hello, i am a new student of dsp. we know for a bandlimited signal,in order to avoid aliasing the samplig rate should be >= 2* maxfrequency..... but what should be the sampling rate for a signal whose spectrum is from (1025)hz (say)... i.e. for a nonbaseband signal....??????? Kindly reply in detail. regards, prijit 

sampling rate ????
Started by ●July 31, 2002
Reply by ●August 2, 200220020802
Since no one else is forthcoming, I'll take a stab at this. In theory,
the minimum sampling frequency required to capture all the information required to reconstruct the signal uniquely is twice the signal's bandwidth. For your example, 1025 Hz is a bandwidth of 15 Hz, so you ought to be able to sample at 30 sps, not 50 sps as required if the signal was "lowpass" or "baseband", as you said. But there's a catch: the bandpass signal must first be downconverted (translated in frequency) from 1025 Hz down to 015 Hz. In this case, that would be more trouble than the savings in sample rate would justify. The downconversion is required so that no two frequencies in the signal spectrum alias to the same frequency between 0 and Fs/2. If each frequency has a unique alias frequency, there's no ambiguity in recontruction. But there are cases where the downconversion isn't necessary. Suppose the signal was 1530 Hz. Now you could sample at 30 sps and the resulting signal would be "aliased" to 015 Hz, but the aliasing doesn't cause information to be lost because the frequencies map unambiguously: 30 Hz becomes 0, 20 Hz becomes 10 Hz, 15 Hz becomes 15 Hz. The spectrum is reversed. To reconstruct this signal, you of course need to know that the samples represent a 1530 Hz signal, not a 015 Hz signal. Even easier is the case 3045 Hz: just sample at 30 sps, and your samples will give the spectrum unreversed, so reconstruction is more straightforward. This approach is often referred to as "subNyquist sampling". I think it's also important to point out that the theoretical minimum of twice the bandwidth is not a practical sample rate because to reconstruct a signal this way you would need an infinite number of samples, and an infinite delay for a causal system. In practice, you need to use a sample rate somewhat higher in order to recontruct with reasonable filters and delays. The other problem is that real signals are almost never truly bandlimited, they typically have some energy beyond the stated bandwidth (especially if the "bandwidth" is given by 3dB points!). There are a lot of subtleties in this subject, witness the extended correspondence to the editor a few years ago in the IEEE Signal Processing Magazine (July 1995, Jan 1996, Sept 1996) when someone published an article claiming that he had "broken the Nyquist barrier" by using the above technique. Hope thats enough detail. If not, look up the references. Mark Egler > Original Message > From: prijit debnath [mailto:] > Sent: Wed, July 31, 2002 3:08 PM > To: > Subject: [matlab] sampling rate ???? > hello, > i am a new student of dsp. we know for a > bandlimited signal,in order to avoid aliasing the > samplig rate should be >= 2* maxfrequency..... > but what should be the sampling rate for a > signal whose spectrum is from (1025)hz (say)... > i.e. for a nonbaseband signal....??????? > Kindly reply in detail. > regards, > prijit > >  Yahoo! Groups Sponsor > ~> > Will You Find True Love? > Will You Meet the One? > Free Love Reading by phone! > http://us.click.yahoo.com/7dY7FD/R_ZEAA/Ey.GAA/wHYolB/TM >  > ~> > > _____________________________________ > Note: If you do a simple "reply" with your email client, only > the author of this message will receive your answer. You > need to do a "reply all" if you want your answer to be > distributed to the entire group. > > _____________________________________ > About this discussion group: > > To Join: > > To Post: > > To Leave: > > Archives: http://www.yahoogroups.com/group/matlab > > More DSPRelated Groups: http://www.dsprelated.com/groups.php3 > > ">http://docs.yahoo.com/info/terms/ 
Reply by ●August 2, 200220020802
On rereading my post, I realized that the spectrumreversed case is no
more difficult than the unreversed case. The reconstruction in both situations is to filter the sample stream with a bandpass filter that passes only the original signal spectrum. Mark Egler > Original Message > From: Egler, Mark > Sent: Fri, August 02, 2002 11:03 AM > To: ' > Subject: RE: [matlab] sampling rate ???? > Since no one else is forthcoming, I'll take a stab at this. > In theory, the > minimum sampling frequency required to capture all the > information required > to reconstruct the signal uniquely is twice the signal's bandwidth. > > For your example, 1025 Hz is a bandwidth of 15 Hz, so you > ought to be able > to sample at 30 sps, not 50 sps as required if the signal was > "lowpass" or > "baseband", as you said. But there's a catch: the bandpass > signal must > first be downconverted (translated in frequency) from 1025 > Hz down to 015 > Hz. In this case, that would be more trouble than the savings > in sample rate > would justify. The downconversion is required so that no two > frequencies in > the signal spectrum alias to the same frequency between 0 and > Fs/2. If each > frequency has a unique alias frequency, there's no ambiguity in > recontruction. > > But there are cases where the downconversion isn't > necessary. Suppose the > signal was 1530 Hz. Now you could sample at 30 sps and the > resulting signal > would be "aliased" to 015 Hz, but the aliasing doesn't cause > information to > be lost because the frequencies map unambiguously: 30 Hz > becomes 0, 20 Hz > becomes 10 Hz, 15 Hz becomes 15 Hz. The spectrum is reversed. > To reconstruct > this signal, you of course need to know that the samples > represent a 1530 > Hz signal, not a 015 Hz signal. > > Even easier is the case 3045 Hz: just sample at 30 sps, and > your samples > will give the spectrum unreversed, so reconstruction is more > straightforward. This approach is often referred to as "subNyquist > sampling". > > I think it's also important to point out that the theoretical > minimum of > twice the bandwidth is not a practical sample rate because to > reconstruct a > signal this way you would need an infinite number of samples, and an > infinite delay for a causal system. In practice, you need to > use a sample > rate somewhat higher in order to recontruct with reasonable > filters and > delays. The other problem is that real signals are almost never truly > bandlimited, they typically have some energy beyond the > stated bandwidth > (especially if the "bandwidth" is given by 3dB points!). > > There are a lot of subtleties in this subject, witness the extended > correspondence to the editor a few years ago in the IEEE > Signal Processing > Magazine (July 1995, Jan 1996, Sept 1996) when someone > published an article > claiming that he had "broken the Nyquist barrier" by using the above > technique. > > Hope thats enough detail. If not, look up the references. > > Mark Egler > > > Original Message > > From: prijit debnath [mailto:] > > Sent: Wed, July 31, 2002 3:08 PM > > To: > > Subject: [matlab] sampling rate ???? > > > > > > hello, > > i am a new student of dsp. we know for a > > bandlimited signal,in order to avoid aliasing the > > samplig rate should be >= 2* maxfrequency..... > > but what should be the sampling rate for a > > signal whose spectrum is from (1025)hz (say)... > > i.e. for a nonbaseband signal....??????? > > Kindly reply in detail. > > regards, > > prijit > > > > > > > >  Yahoo! Groups Sponsor > > ~> > > Will You Find True Love? > > Will You Meet the One? > > Free Love Reading by phone! > > http://us.click.yahoo.com/7dY7FD/R_ZEAA/Ey.GAA/wHYolB/TM > >  > > ~> > > > > _____________________________________ > > Note: If you do a simple "reply" with your email client, only > > the author of this message will receive your answer. You > > need to do a "reply all" if you want your answer to be > > distributed to the entire group. > > > > _____________________________________ > > About this discussion group: > > > > To Join: > > > > To Post: > > > > To Leave: > > > > Archives: http://www.yahoogroups.com/group/matlab > > > > More DSPRelated Groups: http://www.dsprelated.com/groups.php3 > > > > ">http://docs.yahoo.com/info/terms/ > > > > > >  Yahoo! Groups Sponsor > ~> > Access your PC just like Web Mail > http://us.click.yahoo.com/r5uw2C/zncEAA/Ey.GAA/wHYolB/TM >  > ~> > > _____________________________________ > Note: If you do a simple "reply" with your email client, only > the author of this message will receive your answer. You > need to do a "reply all" if you want your answer to be > distributed to the entire group. > > _____________________________________ > About this discussion group: > > To Join: > > To Post: > > To Leave: > > Archives: http://www.yahoogroups.com/group/matlab > > More DSPRelated Groups: http://www.dsprelated.com/groups.php3 > > ">http://docs.yahoo.com/info/terms/ 

Reply by ●August 5, 200220020805
Hi all, can you please explain me some thing about subnyquist sampling. I cannot understand the concept of subnyquit sampling. suppose,the bandwidth is 15 Khz,sampling rate is 30 sps if you need to sample in the range 1530khz,it could be done without downsampling the signal to 015 khz.I am aware that the the frequency gets mapped properly and could be retrived back. In the case of 3045Khz ,i read there is NO MAPPING of signals... questions: Could some one explain in detail how is this done? what is the exatly is happening in 1.1530khz 2.3045khz thank you regards, Bala. 

Reply by ●August 6, 200220020806
In order to understand the Nyquist rate, it is easiest to do so in the FREQUENCY domain rather than in the time domain, which you are trying to do. In the Freq. domain, the signal must be BANDlimited  ie: zero beyond some max. frequency. You must sample at TWICE this max. frequency in order to capture all information. This is because in DT, the frequency domain is periodic, and in order for frequencies not to overlap, you need to sample at twice the max. frequency. I hope this makes sense. Daniar On Mon, 5 Aug 2002, bala sekhar wrote: > Hi all, > > can you please explain me some thing about subnyquist > sampling. > > I cannot understand the concept of subnyquit > sampling. > > suppose,the bandwidth is 15 Khz,sampling rate is 30 > sps > > if you need to sample in the range 1530khz,it could > be done without > downsampling the signal to 015 khz.I am aware that > the the frequency > gets mapped properly and could be retrived back. > > In the case of 3045Khz ,i read there is NO MAPPING of > signals... > > questions: > Could some one explain in detail how is this done? > what is the exatly is happening in > 1.1530khz > 2.3045khz > > thank you > > regards, > Bala. > > > _____________________________________ > Note: If you do a simple "reply" with your email client, only the author of this message will receive your answer. You need to do a "reply all" if you want your answer to be distributed to the entire group. > > _____________________________________ > About this discussion group: > > To Join: > > To Post: > > To Leave: > > Archives: http://www.yahoogroups.com/group/matlab > > More DSPRelated Groups: http://www.dsprelated.com/groups.php3 > > ">http://docs.yahoo.com/info/terms/ > 
Reply by ●August 6, 200220020806
Daniar, Bala Hey guys, Mark Egler's post reply to Prijit Debnath (copy below) from a few days ago is fantastic on this subject. I suggest you read it before you try to recover the ground he has already explained in detail. Jeff Brower DSP sw/hw engineer Signalogic > In order to understand the Nyquist rate, it is easiest to do so in the > FREQUENCY domain rather than in the time domain, which you are trying to > do. > > In the Freq. domain, the signal must be BANDlimited  ie: zero beyond > some max. frequency. You must sample at TWICE this max. frequency in > order to capture all information. This is because in DT, the frequency > domain is periodic, and in order for frequencies not to overlap, you need > to sample at twice the max. frequency. > > I hope this makes sense. > > Daniar > > On Mon, 5 Aug 2002, bala sekhar wrote: > > > Hi all, > > > > can you please explain me some thing about subnyquist > > sampling. > > > > I cannot understand the concept of subnyquit > > sampling. > > > > suppose,the bandwidth is 15 Khz,sampling rate is 30 > > sps > > > > if you need to sample in the range 1530khz,it could > > be done without > > downsampling the signal to 015 khz.I am aware that > > the the frequency > > gets mapped properly and could be retrived back. > > > > In the case of 3045Khz ,i read there is NO MAPPING of > > signals... > > > > questions: > > Could some one explain in detail how is this done? > > what is the exatly is happening in > > 1.1530khz > > 2.3045khz > > > > thank you > > > > regards, > > Bala.  Original Message  Subject: RE: [matlab] sampling rate ???? Date: Fri, 2 Aug 2002 11:29:40 0400 From: "Egler, Mark" <> To: "'" <> On rereading my post, I realized that the spectrumreversed case is no more difficult than the unreversed case. The reconstruction in both situations is to filter the sample stream with a bandpass filter that passes only the original signal spectrum. Mark Egler > Original Message > From: Egler, Mark > Sent: Fri, August 02, 2002 11:03 AM > To: ' > Subject: RE: [matlab] sampling rate ???? > Since no one else is forthcoming, I'll take a stab at this. > In theory, the > minimum sampling frequency required to capture all the > information required > to reconstruct the signal uniquely is twice the signal's bandwidth. > > For your example, 1025 Hz is a bandwidth of 15 Hz, so you > ought to be able > to sample at 30 sps, not 50 sps as required if the signal was > "lowpass" or > "baseband", as you said. But there's a catch: the bandpass > signal must > first be downconverted (translated in frequency) from 1025 > Hz down to 015 > Hz. In this case, that would be more trouble than the savings > in sample rate > would justify. The downconversion is required so that no two > frequencies in > the signal spectrum alias to the same frequency between 0 and > Fs/2. If each > frequency has a unique alias frequency, there's no ambiguity in > recontruction. > > But there are cases where the downconversion isn't > necessary. Suppose the > signal was 1530 Hz. Now you could sample at 30 sps and the > resulting signal > would be "aliased" to 015 Hz, but the aliasing doesn't cause > information to > be lost because the frequencies map unambiguously: 30 Hz > becomes 0, 20 Hz > becomes 10 Hz, 15 Hz becomes 15 Hz. The spectrum is reversed. > To reconstruct > this signal, you of course need to know that the samples > represent a 1530 > Hz signal, not a 015 Hz signal. > > Even easier is the case 3045 Hz: just sample at 30 sps, and > your samples > will give the spectrum unreversed, so reconstruction is more > straightforward. This approach is often referred to as "subNyquist > sampling". > > I think it's also important to point out that the theoretical > minimum of > twice the bandwidth is not a practical sample rate because to > reconstruct a > signal this way you would need an infinite number of samples, and an > infinite delay for a causal system. In practice, you need to > use a sample > rate somewhat higher in order to recontruct with reasonable > filters and > delays. The other problem is that real signals are almost never truly > bandlimited, they typically have some energy beyond the > stated bandwidth > (especially if the "bandwidth" is given by 3dB points!). > > There are a lot of subtleties in this subject, witness the extended > correspondence to the editor a few years ago in the IEEE > Signal Processing > Magazine (July 1995, Jan 1996, Sept 1996) when someone > published an article > claiming that he had "broken the Nyquist barrier" by using the above > technique. > > Hope thats enough detail. If not, look up the references. > > Mark Egler > > > Original Message > > From: prijit debnath [mailto:] > > Sent: Wed, July 31, 2002 3:08 PM > > To: > > Subject: [matlab] sampling rate ???? > > > > > > hello, > > i am a new student of dsp. we know for a > > bandlimited signal,in order to avoid aliasing the > > samplig rate should be >= 2* maxfrequency..... > > but what should be the sampling rate for a > > signal whose spectrum is from (1025)hz (say)... > > i.e. for a nonbaseband signal....??????? > > Kindly reply in detail. > > regards, > > prijit 
Reply by ●August 12, 200220020812
Bala, I think your question about subNyquist sampling was in reply to my posts that Jeff kindly referenced. Your question used kilohertz (kHz) as units for frequency while my post used only hertz (Hz), so if you thought I was saying that you can successfully sample a 1530 kHz signal with only 30 samples per second (sps) then you're wrong; it would require 30 kilosamples per second (ksps). The sample rate must be twice the bandWIDTH, i.e. Fs > 2*(FmaxFmin), AND the resulting aliased spectrum must map every input frequency to a unique aliased frequency. So in the first case, 1530 Hz, sampling at 30 sps gives a reversemapped spectrum from 15 to 0 Hz, i.e. 30 Hz input will map to 0 Hz, and 15 Hz input maps to 15 Hz. Since the sampled signal has a periodic spectrum, the signal can be reconstructed by converting back to continuoustime (i.e with a DA converter) and analog filtering with a bandpass filter with brickwall cutoff frequencies at 15 and 30 Hz. You probably need to draw the periodic spectrum of the sampled signal to visualize this. Now, in the second case, 3045 Hz, sampling at 30 sps causes the 30 Hz input to map to 0 Hz (DC), and the 45 Hz input becomes 15 Hz. This aliasmapping is nonreversed, but as my second post noted, this does not really matter because the same reconstruction approach still works: just change the brickwalls of the analog bandpass filter to 30 Hz and 45 Hz. Does that make sense? Regards, Mark > Original Message > From: Jeff Brower [mailto:] > Sent: Tue, August 06, 2002 11:29 AM > To: Daniar Hussain > Cc: Bala Sekhar; > Subject: Re: [matlab] sampling rate ???? > Daniar, Bala > > Hey guys, Mark Egler's post reply to Prijit Debnath (copy > below) from a few days ago > is fantastic on this subject. I suggest you read it before > you try to recover the > ground he has already explained in detail. > > Jeff Brower > DSP sw/hw engineer > Signalogic > > > In order to understand the Nyquist rate, it is easiest to > do so in the > > FREQUENCY domain rather than in the time domain, which you > are trying to > > do. > > > > In the Freq. domain, the signal must be BANDlimited  ie: > zero beyond > > some max. frequency. You must sample at TWICE this max. > frequency in > > order to capture all information. This is because in DT, > the frequency > > domain is periodic, and in order for frequencies not to > overlap, you need > > to sample at twice the max. frequency. > > > > I hope this makes sense. > > > > Daniar > > > > On Mon, 5 Aug 2002, bala sekhar wrote: > > > > > Hi all, > > > > > > can you please explain me some thing about subnyquist > > > sampling. > > > > > > I cannot understand the concept of subnyquit > > > sampling. > > > > > > suppose,the bandwidth is 15 Khz,sampling rate is 30 > > > sps > > > > > > if you need to sample in the range 1530khz,it could > > > be done without > > > downsampling the signal to 015 khz.I am aware that > > > the the frequency > > > gets mapped properly and could be retrived back. > > > > > > In the case of 3045Khz ,i read there is NO MAPPING of > > > signals... > > > > > > questions: > > > Could some one explain in detail how is this done? > > > what is the exatly is happening in > > > 1.1530khz > > > 2.3045khz > > > > > > thank you > > > > > > regards, > > > Bala. > 
