Ok I am sampling with an ordinary A/D (not sigma-delta) at 11025kHz which mean I need any noise to be attenuated at half sampling which is at 5512.5Hz. I have read that the nosie level needs to be less that the R.M.S Quantisation Level of my A/D. Now I swing +or - 10 volts with 16 bits. So my Quantisation level is delta = dynamic range/2^16=20/65536=0.000305176 volts. (or 0.305mV) Now my Quantisaton RMS voltage is delta/sqrt(12) =88.096 micro volts. So my noise needs to be lower than this at Fs/2 and then it will be at least as low as the quantistaion noise. Suppose I use a Butterworth filter (3dB passband freq)with passband freq of 4kHz. To go from full swing of 10 volts to 88.096 micro volts requires an attenuation in the stopband of 100dB approx - with a stopband freq of Fs/2=5512Hz. The order of my filter will then be n=log(10^0.1*100-1)^0.5/log(1.378) which is approx 36th order!! What am I doing wrong...is my 4kHz passband assuming too much - do I have to sacrifice this? Naebad
Anti-Aliasing filter
Started by ●August 23, 2005
Reply by ●August 23, 20052005-08-23
OOps- I forgot that should be a full swing in rms ie 10/Sqrt(2) and not 10 when calculating the attenuation but it doesnt help much. Naebad
Reply by ●August 23, 20052005-08-23
naebad wrote:> Ok I am sampling with an ordinary A/D (not sigma-delta) at 11025kHz > which mean I need any noise to be attenuated at half sampling which is > at 5512.5Hz. I have read that the nosie level needs to be less that the > R.M.S Quantisation Level of my A/D. Now I swing +or - 10 volts with 16 > bits. So my Quantisation level is > > delta = dynamic range/2^16=20/65536=0.000305176 volts. > > (or 0.305mV) > > Now my Quantisaton RMS voltage is delta/sqrt(12) > > =88.096 micro volts. > > So my noise needs to be lower than this at Fs/2 and then it will be at > least as low as the quantistaion noise. > > Suppose I use a Butterworth filter (3dB passband freq)with passband > freq of 4kHz. To go from full swing of 10 volts to 88.096 micro volts > requires an attenuation in the stopband of 100dB approx - with a > stopband freq of Fs/2=5512Hz. > > The order of my filter will then be > > n=log(10^0.1*100-1)^0.5/log(1.378) > > which is approx 36th order!! > > What am I doing wrong...is my 4kHz passband assuming too much - do I > have to sacrifice this? > > Naebad >This is why most systems engineers want to oversample and do some filtering in the digital domain -- it's much easier to start with a reasonable order for your analog filter and work from there. You only have to have that severe of attenuation if you want to slam your system with a full-range signal at 5.5kHz. If you know for sure that your actual spectral content will be lower you can work with that. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Reply by ●August 23, 20052005-08-23
You will probably need to relax your filter requirements a bit to come up with a reasonable order filter. Either start rolling off sooner, or accept more noise. Granted it is nice to get your aliasing components down below the ADC noise floor for the worst case input (full scale at 1/2FS), but maybe you can live with less? Or maybe you know your input signal will never be that worst case? Your other option is to sample at a higher frequency and filter digitally. Best wishes! -- Jon Harris SPAM blocker in place: Remove 99 (but leave 7) to reply "naebad" <minnaebad@yahoo.co.uk> wrote in message news:1124826795.554026.7640@g43g2000cwa.googlegroups.com...> Ok I am sampling with an ordinary A/D (not sigma-delta) at 11025kHz > which mean I need any noise to be attenuated at half sampling which is > at 5512.5Hz. I have read that the nosie level needs to be less that the > R.M.S Quantisation Level of my A/D. Now I swing +or - 10 volts with 16 > bits. So my Quantisation level is > > delta = dynamic range/2^16=20/65536=0.000305176 volts. > > (or 0.305mV) > > Now my Quantisaton RMS voltage is delta/sqrt(12) > > =88.096 micro volts. > > So my noise needs to be lower than this at Fs/2 and then it will be at > least as low as the quantistaion noise. > > Suppose I use a Butterworth filter (3dB passband freq)with passband > freq of 4kHz. To go from full swing of 10 volts to 88.096 micro volts > requires an attenuation in the stopband of 100dB approx - with a > stopband freq of Fs/2=5512Hz. > > The order of my filter will then be > > n=log(10^0.1*100-1)^0.5/log(1.378) > > which is approx 36th order!! > > What am I doing wrong...is my 4kHz passband assuming too much - do I > have to sacrifice this? > > Naebad >
Reply by ●August 24, 20052005-08-24
"naebad" <minnaebad@yahoo.co.uk> wrote in message news:1124826795.554026.7640@g43g2000cwa.googlegroups.com... [snip]> What am I doing wrong...is my 4kHz passband assuming too much - do I > have to sacrifice this? > > NaebadIt depends on what you are trying to do with the signal. You may be able to live with aliasing of stuff just above fs/2. This will cut your filter poles in half. e.g. fs=11kHz and signal BW of 4kHz; interference between 5.5kHz and 7kHz folds back into the band between 5.5k and 4k (which you are ignoring anyway). So, your AA filter needs to be down -96dB (assuming full scale interference is possible) at 7kHz, not 5.5kHz. That's an 18 pole butterworth instead of 36. Others have suggested relaxing the stop band attenuation. A related trick is to use a Cauer filter alignment. IIRC you specify passband ripple and stop band attenuation for a Cauer. The stop band doesn't drop forever (like a Butterworth or Bessel) - it has little bumps in the response. What you lose in stop band, you gain in faster transition band. The net result of Cauer and 7kHz+ stop band will be many fewer poles (my WAG would be about 9). Bob
Reply by ●August 24, 20052005-08-24
Bob wrote:> "naebad" <minnaebad@yahoo.co.uk> wrote in message > news:1124826795.554026.7640@g43g2000cwa.googlegroups.com... > > [snip] > > >>What am I doing wrong...is my 4kHz passband assuming too much - do I >>have to sacrifice this? >> >>Naebad > > > It depends on what you are trying to do with the signal. You may be able to > live with aliasing of stuff just above fs/2. This will cut your filter poles > in half. e.g. fs=11kHz and signal BW of 4kHz; interference between 5.5kHz > and 7kHz folds back into the band between 5.5k and 4k (which you are > ignoring anyway). So, your AA filter needs to be down -96dB (assuming full > scale interference is possible) at 7kHz, not 5.5kHz. That's an 18 pole > butterworth instead of 36. > > Others have suggested relaxing the stop band attenuation. A related trick is > to use a Cauer filter alignment. IIRC you specify passband ripple and stop > band attenuation for a Cauer. The stop band doesn't drop forever (like a > Butterworth or Bessel) - it has little bumps in the response. What you lose > in stop band, you gain in faster transition band. The net result of Cauer > and 7kHz+ stop band will be many fewer poles (my WAG would be about 9).Tim's suggestion, oversampling, is at the heart of most practical approaches. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 24, 20052005-08-24
"Jerry Avins" <jya@ieee.org> wrote in message news:o8OdnYAImb2oPJHeRVn-qw@rcn.net...> Bob wrote: > > "naebad" <minnaebad@yahoo.co.uk> wrote in message > > news:1124826795.554026.7640@g43g2000cwa.googlegroups.com... > >> Tim's suggestion, oversampling, is at the heart of most practical > approaches. > > JerryTrue. My suggestions are useful if oversample isn't an option e.g. because the ADC to oversample doesn't exist or is too expensive. 11kHz at 16bits is easily oversampled. Bob
Reply by ●August 24, 20052005-08-24
"Bob" <SkiBoyBob@excite.com> wrote in news:3n3p8dF19jontU1@individual.net:> > "Jerry Avins" <jya@ieee.org> wrote in message > news:o8OdnYAImb2oPJHeRVn-qw@rcn.net... >> Bob wrote: >> > "naebad" <minnaebad@yahoo.co.uk> wrote in message >> > news:1124826795.554026.7640@g43g2000cwa.googlegroups.com... >> > > >> Tim's suggestion, oversampling, is at the heart of most practical >> approaches. >> >> Jerry > > True. My suggestions are useful if oversample isn't an option e.g. > because the ADC to oversample doesn't exist or is too expensive. 11kHz > at 16bits is easily oversampled. > > Bob > > >I have a question that no one has asked. Do you need to use a SAR converter? The antialiasing filter problem basically goes away with a sigma delta converter since the actual sampling rate is very much higher than the effective sample rate. The penalty for using a sigma delta converter is group delay. This is usually the only reason a SAR converter is used instead of a sigma delta at these frequencies. You might be able to use a "trick". If you have sufficient signal processing power, you can oversample and use digital filters. In the sigma delta case, you can decimate with IIR filters to sample at a lower sampling rate with a relatively small group delay. Analog antialiasing filters are going to have about the same delay as digital IIR filters -- Al Clark Danville Signal Processing, Inc. -------------------------------------------------------------------- Purveyors of Fine DSP Hardware and other Cool Stuff Available at http://www.danvillesignal.com
Reply by ●August 24, 20052005-08-24
Jerry Avins wrote:> Tim's suggestion, oversampling, is at the heart of most practical > approaches.There are systems where oversampling is impossible. For example - hard disk drives, where the sampling rate for the VCM control is closely related to the spindle RPM, which is very difficult to increase. --JS
Reply by ●August 24, 20052005-08-24
Al Clark wrote:> "Bob" <SkiBoyBob@excite.com> wrote in > news:3n3p8dF19jontU1@individual.net: > > >>"Jerry Avins" <jya@ieee.org> wrote in message >>news:o8OdnYAImb2oPJHeRVn-qw@rcn.net... >> >>>Bob wrote: >>> >>>>"naebad" <minnaebad@yahoo.co.uk> wrote in message >>>>news:1124826795.554026.7640@g43g2000cwa.googlegroups.com... >>>> >> >>>Tim's suggestion, oversampling, is at the heart of most practical >>>approaches. >>> >>>Jerry >> >>True. My suggestions are useful if oversample isn't an option e.g. >>because the ADC to oversample doesn't exist or is too expensive. 11kHz >>at 16bits is easily oversampled. >> >>Bob >> >> >> > > > I have a question that no one has asked. > > Do you need to use a SAR converter? The antialiasing filter problem > basically goes away with a sigma delta converter since the actual > sampling rate is very much higher than the effective sample rate.It does not. The internal oversampling allows averaging conversions at low precision (typically, one bit) to achieve a single sample at high precision PROVIDED that anti-alias filtering for the final sample rate has been applied.> The penalty for using a sigma delta converter is group delay. This is > usually the only reason a SAR converter is used instead of a sigma delta > at these frequencies. > > You might be able to use a "trick". If you have sufficient signal > processing power, you can oversample and use digital filters. In the > sigma delta case, you can decimate with IIR filters to sample at a lower > sampling rate with a relatively small group delay. Analog antialiasing > filters are going to have about the same delay as digital IIR filtersIt comes down again to oversampling. The type of converter makes no difference. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
