That's right. Chapter 2 of Rick's book, "Understanding Digital Signal Processing" (2nd edition), contains the clearest and most complete discussion of band-pass sampling I've seen anywhere. Believe it or not, just satisfying Nyquist isn't enough. As his table indicates, there are bands of allowed and prohibited rates. Jerry Thomas Magma wrote:>>Fs_ranges = >> >> 17.0 -to- 26.0 >> 11.333333 -to- 13.0 >> 8.5 -to- 8.666666 > > > Hi Rick, > > Are you saying that my suggested 10 kHz sample rate would not work? (I > understand that I might have done the math wrong.) > > Cheers, > Thomas > > "Rick Lyons" <R.Lyons@_BOGUS_ieee.org> wrote in message > news:42a6def5.1763256125@news.sf.sbcglobal.net... > >>On 7 Jun 2005 15:09:14 -0700, sheepshaggerx@yahoo.co.uk wrote: >> >> >>>Dear folks, >>> >>>I was wondering if you could help me with this problem. I have an >>>accelerometer with a resonance of say 15kHz. I need to do envelope >>>detection of this (acts a bit like AM with 15kHz as the 'carrier'). The >>>bandwidth of this signal is lets say 4kHz so that we bandlimit from >>>13kHz up to 17kHz. Now suppose I sample at 8kHz - is this ok? I assume >>>I get a spectrum that goes from 5kHz (13-8) to 9kHz (17-8) - is this >>>right? Do I then need to bandlimit the undersampled signal or will this >>>do the trick or what must I sample at? Also, the accelerometer has a >>>natural resonance and hence do I need to bandlimit before sampling ie >>>can I use the natural filtering roll-off of the transducer? >>> >>> >>>Thanks >> >> >>Hi Sheepshagger, >> >> as Thomas said, an 8 kHz sample rate will >>not work. If your analog signal is *perfectly* >>bandlimited to 4 kHz, the acceptable sample rates >>are in the following ranges (kHz): >> >>Fs_ranges = >> >> 17.0 -to- 26.0 >> 11.333333 -to- 13.0 >> 8.5 -to- 8.666666 >> >> >>Choosing an acceptable sample rate depends on the >>shape of the spectrum of your analog signal. >>Does your signal's 4 kHz-wide spectrum look like: >> >> >> |<-- 4 kHz -->| >> **************** >> * * >> * * >> * * >> * * >> * * >> * * >> * * >> --------------------------------> Freq >> >>or does it look like the following >> >> >> >> |<-- 4 kHz -->| >> **************** >> * * >> * * >> * * >> * * >> * * >> * * >> * * >>---------------------------------------> Freq >> >>The answer to the above question makes all the difference >>in the world when it comes to selecting an acceptable >>bandpass sample rate. >> >>See Ya', >>[-Rick-] >> > > >-- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Undersampling Question
Started by ●June 7, 2005
Reply by ●June 8, 20052005-06-08
Reply by ●June 8, 20052005-06-08
Ok I found my mistake. Thanks. "Jerry Avins" <jya@ieee.org> wrote in message news:-ZWdnbN46-loujrfRVn-gw@rcn.net...> That's right. Chapter 2 of Rick's book, "Understanding Digital Signal > Processing" (2nd edition), contains the clearest and most complete > discussion of band-pass sampling I've seen anywhere. Believe it or not, > just satisfying Nyquist isn't enough. As his table indicates, there are > bands of allowed and prohibited rates. > > Jerry > > Thomas Magma wrote: >>>Fs_ranges = >>> >>> 17.0 -to- 26.0 >>> 11.333333 -to- 13.0 >>> 8.5 -to- 8.666666 >> >> >> Hi Rick, >> >> Are you saying that my suggested 10 kHz sample rate would not work? (I >> understand that I might have done the math wrong.) >> >> Cheers, >> Thomas >> >> "Rick Lyons" <R.Lyons@_BOGUS_ieee.org> wrote in message >> news:42a6def5.1763256125@news.sf.sbcglobal.net... >> >>>On 7 Jun 2005 15:09:14 -0700, sheepshaggerx@yahoo.co.uk wrote: >>> >>> >>>>Dear folks, >>>> >>>>I was wondering if you could help me with this problem. I have an >>>>accelerometer with a resonance of say 15kHz. I need to do envelope >>>>detection of this (acts a bit like AM with 15kHz as the 'carrier'). The >>>>bandwidth of this signal is lets say 4kHz so that we bandlimit from >>>>13kHz up to 17kHz. Now suppose I sample at 8kHz - is this ok? I assume >>>>I get a spectrum that goes from 5kHz (13-8) to 9kHz (17-8) - is this >>>>right? Do I then need to bandlimit the undersampled signal or will this >>>>do the trick or what must I sample at? Also, the accelerometer has a >>>>natural resonance and hence do I need to bandlimit before sampling ie >>>>can I use the natural filtering roll-off of the transducer? >>>> >>>> >>>>Thanks >>> >>> >>>Hi Sheepshagger, >>> >>> as Thomas said, an 8 kHz sample rate will >>>not work. If your analog signal is *perfectly* >>>bandlimited to 4 kHz, the acceptable sample rates >>>are in the following ranges (kHz): >>> >>>Fs_ranges = >>> >>> 17.0 -to- 26.0 >>> 11.333333 -to- 13.0 >>> 8.5 -to- 8.666666 >>> >>> >>>Choosing an acceptable sample rate depends on the >>>shape of the spectrum of your analog signal. >>>Does your signal's 4 kHz-wide spectrum look like: >>> >>> >>> |<-- 4 kHz -->| >>> **************** >>> * * >>> * * >>> * * >>> * * >>> * * >>> * * >>> * * >>> --------------------------------> Freq >>> >>>or does it look like the following >>> >>> >>> >>> |<-- 4 kHz -->| >>> **************** >>> * * >>> * * >>> * * >>> * * >>> * * >>> * * >>> * * >>>---------------------------------------> Freq >>> >>>The answer to the above question makes all the difference >>>in the world when it comes to selecting an acceptable >>>bandpass sample rate. >>> >>>See Ya', >>>[-Rick-] >>> >> >> >> > > > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������
Reply by ●June 8, 20052005-06-08
"Rick Lyons" <R.Lyons@_BOGUS_ieee.org> ha scritto nel messaggio news:42a6def5.1763256125@news.sf.sbcglobal.net...> On 7 Jun 2005 15:09:14 -0700, sheepshaggerx@yahoo.co.uk wrote: > >>Dear folks, >> >>I was wondering if you could help me with this problem. I have an >>accelerometer with a resonance of say 15kHz. I need to do envelope >>detection of this (acts a bit like AM with 15kHz as the 'carrier'). The >>bandwidth of this signal is lets say 4kHz so that we bandlimit from >>13kHz up to 17kHz. Now suppose I sample at 8kHz - is this ok? I assume >>I get a spectrum that goes from 5kHz (13-8) to 9kHz (17-8) - is this >>right? Do I then need to bandlimit the undersampled signal or will this >>do the trick or what must I sample at? Also, the accelerometer has a >>natural resonance and hence do I need to bandlimit before sampling ie >>can I use the natural filtering roll-off of the transducer? >> >> >>Thanks > > > Hi Sheepshagger, > > as Thomas said, an 8 kHz sample rate will > not work. If your analog signal is *perfectly* > bandlimited to 4 kHz, the acceptable sample rates > are in the following ranges (kHz): > > Fs_ranges = > > 17.0 -to- 26.0 > 11.333333 -to- 13.0 > 8.5 -to- 8.666666 > > > Choosing an acceptable sample rate depends on the > shape of the spectrum of your analog signal. > Does your signal's 4 kHz-wide spectrum look like: > > > |<-- 4 kHz -->| > **************** > * * > * * > * * > * * > * * > * * > * * > --------------------------------> Freq > > or does it look like the following > > > > |<-- 4 kHz -->| > **************** > * * > * * > * * > * * > * * > * * > * * > ---------------------------------------> Freq > > The answer to the above question makes all the difference > in the world when it comes to selecting an acceptable > bandpass sample rate. > > See Ya', > [-Rick-] >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. 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
Reply by ●June 8, 20052005-06-08
Angelo Ricotta wrote:> "Rick Lyons" <R.Lyons@_BOGUS_ieee.org> ha scritto nel messaggio > news:42a6def5.1763256125@news.sf.sbcglobal.net... > >>On 7 Jun 2005 15:09:14 -0700, sheepshaggerx@yahoo.co.uk wrote: >> >> >>>Dear folks, >>> >>>I was wondering if you could help me with this problem. I have an >>>accelerometer with a resonance of say 15kHz. I need to do envelope >>>detection of this (acts a bit like AM with 15kHz as the 'carrier'). The >>>bandwidth of this signal is lets say 4kHz so that we bandlimit from >>>13kHz up to 17kHz. Now suppose I sample at 8kHz - is this ok? I assume >>>I get a spectrum that goes from 5kHz (13-8) to 9kHz (17-8) - is this >>>right? Do I then need to bandlimit the undersampled signal or will this >>>do the trick or what must I sample at? Also, the accelerometer has a >>>natural resonance and hence do I need to bandlimit before sampling ie >>>can I use the natural filtering roll-off of the transducer? >>> >>> >>>Thanks >> >> >>Hi Sheepshagger, >> >> as Thomas said, an 8 kHz sample rate will >>not work. If your analog signal is *perfectly* >>bandlimited to 4 kHz, the acceptable sample rates >>are in the following ranges (kHz): >> >>Fs_ranges = >> >> 17.0 -to- 26.0 >> 11.333333 -to- 13.0 >> 8.5 -to- 8.666666 >> >> >>Choosing an acceptable sample rate depends on the >>shape of the spectrum of your analog signal. >>Does your signal's 4 kHz-wide spectrum look like: >> >> >> |<-- 4 kHz -->| >> **************** >> * * >> * * >> * * >> * * >> * * >> * * >> * * >> --------------------------------> Freq >> >>or does it look like the following >> >> >> >> |<-- 4 kHz -->| >> **************** >> * * >> * * >> * * >> * * >> * * >> * * >> * * >>---------------------------------------> Freq >> >>The answer to the above question makes all the difference >>in the world when it comes to selecting an acceptable >>bandpass sample rate. >> >>See Ya', >>[-Rick-] >> > > 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. 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? > AngeloSuppose the sample rate drifts a bit. What happens to the aliases then? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●June 8, 20052005-06-08
"Jerry Avins" <jya@ieee.org> ha scritto nel messaggio news:aYidnYJTIO77zTrfRVn-uQ@rcn.net...> Angelo Ricotta wrote: >> "Rick Lyons" <R.Lyons@_BOGUS_ieee.org> ha scritto nel messaggio >> news:42a6def5.1763256125@news.sf.sbcglobal.net... >> >>>On 7 Jun 2005 15:09:14 -0700, sheepshaggerx@yahoo.co.uk wrote: >>> >>> >>>>Dear folks, >>>> >>>>I was wondering if you could help me with this problem. I have an >>>>accelerometer with a resonance of say 15kHz. I need to do envelope >>>>detection of this (acts a bit like AM with 15kHz as the 'carrier'). The >>>>bandwidth of this signal is lets say 4kHz so that we bandlimit from >>>>13kHz up to 17kHz. Now suppose I sample at 8kHz - is this ok? I assume >>>>I get a spectrum that goes from 5kHz (13-8) to 9kHz (17-8) - is this >>>>right? Do I then need to bandlimit the undersampled signal or will this >>>>do the trick or what must I sample at? Also, the accelerometer has a >>>>natural resonance and hence do I need to bandlimit before sampling ie >>>>can I use the natural filtering roll-off of the transducer? >>>> >>>> >>>>Thanks >>> >>> >>>Hi Sheepshagger, >>> >>> as Thomas said, an 8 kHz sample rate will >>>not work. If your analog signal is *perfectly* >>>bandlimited to 4 kHz, the acceptable sample rates >>>are in the following ranges (kHz): >>> >>>Fs_ranges = >>> >>> 17.0 -to- 26.0 >>> 11.333333 -to- 13.0 >>> 8.5 -to- 8.666666 >>> >>> >>>Choosing an acceptable sample rate depends on the >>>shape of the spectrum of your analog signal. >>>Does your signal's 4 kHz-wide spectrum look like: >>> >>> >>> |<-- 4 kHz -->| >>> **************** >>> * * >>> * * >>> * * >>> * * >>> * * >>> * * >>> * * >>> --------------------------------> Freq >>> >>>or does it look like the following >>> >>> >>> >>> |<-- 4 kHz -->| >>> **************** >>> * * >>> * * >>> * * >>> * * >>> * * >>> * * >>> * * >>>---------------------------------------> Freq >>> >>>The answer to the above question makes all the difference >>>in the world when it comes to selecting an acceptable >>>bandpass sample rate. >>> >>>See Ya', >>>[-Rick-] >>> >> >> 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. 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 > > Suppose the sample rate drifts a bit. What happens to the aliases then? > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������I used to do a trick, even if in a different situation. Feed the 15kHz carrier into a pulse multiplier which puts out fs=(h/k)*fcarrier with h,k integers (I designed one for a SODAR system). For example fs=10kHz=(2/3)*15kHz. In this way you synchronize and then compensate for drifts. Angelo
Reply by ●June 9, 20052005-06-09
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, 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. 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 ;) Martin -- Sphinx of black quartz, judge my vow! --David Lemon
Reply by ●June 9, 20052005-06-09
Yes. Martin Eisenberg wrote:> 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, 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. 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 ;) > > > Martin >:-) Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●June 9, 20052005-06-09
Jerry, you're a sly fox! -- The man who does not read good books has no advantage over the man who cannot read them. --Mark Twain
Reply by ●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? >AngeloHumm, 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-]
Reply by ●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
