Reply by Vladimir Vassilevsky November 1, 20102010-11-01

steveu wrote:
>> >>Roman Rumian wrote: >> >> >>>2010-10-29 18:23, Tim Wescott wrote: >>>(...) >>> >>> >>>>If the other links that you've gotten haven't helped, read this: >>>>http://www.wescottdesign.com/articles/Sampling/sampling.html >>> >>> >>>thank you for this article. >>>These days we were preparing new audio engineering lab examples, and >>>have noticed and checked that EVERY audio A/D converter from Cirrus, >>>AKM, Analog Devices, TI and Wolfson has digital decimation filter >>>(probably half band) introducing aliasing. For normalized Fs/2 frequency > > >>>each has attenuation above the level of quantization noise, so for >>>Fs=48kHz we can easily observe aliasing for frequencies up to 26 kHz. >>>This aliasing effect starts at 22kHz, not audible for humans, but why >>>not use filter eliminating aliasing definitively ? >> >>The aliasing in the inaudible area is unimportant, especially as it does >>not affect the specmanship. Eliminating this aliasing will cost more >>taps of the filter; that could have noticeable impact on the power >>consumption and the cost of silicon. >> >>There is the other problem with delta sigma ADCs: aliasing from the >>vicinity of the frequency of the modulator (several MHz typ.). There is >>not much of attenuation there; only a basic RC lowpass. This can create >>serious problems with EMI succeptibility. > > > You need to take care with those RC filters. Assuming the ADC has a > differential input, you filter with two resistors in the leads, and one > capacitor across them. Then you use 2 capacitors of some small enough value > to still have reasonable RF properties - maybe 22pF or 33pF - to ground > from the two leads. Make sure the ground side of these two capacitor is > grounded at the same point in space, to avoid injecting differential noise. > Now you have a simple RC filter that rolls off the response nicely, before > the horrors at the modulator frequency, and which also has few problems > with EMI susceptibility.
The 1st order filter will make for only ~50dB of alias attenuation at the very best case. I had to make 2nd order filters. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by Rune Allnor November 1, 20102010-11-01
On Oct 29, 5:23&#2013266080;pm, Tim Wescott <t...@seemywebsite.com> wrote:
> On 10/29/2010 12:26 AM, Deamon wrote: > > > Please I am a complete newbie in Signal analysis and modelling and I > > am quite confused &#2013266080;about the use of &#2013266080;Nyquist theorem in sampling .Does > > this Nyquist criterion affect the &#2013266080;rate at which data is transferred > > that is &#2013266080;the data rate ? > > No more than quantum theory affects how electrons behave in a > semiconductor -- it's rather the other way around. > > > I have &#2013266080;read the wikiopedia saying that I > > must sample at twice the bandwidth to be able to recontruct a signal > > perfectly But I don't understand the concept . If I sample at 2B then > > it is bigger than the wave itself . > > If the other links that you've gotten haven't helped, read this:http://www.wescottdesign.com/articles/Sampling/sampling.html > > I believe it shows pretty early on why you need to sample at over 2B to > completely capture a signal.
Don't know how early it appears in the article (I didn't browse the whole thing) but the key is figure 2. Understand that figure, and you understand the sampling theorem. Rune
Reply by steveu November 1, 20102010-11-01
> > >Roman Rumian wrote: > >> 2010-10-29 18:23, Tim Wescott wrote: >> (...) >> >>> If the other links that you've gotten haven't helped, read this: >>> http://www.wescottdesign.com/articles/Sampling/sampling.html >> >> >> thank you for this article. >> These days we were preparing new audio engineering lab examples, and >> have noticed and checked that EVERY audio A/D converter from Cirrus, >> AKM, Analog Devices, TI and Wolfson has digital decimation filter >> (probably half band) introducing aliasing. For normalized Fs/2 frequency
>> each has attenuation above the level of quantization noise, so for >> Fs=48kHz we can easily observe aliasing for frequencies up to 26 kHz. >> This aliasing effect starts at 22kHz, not audible for humans, but why >> not use filter eliminating aliasing definitively ? > >The aliasing in the inaudible area is unimportant, especially as it does >not affect the specmanship. Eliminating this aliasing will cost more >taps of the filter; that could have noticeable impact on the power >consumption and the cost of silicon. > >There is the other problem with delta sigma ADCs: aliasing from the >vicinity of the frequency of the modulator (several MHz typ.). There is >not much of attenuation there; only a basic RC lowpass. This can create >serious problems with EMI succeptibility.
You need to take care with those RC filters. Assuming the ADC has a differential input, you filter with two resistors in the leads, and one capacitor across them. Then you use 2 capacitors of some small enough value to still have reasonable RF properties - maybe 22pF or 33pF - to ground from the two leads. Make sure the ground side of these two capacitor is grounded at the same point in space, to avoid injecting differential noise. Now you have a simple RC filter that rolls off the response nicely, before the horrors at the modulator frequency, and which also has few problems with EMI susceptibility. Steve
Reply by Deamon November 1, 20102010-11-01
Thanks Guys it was quite trashed out. I loved the analogy of the
string and the number of modes best. Thanks for the help. All the
links also helped .

Reply by Vladimir Vassilevsky October 30, 20102010-10-30

Roman Rumian wrote:

> 2010-10-29 18:23, Tim Wescott wrote: > (...) > >> If the other links that you've gotten haven't helped, read this: >> http://www.wescottdesign.com/articles/Sampling/sampling.html > > > thank you for this article. > These days we were preparing new audio engineering lab examples, and > have noticed and checked that EVERY audio A/D converter from Cirrus, > AKM, Analog Devices, TI and Wolfson has digital decimation filter > (probably half band) introducing aliasing. For normalized Fs/2 frequency > each has attenuation above the level of quantization noise, so for > Fs=48kHz we can easily observe aliasing for frequencies up to 26 kHz. > This aliasing effect starts at 22kHz, not audible for humans, but why > not use filter eliminating aliasing definitively ?
The aliasing in the inaudible area is unimportant, especially as it does not affect the specmanship. Eliminating this aliasing will cost more taps of the filter; that could have noticeable impact on the power consumption and the cost of silicon. There is the other problem with delta sigma ADCs: aliasing from the vicinity of the frequency of the modulator (several MHz typ.). There is not much of attenuation there; only a basic RC lowpass. This can create serious problems with EMI succeptibility. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by Tim Wescott October 30, 20102010-10-30
On 10/30/2010 07:25 AM, Roman Rumian wrote:
> 2010-10-29 18:23, Tim Wescott wrote: > (...) >> If the other links that you've gotten haven't helped, read this: >> http://www.wescottdesign.com/articles/Sampling/sampling.html > > thank you for this article. > These days we were preparing new audio engineering lab examples, and > have noticed and checked that EVERY audio A/D converter from Cirrus, > AKM, Analog Devices, TI and Wolfson has digital decimation filter > (probably half band) introducing aliasing. For normalized Fs/2 frequency > each has attenuation above the level of quantization noise, so for > Fs=48kHz we can easily observe aliasing for frequencies up to 26 kHz. > This aliasing effect starts at 22kHz, not audible for humans, but why > not use filter eliminating aliasing definitively ?
In a general purpose ADC it's because that may not be what the system designer wants -- certainly in the case of an ADC in a close-loop control system, the system designer is going to be very twitchy about phase delay artifacts from anti-aliasing filters, and in other systems the system designer may be intentionally subsampling, and the alias may be exactly the signal that he wants to pass through the ADC. For purpose-designed audio ADCs this becomes more smoky, because presumably the ADCs are designed for systems where anti-aliasing is always going to happen. I can think of a few reasons not to include them in the chip, though: One, because it's hard to make really good mixed-signal chips, and from a system design perspective it may be cheaper to use active filtering before the ADC that use parts from an all-analog process. Two, because every audio system designer is going to have his own opinion about the best anti-alias filtering, and they're going to view anything that you do inside your ADC as "getting in the way". Three, no one's thought of it (or it's only just now becoming practical), and next year that's all you'll be able to get. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by Roman Rumian October 30, 20102010-10-30
2010-10-29 18:23, Tim Wescott wrote:
(...)
> If the other links that you've gotten haven't helped, read this: > http://www.wescottdesign.com/articles/Sampling/sampling.html
thank you for this article. These days we were preparing new audio engineering lab examples, and have noticed and checked that EVERY audio A/D converter from Cirrus, AKM, Analog Devices, TI and Wolfson has digital decimation filter (probably half band) introducing aliasing. For normalized Fs/2 frequency each has attenuation above the level of quantization noise, so for Fs=48kHz we can easily observe aliasing for frequencies up to 26 kHz. This aliasing effect starts at 22kHz, not audible for humans, but why not use filter eliminating aliasing definitively ? Kind regards Roman Rumian
Reply by Bryan October 29, 20102010-10-29
On Oct 29, 9:23&#2013266080;am, Tim Wescott <t...@seemywebsite.com> wrote:
> On 10/29/2010 12:26 AM, Deamon wrote: > > > Please I am a complete newbie in Signal analysis and modelling and I > > am quite confused &#2013266080;about the use of &#2013266080;Nyquist theorem in sampling .Does > > this Nyquist criterion affect the &#2013266080;rate at which data is transferred > > that is &#2013266080;the data rate ? > > No more than quantum theory affects how electrons behave in a > semiconductor -- it's rather the other way around. > > > I have &#2013266080;read the wikiopedia saying that I > > must sample at twice the bandwidth to be able to recontruct a signal > > perfectly But I don't understand the concept . If I sample at 2B then > > it is bigger than the wave itself . > > If the other links that you've gotten haven't helped, read this:http://www.wescottdesign.com/articles/Sampling/sampling.html > > I believe it shows pretty early on why you need to sample at over 2B to > completely capture a signal. > > Keep in mind that as a speed limit, capturing signals at the Nyquist > rate is a task more akin to accelerating particles to the speed of light > than it is to leaning against a door: the closer to the Nyquist rate you > try to sample, the more difficult the job gets, and the more side > effects your signal will suffer. > > > I did like to go on to DSP stuffs > > but I got to learn the basics first. > > > Incase it help I have a Physics Background . > > Actually, the Nyquist rate is derived from more basic stuff. &#2013266080;It helps a > lot to have a thorough understanding of signal analysis in the Fourier > domain. &#2013266080;If you _thoroughly_ understand the Fourier transform and if you > have a good understanding (I won't say "full") of the application of the > Dirac delta functional to Fourier transform analysis, then the Nyquist > theorem and it's many ramifications just kind of jumps out and barks at > you, then curls up by your feet for a nap. > > (Note that my analysis above avoids the Dirac delta -- it's a great > shortcut, once you spend a _lot_ of time understanding it. &#2013266080;So for > things like casual articles, I avoid it like the plague. &#2013266080;Were I writing > a signal processing book, I'd make you learn it, then I'd use it all over). > > -- > > Tim Wescott > Wescott Design Serviceshttp://www.wescottdesign.com > > Do you need to implement control loops in software? > "Applied Control Theory for Embedded Systems" was written for you. > See details athttp://www.wescottdesign.com/actfes/actfes.html
Excellent write-up; thank you for sharing. I was going to mention the pitfalls of sampling right at the Nyquist rate if you happen to sample at just the right phase but I thought I might have already overwhelmed the OP. And I agree. It took probably 2 years to fully (if I can truly say that; most likely I cannot) understand frequency domain analysis for me, and it took viewing the problem from as many angles as possible. Actually Lyon's book does a fantastic job in retrospect and would have shortened the time of understanding. The 3-dimensional views of the Fourier transform are an indispensable perspective on the topic in regard to full understanding (to the OP: he actually was the 2nd reply to your question).
Reply by Bryan October 29, 20102010-10-29
On Oct 29, 12:26&#2013266080;am, Deamon <persistence...@gmail.com> wrote:
> Please I am a complete newbie in Signal analysis and modelling and I > am quite confused &#2013266080;about the use of &#2013266080;Nyquist theorem in sampling .Does > this Nyquist criterion affect the &#2013266080;rate at which data is transferred > that is &#2013266080;the data rate ? I have &#2013266080;read the wikiopedia saying that I > must sample at twice the bandwidth to be able to recontruct a signal > perfectly But I don't understand the concept . If I sample at 2B then > it is bigger than the wave itself . &#2013266080;I did like to go on to DSP stuffs > but I got to learn the basics first. > > Incase it help I have a Physics Background .
There are quite a few ways to approach the Nyquist-Shannon sampling theorem. It sounds like you want an intuitively satisfying answer. I assume you're familiar with basic Fourier series and the Fourier transform, and the notion that a signal can be decomposed (in most cases) to a superposition of sinusoids with different amplitudes and phases. That said, you should be able to understand that the baseband bandwidth is defined by the highest frequency sinusoid in this superposition. Let's just focus on this one frequency, and pretend that it is the only content of your signal. So let's sample it by hand. You get to place one point every cycle if you sample at that frequency (at 1B as you defined it above). So where do you place it? Every positive peak? Now give that sequence of samples to someone and tell them to recreate the signal. Always it appears like a flat line (either zero, or a DC offset). Now let's say I give you 2 points per cycle (sampling at 2B as it were). Then you can place a dot at every positive peak, as well as every negative peak. Knowing that the ideal kernel for reconstruction is the normalized sinc function (see Whittaker-Shannon interpolation formula, this only applies for ideal reconstruction), one can easily recreate the signal. More intuitively, look up the concept of zero-order hold. Using this, we would end up with a square wave of our original frequency which could be low pass filtered (equivalent of being convolved with a normalized sinc function so it approximates the Whittaker-Shannon interpolation formula or perfectly implements it for ideal brick wall low pass filters). Obviously this is strictly an intuitive definition and should be taken at face value. Another way would be to discretize the signal mathematically using the sampling rate, and then attempt to make the waveform continuous again mathematically, and you'll see if it wasn't sampled at the Nyquist rate, you won't end up with your original frequency. There are many other ways of looking at this, so let me know if you have a preferred approach and I'll do my best to explain it that way.
Reply by Tim Wescott October 29, 20102010-10-29
On 10/29/2010 11:47 AM, glen herrmannsfeldt wrote:
> Tim Wescott<tim@seemywebsite.com> wrote: >> On 10/29/2010 12:26 AM, Deamon wrote: >>> Please I am a complete newbie in Signal analysis and modelling and I >>> am quite confused about the use of Nyquist theorem in sampling .Does >>> this Nyquist criterion affect the rate at which data is transferred >>> that is the data rate ? > >> No more than quantum theory affects how electrons behave in a >> semiconductor -- it's rather the other way around. > > Actually, it is right. > > The actual Nyquist problem, as I wrote previously, was how fast > telegraph pulses could be sent through a bandwidth limited medium. > > (I used to have a copy of the paper. I don't know that there are > any copies on the web, though.) > > The math for sending pulses through an analog channel, and for > sampling an analog input, are (close enough to) the same. > > I haven't tried to make an argument for or against the electron > behavior question, but pretty often QM has the same symmetry.
I think I was being excessively pedantic and stating things poorly. I was reacting to his phrasing, which doesn't really capture the essence of the Nyquist/Shannon/That Russian Guy theorem -- that you can quantify some of the information content of a signal as "bandwidth", and make a limit out of that which relates to sampling rate. Then I chose a poor analogy... -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html