# Need proofs about digital comminucation

Started by April 15, 2004
```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(&#4294967295;) = E[N(t+&#4294967295;)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 :)
```
```"ford" <ford_usa_mustang@yahoo.fr> wrote in message
> 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(&#4294967295;) = E[N(t+&#4294967295;)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...

```
```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(&#4294967295;) = E[N(t+&#4294967295;)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 orthonormals

You 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
```
```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
>> 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(&#4294967295;) = E[N(t+&#4294967295;)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
```
```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
>>> 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(&#4294967295;) = E[N(t+&#4294967295;)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.

```
```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
>>
>>>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(&#4294967295;) = E[N(t+&#4294967295;)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

Might 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.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;

```
```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
>>>
>>>>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(&#4294967295;) = E[N(t+&#4294967295;)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
```
```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.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;

```
```"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."

```
```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.
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;

```