclopedic knowledge like Dilip's or Clay's or yours, but if they turned out to be relatively clueless about what they claimed as their strong points, There was no point discussing much else. Either they were weak overall, or they were bullshitting me by saying what they thought I wanted to hear. Thumbs down! On the other hand, -- here's the tie in -- I was quite willing to accept, "I don't know, but I know where to look it up" about almost anything but Ohm's Law and superposition. So maybe when some of these budding engineers go for a job interview, they'll say, "I don't know, but I can ask the friendly folk at comp.dsp." Keep smiling! Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 16, 20042004-04-16
kal wrote:> On Fri, 16 Apr 2004 03:34:54 GMT, eric.jacobsen@delete.ieee.org (Eric > Jacobsen) wrote: > > >>On Thu, 15 Apr 2004 13:12:18 -0400, "James Calivar" >><amheiserbush@yahoo.com.au> wrote: >> >> >>>"ford" <ford_usa_mustang@yahoo.fr> wrote in message >>>news:9fe525a9.0404150420.48a5d0ba@posting.google.com... >>> >>>>Hi everybody, >>>>I need some help to prove thses statements : >>>> >>>>1)Show that white noise has a power-spectral density SNw(f) = >>>>N0=2 knowing that SN(f) is the Fourier transform of the autocorrela- >>>>tion function R(�) = E[N(t+�)N(t)] of the stationary noise process >>>>N(t). >>>> >>>>2)Show that the sinc-pulse: >>>>p(t) =sin((pi*t)/T) /((pi*t)/T) T^0.5 is the inverse Fourier transform >>>>of the spectrum >>>>P(f) = T^0.5 for |f| < 1 / (2T) >>>> 0 for |f| > 1 / (2T) >>>>3) Show that sinc-pulses are orthonormals >>>> >>>>Thanks in advance :) >>> >>>Final exam time already, huh? Good luck to you. You might want to try >>>studying your textbook a little bit before turning in a blank paper... >> >>Yeah, is it just me, or are people getting less creative about >>disguising classwork here? Some of the recent appearances are pretty >>obvious... > > > I think the law of large numbers are at work here. I am sure the > letters from nigerian princes which want to transfer money to US and > give you some portion of it are pretty obviously bogus to you but > still they get some people. As the reach of comp.dsp is getting > larger, I am sure some people are responding to even the most obvious > homework problems. >So if there's a FAQ for the list (is there a FAQ?) then "how can I do my homework using the list" should say "hit the books?". I wonder how many of these people are just lazy and how many are truly desperate. Some scholarship programs can be pretty harsh about low grades, and you often don't realize that you're bombing a class until it's too late to withdraw. Not that we should all jump in and do everyone's spring exams, mind, but the thought does keep me from typing in a lot of snide comments. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●April 16, 20042004-04-16
Tim Wescott wrote: ...> So if there's a FAQ for the list (is there a FAQ?) then "how can I do my > homework using the list" should say "hit the books?".The real FAQ is at http://www.bdti.com/faq/dsp_faq.htm. A "procedural FAQ" developed by several of us has a brief mention of homework. You can add words to it if you like. http://users.erols.com/jyavins/procfaq.htm> I wonder how many of these people are just lazy and how many are truly > desperate. Some scholarship programs can be pretty harsh about low > grades, and you often don't realize that you're bombing a class until > it's too late to withdraw. Not that we should all jump in and do > everyone's spring exams, mind, but the thought does keep me from typing > in a lot of snide comments.I think that derision of any kind is out of place, and while straight- faced parody and misdirection is a tempting way to display cleverness, it's too likely to be hurtful to make it worth risking. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 17, 20042004-04-17
"Jerry Avins" <jya@ieee.org> wrote in message news:4080150b$0$16451$61fed72c@news.rcn.com...> Tim Wescott wrote: > > > > I wonder how many of these people are just lazy and how many are truly > > desperate. Some scholarship programs can be pretty harsh about low > > grades, and you often don't realize that you're bombing a class until > > it's too late to withdraw. Not that we should all jump in and do > > everyone's spring exams, mind, but the thought does keep me from typing > > in a lot of snide comments. > > I think that derision of any kind is out of place, and while straight- > faced parody and misdirection is a tempting way to display cleverness, > it's too likely to be hurtful to make it worth risking. > > JerryI disagree. Look, we've all been through the undergrad wringer (and some of us the graduate school wringer, as well), right? My experience in both undergraduate and graduate programs has showed me that there are basically two types of students - those that bust ass and do the best they can to understand the material, and those that are just in it to get a piece of paper at the end of 4+ years, with minimal effort expended. If a student really doesn't have enough of a clue to know whether or not they are going to fail a class until this point of the semester (2/3 of the way through), then they either haven't been paying attention or they're just not hitting the books hard enough. In either case, if they don't learn the material, they should not receive a passing grade (or at least not a good grade). That's the way it is. I don't have any sympathy for people who are looking for handouts. "Teach a man to fish" and all that - I'm sorry, but the OP's post was so obviously desparate for a freebie that it made me cringe. I mean come on - show that the sinc-pulse is the inverse Fourier transform of whatever spectral function?? That is the classic "proof left as exercise for the reader."
Reply by ●April 17, 20042004-04-17
James Calivar wrote:> "Jerry Avins" <jya@ieee.org> wrote in message > news:4080150b$0$16451$61fed72c@news.rcn.com... > >>Tim Wescott wrote: >> >> >> >>>I wonder how many of these people are just lazy and how many are truly >>>desperate. Some scholarship programs can be pretty harsh about low >>>grades, and you often don't realize that you're bombing a class until >>>it's too late to withdraw. Not that we should all jump in and do >>>everyone's spring exams, mind, but the thought does keep me from typing >>>in a lot of snide comments. >> >>I think that derision of any kind is out of place, and while straight- >>faced parody and misdirection is a tempting way to display cleverness, >>it's too likely to be hurtful to make it worth risking. >> >>Jerry > > > I disagree. Look, we've all been through the undergrad wringer (and some of > us the graduate school wringer, as well), right? My experience in both > undergraduate and graduate programs has showed me that there are basically > two types of students - those that bust ass and do the best they can to > understand the material, and those that are just in it to get a piece of > paper at the end of 4+ years, with minimal effort expended. If a student > really doesn't have enough of a clue to know whether or not they are going > to fail a class until this point of the semester (2/3 of the way through), > then they either haven't been paying attention or they're just not hitting > the books hard enough. In either case, if they don't learn the material, > they should not receive a passing grade (or at least not a good grade). > That's the way it is. > > I don't have any sympathy for people who are looking for handouts. "Teach a > man to fish" and all that - I'm sorry, but the OP's post was so obviously > desparate for a freebie that it made me cringe. I mean come on - show that > the sinc-pulse is the inverse Fourier transform of whatever spectral > function?? That is the classic "proof left as exercise for the reader."But it's not just the gadfly student who reads the message. Suppose that some poor schlub like me or Owlett, with a tenuous hold on that particular topic and without an instructor at all, reads it and misses the put-on. You've done that self-taught student a disservice that should haunt you. It's just not worth it. The standards we use when face to face don't carry over to the friendly anonymity we experience here. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
