bittel@zodiac.rutgers.edu (02/20/91)
In article <1991Feb17.115102.15399@Neon.Stanford.EDU>, zimmer@calvin.stanford.edu (Andrew Zimmerman) writes: >>> > "The sample frequency must be at least twice the highest frequency >>> >component within the analog signal for an accurate representation of the >>> >analog signal". >> >>I think this should be "GREATER than twice the highest frequency >>component". > > Just to nit-pick, it should be "GREATER then twice the bandwidth of the > signal", not twice the highest frequency. > > Andrew > zimmer@calvin.stanford.edu I had a professor that loved to explain the sampling theory this way. It is not correct!!! What does the bandwidth have to do with it??? Say you have a signal with frequency components from 5000 to 5100 Hz. The bandwidth is 100 Hz.. Does that mean you can sample at 200 samp/sec and get the signal??? NO!! Fs >= 2fmax Enough said. NJIT student who finally passed EE333.
fritz@mit-caf.MIT.EDU (Frederick Herrmann) (02/22/91)
In article <605.27c28109@zodiac.rutgers.edu> bittel@zodiac.rutgers.edu writes: >I had a professor that loved to explain the sampling theory this way. >It is not correct!!! What does the bandwidth have to do with it??? >Say you have a signal with frequency components from 5000 to 5100 Hz. >The bandwidth is 100 Hz.. Does that mean you can sample at 200 samp/sec and >get the signal??? NO!! YES!! Your professor was right. You have to sample for all time, of course, but you can get the signal. That's why you need anti-alias filters, so you get the band you want. Without a filter, all the 100Hz bands you can think of get aliased to the same place. 0-100 Hz, 5-5.1 KHz, 1-1.0000001 GHz. How do you think digital sampling scopes work? The HP54501A has a 100 MHz bandwidth, but samples at only 10 Msamples/sec. Yes, I know these instruments do a lot more than simple sampling, but they do acquire signals faster than their sampling rate. And they do alias, if you're not careful then what you see may not be what you got. >Enough said. Apparently not, but this thread goes into the kill file real soon now... - Frederick P. Herrmann fritz@caf.mit.edu
danr@ais.org (Daniel Romanchik) (02/23/91)
In article <5782@mit-caf.MIT.EDU> fritz@mit-caf.UUCP (Frederick Herrmann) writes: >In article <605.27c28109@zodiac.rutgers.edu> bittel@zodiac.rutgers.edu writes: >>I had a professor that loved to explain the sampling theory this way. >>It is not correct!!! What does the bandwidth have to do with it??? >>Say you have a signal with frequency components from 5000 to 5100 Hz. >>The bandwidth is 100 Hz.. Does that mean you can sample at 200 samp/sec and >>get the signal??? NO!! > >YES!! Your professor was right. You have to sample for all time, of course, >but you can get the signal. > >That's why you need anti-alias filters, so you get the band you want. Without >a filter, all the 100Hz bands you can think of get aliased to the same place. >0-100 Hz, 5-5.1 KHz, 1-1.0000001 GHz. > >How do you think digital sampling scopes work? The HP54501A has a 100 MHz >bandwidth, but samples at only 10 Msamples/sec. Yes, I know these instruments >do a lot more than simple sampling, but they do acquire signals faster than >their sampling rate. And they do alias, if you're not careful then >what you see may not be what you got. The Nyquist criteria really only applies to single-shot sampling. The scope that you mention above can really only measure signals at 100 MHz if they are repetitive signals. The scope takes a sample or two on successive cycles, and then recreates the waveform from samples from many cycles. This is the reason the sampling rate may be much less than the analog bandwidth. The reason DSOs can acquire signals faster than their sampling rate is that they do a lot more than simple sampling, *and* that there are restrictions on the signals they can measure. Have fun, Dan =============================================================================== Dan Romanchik | writer@irie.ais.org Technical Editor | CI$: 76236,2372 Test and Measurement World | (313) 930-6564 =============================================================================== If it ain't broke, don't fix it. ===============================================================================
jgk@osc.COM (Joe Keane) (02/27/91)
In article <605.27c28109@zodiac.rutgers.edu> bittel@zodiac.rutgers.edu writes: >I had a professor that loved to explain the sampling theory this way. >It is not correct!!! What does the bandwidth have to do with it??? >Say you have a signal with frequency components from 5000 to 5100 Hz. >The bandwidth is 100 Hz.. Does that mean you can sample at 200 samp/sec and >get the signal??? NO!! Yes, you can. The signal you mention is close to periodic. It can be considered as a 5050 Hz sine wave modulated by some signal with no components at frequencies greater than 50 Hz. If you look at a short segment of the waveform, it's going to look like something between a 5000 Hz sine wave and a 5010 Hz sine wave. There's no point in sampling enough to get the shape of the waveform, because we already know what it's going to look like. You just need to sample enough to determine the modulating signal. Actually there is one frequency (5000 Hz) where we are missing one of the components, since it is a multiple of the sampling frequency. As mentioned before, this is just a problem with the method of sampling. It can be eliminated by shifting the signal up or down a bit in frequency, or using other sampling methods. This is the reason the sampling scopes mentioned before can work. If the shape of a waveform is not changing rapidly, it only takes up a small amount of bandwidth. In other words, you don't need much information to describe it. There are components at the fundamental frequency and harmonics, but they occupy narrow bands. The width of the bands is proportional to the speed at which the waveform is changing.
Luns.Tee@f646.n250.z1.fidonet.org (Luns Tee) (03/02/91)
b> I had a professor that loved to explain the sampling theory this way. b> It is not correct!!! What does the bandwidth have to do with it??? b> Say you have a signal with frequency components from 5000 to 5100 Hz. b> The bandwidth is 100 Hz.. Does that mean you can sample at 200 b> samp/sec and b> get the signal??? NO!! I haven't formally studied any of this stuff, but I'm tempted to agree that the sampling rate being freater than twice the bandwidth is enough to capture all information. What you sample may not necessarily be in a form from which you can reconstruct the original signal easily, but all th information is there to do so. My original way of thinking was that if you were to feed your signal through a frequency converter down to DC, your original bandwidth becomes your highest frequency. Sample this. Reconstruct it, and frequency convert it back to where it came from and you have your 5000 to 5100hz signal. You'd need some pretty good antialiasing however. But then again, if you take 200 samples/sec of your 5000 to 5100hz signal, provided there's nothing outside of that frequency range, everything in that signal will be intentionally aliased into 0-200 hz, without any overlapping. All the information is there, just getting it out is a little difficult.
bobw@col.hp.com (Bob Witte) (03/13/91)
> >In article <605.27c28109@zodiac.rutgers.edu> bittel@zodiac.rutgers.edu writes: >>I had a professor that loved to explain the sampling theory this way. >>It is not correct!!! What does the bandwidth have to do with it??? >>Say you have a signal with frequency components from 5000 to 5100 Hz. >>The bandwidth is 100 Hz.. Does that mean you can sample at 200 samp/sec and >>get the signal??? NO!! > >YES!! Your professor was right. You have to sample for all time, of course, >but you can get the signal. > >That's why you need anti-alias filters, so you get the band you want. Without >a filter, all the 100Hz bands you can think of get aliased to the same place. >0-100 Hz, 5-5.1 KHz, 1-1.0000001 GHz. I agree with you here. > >How do you think digital sampling scopes work? The HP54501A has a 100 MHz >bandwidth, but samples at only 10 Msamples/sec. Yes, I know these instruments >do a lot more than simple sampling, but they do acquire signals faster than >their sampling rate. And they do alias, if you're not careful then >what you see may not be what you got. I don't agree here, though. Digital scopes often are designed with a low sample rate relative to the bandwidth. Such scopes work only on repetitive signals, taking advantage of the fact that the scope gets several "passes" at the waveform to acquire the entire signal. Keeping track of the time between a particular sample and the trigger event allows the scope to put together a good reproduction of the waveform. In this case, the waveform is definitely not bandlimited to fs/2, otherwise you wouldn't get a 100 MHz bandwidth with a 10 MSa/sec sample rate. This is "undersampling" but is distinctly different than the previous case. -------------------------------------------------------------------- Bob Witte HP Colorado Springs Division bobw@col.hp.com P.O. Box 2197 Phone:(719) 590-3230 Colorado Springs, CO 80901 Radio: KB0CY "Of course, then again, I've been wrong before." --------------------------------------------------------------------