Reply by Jerry Avins June 28, 20052005-06-28
Rick Lyons wrote:
> On Mon, 20 Jun 2005 07:11:34 GMT, "Angelo Ricotta" > <a.ricotta@isac.cnr.it> wrote: > > > > (snipped) > >>Thank you Rick for your kindness. May I ask you how did you find your >>inequalities? As I already explained, I deduced mine from a diagram on a >>Bendat & Piersol book, with a simple reasoning. >> >>Angelo >> > > > Hi, > Oh shoot. That was so many years ago. > I think I found the inequality somewhere and > then I graphically proved to myself that it > was correct. My little graphical proof is > in Chapter 2 of my DSP book.
If you write the inequality as two separate equalities and examine individual values of m, the aliases just "knock at the gate". 2Fc-B ------- = Fs m 2Fc+B Fs = ------- m+1 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;
Reply by Rick Lyons June 27, 20052005-06-27
On Mon, 20 Jun 2005 07:11:34 GMT, "Angelo Ricotta"
<a.ricotta@isac.cnr.it> wrote:

>
(snipped)
> >Thank you Rick for your kindness. May I ask you how did you find your >inequalities? As I already explained, I deduced mine from a diagram on a >Bendat & Piersol book, with a simple reasoning. > >Angelo >
Hi, Oh shoot. That was so many years ago. I think I found the inequality somewhere and then I graphically proved to myself that it was correct. My little graphical proof is in Chapter 2 of my DSP book. Take care, [-Rick-]
Reply by Angelo Ricotta June 20, 20052005-06-20
"Rick Lyons" <R.Lyons@_BOGUS_ieee.org> ha scritto nel messaggio 
news:42b56829.33559875@news.sf.sbcglobal.net...
> On Thu, 16 Jun 2005 06:44:20 GMT, "Angelo Ricotta" > <a.ricotta@isac.cnr.it> wrote: > >> >>"Rick Lyons" <R.Lyons@_BOGUS_ieee.org> ha scritto nel messaggio >>news:42ad824a.131233312@news.sf.sbcglobal.net... >>> On Fri, 10 Jun 2005 19:40:39 GMT, "Angelo Ricotta" >>> <a.ricotta@isac.cnr.it> wrote:
[omissis]
> Hi, > > here's what I use. The acceptable ranges of > Fs in bandpass sampling are: > > > 2Fc-B 2Fc+B > ------- > Fs > ------- > m m+1 > > where: > > Fc is the center freq of the analog bandpass signal, > B is the bandwidth of the analog bandpass signal, and > m is 1, 2, 3, etc.
This coincides with my formulation taking: m=n, B=fh-fl and Fc=(fh+fl)/2 then 2fl/n>Fs>2fh/(n+1) with n=0,1,2,3... I include n=0 to take into account the original Nyquist criterion.
> Different values of "m" give the different acceptable > ranges of Fs. But, of course, Fs can NEVER be less > than 2B.
You don't need to postulate it because it is implicit in the above inequalities as I showed in deducting my formulae.
> I hope that makes some sense.
Thank you Rick for your kindness. May I ask you how did you find your inequalities? As I already explained, I deduced mine from a diagram on a Bendat & Piersol book, with a simple reasoning. Angelo
> See Ya', > [-Rick-] >
Reply by Rick Lyons June 19, 20052005-06-19
On Thu, 16 Jun 2005 06:44:20 GMT, "Angelo Ricotta"
<a.ricotta@isac.cnr.it> wrote:

> >"Rick Lyons" <R.Lyons@_BOGUS_ieee.org> ha scritto nel messaggio >news:42ad824a.131233312@news.sf.sbcglobal.net... >> On Fri, 10 Jun 2005 19:40:39 GMT, "Angelo Ricotta" >> <a.ricotta@isac.cnr.it> wrote: >> >> Hi Angelo, >> >> Darn. I'm not sure what you mean by >> "my approach". It's Monday right now >> and I'll be away from my computer for the rest of >> the week. (I say that so you don't think >> I'm ignoring you in case you post another >> message this week.) >> >> See ya', >> [-Rick-] >> >I asked that because you said in a previous post on the thread "An >intriguing story about undersampling": >"I experimented with your method (comparing it with >a method that I use to compute Fs) and your >scheme sure seems to work just fine." > >So I was wandering what could be your method to compute all the permitted >frequencies. >(Don't worry about the date of your answer, even I do not access the >newsgroup so frequently because job timings) > >Angelo
Hi, here's what I use. The acceptable ranges of Fs in bandpass sampling are: 2Fc-B 2Fc+B ------- > Fs > ------- m m+1 where: Fc is the center freq of the analog bandpass signal, B is the bandwidth of the analog bandpass signal, and m is 1, 2, 3, etc. Different values of "m" give the different acceptable ranges of Fs. But, of course, Fs can NEVER be less than 2B. I hope that makes some sense. See Ya', [-Rick-]
Reply by Angelo Ricotta June 16, 20052005-06-16
"Rick Lyons" <R.Lyons@_BOGUS_ieee.org> ha scritto nel messaggio 
news:42ad824a.131233312@news.sf.sbcglobal.net...
> On Fri, 10 Jun 2005 19:40:39 GMT, "Angelo Ricotta" > <a.ricotta@isac.cnr.it> wrote: > > Hi Angelo, > > Darn. I'm not sure what you mean by > "my approach". It's Monday right now > and I'll be away from my computer for the rest of > the week. (I say that so you don't think > I'm ignoring you in case you post another > message this week.) > > See ya', > [-Rick-] >
I asked that because you said in a previous post on the thread "An intriguing story about undersampling": "I experimented with your method (comparing it with a method that I use to compute Fs) and your scheme sure seems to work just fine." So I was wandering what could be your method to compute all the permitted frequencies. (Don't worry about the date of your answer, even I do not access the newsgroup so frequently because job timings) Angelo
Reply by Rick Lyons June 13, 20052005-06-13
On Fri, 10 Jun 2005 19:40:39 GMT, "Angelo Ricotta"
<a.ricotta@isac.cnr.it> wrote:

>
(snipped)
> >P.S. I read in this thread you wrote a book on DSP. I saw the sample on >Amazon and it seems interesting. I am trying to buy it through our >librarian. In the meanwhile could you explain me what is your approach to >undersampling?
Hi Angelo, Darn. I'm not sure what you mean by "my approach". It's Monday right now and I'll be away from my computer for the rest of the week. (I say that so you don't think I'm ignoring you in case you post another message this week.) See ya', [-Rick-]
Reply by Ben Bradley June 11, 20052005-06-11
On 9 Jun 2005 14:02:34 GMT, Martin Eisenberg
<martin.eisenberg@udo.edu> used his digits to comment on the
processing of text signals:

>Jon Harris wrote: > >> My $0.02: if you are actively following a thread, top posting >> is easier to deal with since you always see the latest >> information immediately.
>> If you are coming in late to an >> existing thread, bottom posting is better since you can read in >> natural chronological order. BTW, the same issue exists with >> blogs now too! Most of them are "top-posted" so the latest entry >> is always the first thing you see. > >That makes a lot of sense when the individual pieces of information >are largely independent,
You mean like when today, we comment on Tom Delay and who says he should be out, and last week we were commenting on Tom Delay and who said... oh never mind. But yes, blog entries are more than likely independent comments, as opposed to Usenet/email list/forum posts that quote and respond to text from previous Usenet/email list/forum posts, where top-posting is still a bad practice after all these years..
>and I expect sites to be structured that way >by default. Some time ago I peeked into the literary section of one >magazine's online presence and just chose the first entry. It was a >short prose contest. I got inspired, but when I looked where to send >my piece I found that the contest dated from 1998! > >On the other hand, the common way of responding to a Usenet post >piecemeal dissolves the distinction between top- and bottom-posting >anyway.
I do interspersed, and comment AFTER the statement I'm commenting on, so it flows like a conversation, instead of the response-then-statement type post that top-posting genrates.
>Like Eric I have no trouble reading either, although I deem >bottom-posting courteous as it is more useful in somewhat branchy >threads where a response's context may be unclear at first even if >you know the history. But then, folks who will quote a whole treatise >adding two lines should be *required* to top-post ;)
I saw Jerry's response. Can we also require that such followups be directed to dev.null?
> > >Martin
----- http://mindspring.com/~benbradley
Reply by Angelo Ricotta June 10, 20052005-06-10
"Rick Lyons" <R.Lyons@_BOGUS_ieee.org> ha scritto nel messaggio 
news:42a9805f.1935649968@news.sf.sbcglobal.net...
> On Wed, 08 Jun 2005 19:00:45 GMT, "Angelo Ricotta" > <a.ricotta@isac.cnr.it> wrote: > > (snipped) > > > Hi, > >>All right about the shape of the spectrum. But there is another aspect. I >>understood that the original post said that the amplitude modulating >>signal >>had a bandwidth of 4 kHz. > > Ah. I interpreted the original post to say that the > amplitude **modulated** signal had a bandwidth of 4 kHz. > (Energy from 13 kHz -to- 17 kHz.) >
I think that sheepshaggerx should tell us about the bandwidth.
>>So that the modulated spectrum has a 8kHz band, +- >>4kHz simmetrical around the 15kHz carrier and each sideband carries the >>same >>information. Choose, e.g., the sideband 11-15 kHz. The formulae 2*fh/(n+1) >>< >>fs < 2*fl/n with n < fl/(fh-fl) integer, give, for the allowed sampling >>frequencies, the intervals 10kHz < fs < 11 kHz, >>15kHz <fs < 22 and, of course, 30 kHz < fs. In that particular case, to >>avoid prefiltering the signal before sampling, it is better to choose fs = >>10 or 15 or 30 kHz. The spectrum will fold on itself around 15 kHz but >>being >>the same there is no loss of information. Is it a smart use of aliasing? >>What do you think? >>Angelo > > Humm, thinking about an 8 kHz-wide signal centered at 15 kHz, > it seems to me that if Fs = 10 kHz, the spectral > replications of the digitized signal would land right > on top of each other. Unless I've made a mistake. > Oops, wait a second. For an 8 kHz-wide signal, Fs would > have be no less than 16 kHz, right? Or have I > misunderstood the problem? > > [-Rick-] > >
Of course, if you want to recover the whole 8 kHz band, you know, you have to use 19 < fs < 22 or 38 < fs (all in kHz). But because in the AM modulation the two sidebands carry the same information, I think it is redundant to do that. To minimize the sample rate, one can recover a single sideband of 4 kHz (assuming the whole band is 8 kHz), precisely the left band. Doing so without filtering the sideband (in this case difficult) means that you permit to the spectrum to fold on itself but, being the two sidebands simmetric to respect to the center frequency, they overlap without loss of information. The same reasoning apply if the whole bandwidth is 4 kHz. In this case the sidebands are +- 2 kHz and then the minimum range of permitted sampling frequencies, to recover the 2 kHz band, is 30/7 < fs < 26/6, and the minimum frequency is fs = 30/7 kHz. The problem could be the drift of the carrier or of the sampling rate, as pointed out by Jerry. I used to solve a similar problem taking the carrier, multiplying its frequency by a suitable number to obtain the sampling frequency. In that way you lock the two frequencies. Angelo P.S. I read in this thread you wrote a book on DSP. I saw the sample on Amazon and it seems interesting. I am trying to buy it through our librarian. In the meanwhile could you explain me what is your approach to undersampling?
Reply by glen herrmannsfeldt June 10, 20052005-06-10
I agree, even though this one isn't that long.  Though it might be that
I believe that more when the new post isn't expected to have any 
follow-ups, which is often true for one line replies to page long posts. 
  About half the time I won't page down if I don't see at least one line 
in my browser window of about 24 lines.

Jerry Avins wrote:

> Yes. > > Martin Eisenberg wrote:
(snip)
>> On the other hand, the common way of responding to a Usenet post >> piecemeal dissolves the distinction between top- and bottom-posting >> anyway. Like Eric I have no trouble reading either, although I deem >> bottom-posting courteous as it is more useful in somewhat branchy >> threads where a response's context may be unclear at first even if you >> know the history. But then, folks who will quote a whole treatise >> adding two lines should be *required* to top-post ;)
And especially those adding one, or even no lines! -- glen
Reply by Rick Lyons June 10, 20052005-06-10
On Wed, 08 Jun 2005 19:00:45 GMT, "Angelo Ricotta"
<a.ricotta@isac.cnr.it> wrote:

  (snipped)


Hi,

>All right about the shape of the spectrum. But there is another aspect. I >understood that the original post said that the amplitude modulating signal >had a bandwidth of 4 kHz.
Ah. I interpreted the original post to say that the amplitude **modulated** signal had a bandwidth of 4 kHz. (Energy from 13 kHz -to- 17 kHz.)
>So that the modulated spectrum has a 8kHz band, +- >4kHz simmetrical around the 15kHz carrier and each sideband carries the same >information. Choose, e.g., the sideband 11-15 kHz. The formulae 2*fh/(n+1) < >fs < 2*fl/n with n < fl/(fh-fl) integer, give, for the allowed sampling >frequencies, the intervals 10kHz < fs < 11 kHz, >15kHz <fs < 22 and, of course, 30 kHz < fs. In that particular case, to >avoid prefiltering the signal before sampling, it is better to choose fs = >10 or 15 or 30 kHz. The spectrum will fold on itself around 15 kHz but being >the same there is no loss of information. Is it a smart use of aliasing? >What do you think? >Angelo
Humm, thinking about an 8 kHz-wide signal centered at 15 kHz, it seems to me that if Fs = 10 kHz, the spectral replications of the digitized signal would land right on top of each other. Unless I've made a mistake. Oops, wait a second. For an 8 kHz-wide signal, Fs would have be no less than 16 kHz, right? Or have I misunderstood the problem? [-Rick-]