What Nyquist Didn't Say

Tim,

You might like to include in your paper a discussion on complex sampling,
and explain why the rate can be half that of real sampling yet still
comply with the Nyquist criterion.

Jeff

Mike Monett wrote:
> "Helmut Sennewald" <helmutsennewald@t-online.de> wrote:
>
>   > "Mike    Monett"     <No@email.adr>     schrieb    im  Newsbeitrag
>   > news:Xns984E39E43288BNoemailadr@208.49.80.251...
>
>   >> miso@sushi.com wrote:
>
>   >>> Note that the Bessel filter will ring at higher orders.  I don't
>   >>> have my  copy of Zverev handy, but I think the  Bessel  rings at
>   >>> 4th order and higher.
>
>   >> Are you sure about that? Here is a 9th order 1 MHz Bessel for
>   >> LTspice. (Save as a CKT file)
>
>   >> * UTS Mike Monett
>   >> * Converted From Micro Cap Source file to LTspice
>   >> *
>   >> C1 0 1 248.3PF
>   >> C2 0 2 1200.0PF
>   >> C3 0 3 2007.3PF
>   >> C4 0 4 2749.9PF
>   >> C5 0 Vout 7209.4PF
>   >> L1 1 2 1.8UH
>   >> L2 2 3 4.1UH
>   >> L3 3 4 5.9UH
>   >> L4 4 Vout 8.6UH
>   >> R1 Vin 1 50
>   >> R5 0 Vout 50
>   >> V1 Vin 0 DC 0 PULSE (0 1 0 0 0 2.5e-006 5e-006)
>   >> .TRAN 1e-008 10u 0 1n UIC
>   >> .PRINT TRAN V(VOUT) V(VIN)
>   >> .PLOT TRAN V(VOUT) V(VIN)
>   >> .PROBE
>   >> .END
>   >> ;$SpiceType=SPICE3
>
>   >> It doesn't ring.
>
>   >> Regards,
>
>   >> Mike Monett
>
>   > Hello Mike,
>
>   > It seems  you have overlooked that LTspice assumes a  certain rise
>   > and fall time if you specify t_rise=0 or t_fall=0.
>
>   > V1 Vin 0 DC 0 PULSE (0 1 0 0 0 2.5e-006 5e-006)
>
>   > LTspice assumes in this case trise = fall = 10%*Twidth = 250ns
>
>   > This is the reason why you see no overshoot.
>
>   > Now we use fast edges.
>
>   > V1 Vin 0 DC 0 PULSE (0 1 0 1n 1n 2.5e-006 5e-006)
>
>   > You will see about 1.6x% overshoot. By the way, I am not  sure how
>   > precise the  choosen component values are to get the  ideal Bessel
>   > filter response. Bessel filters have indeed overshoot in  the step
>   > response.
>
>   > Best regards,
>   > Helmut
>
>   Hi Helmut,
>
>   Thanks for taking a look at this, and for pointing out  that LTspice
>   changes the rise and fall times if you do not specify the  values. I
>   am still learning how LTspice works, and these unexpected variations
>   from other SPICE programs can be major pitfalls.
>
>   In this  case,  the amount of overshoot is very small,  and  I'm not
>   sure if  the 1.6% is not caused by the way the component  values are
>   rounded.
>
>   I use  this filter program for general filter design.  The component
>   values were calculated for the theoretical values and  the inductors
>   were rounded  to 2 significant digits. This reflects  the difficulty
>   in obtaining precision inductors, particularly at VHF and UHF.
>
>   The capacitors  were rounded to tenths of a pf. This is  because the
>   program is  used mostly for work at VHF and UHF, where the  caps are
>   much smaller.  It  may well be that  using  the  correct theoretical
>   values for  the components may reduce or eliminate the  small amount
>   of overshoot you measured.
>
>   However, there is still the practical matter of  obtaining inductors
>   and capacitors  with the needed precision, and any  practical filter
>   will have  imperfect  components.   I   have  found  the  Bessel and
>   Equiripple to  be much more tolerant of errors  in  component values
>   than other filter types, and still give good performance.
>
>   If we are concerned about such small values of overshoot, we need to
>   repeat this using the correct theoretical values for the components.
>   Even so,  an  overshoot of 1.6% is not in the same  category  as the
>   overshoot from Butterworth or other non-linear phase  filters, which
>   may have  ten  percent or more, depending on  the  sharpness  of the
>   cutoff. In practise, the Bessel and Equiripple are considered linear
>   phase filters, and have negligible overshoot.
>
>   For example, a Butterworth or other nonlinear group delay filter may
>   cause excessive timing errors when used to filter digital data. This
>   can be minimized by changing to a Bessel or Equiripple filter.
>
>   So practically  speaking,  the   Bessel  and  Equiripple distinguish
>   themselves from  other filters by the constant  group  delay through
>   the filter bandpass, and the low or non-existant overshoot.
>
>   Regards,
>
>   Mike Monett
>
>   Antiviral, Antibacterial Silver Solution:
>   http://silversol.freewebpage.org/index.htm
>   SPICE Analysis of Crystal Oscillators:
>   http://silversol.freewebpage.org/spice/xtal/clapp.htm
>   Noise-Rejecting Wideband Sampler:
>   http://www3.sympatico.ca/add.automation/sampler/intro.htm

You really need to look at theory versus what spice predicts. The input
is an ideal step. As you do the convolution, the negative region of the
impulse response subtracts from the result, making the signal drop in
value, then the postive regions make the result increase in value,
hence ringing.. The Gaussian impulse response is always positive, hence
the convolution output can't decrease as time increases.

Linear phase alone is not enough to stop ringing.

The discrete time situation is easier to understand, especially if you
consider a finite impulse response filter. The response of a FIR filter
to a step input is the the sum of the tap coefficients from one to N.
That is, the first output is the first tap. The second output is the
sum of the first two taps, etc. If no tap is negative, then the output
always rises, hence no ringing.

No circuits were simulated in writing this post. ;-)

On 30 Sep 2006 17:33:25 -0700, miso@sushi.com wrote:

[snip]
>
>No circuits were simulated in writing this post. ;-)

Bwahahahaha!  ROTFLMAO!

                                        ...Jim Thompson
-- 
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.

"Ban" <bansuri@masterweb.it> wrote:
> 
> Bessel filters do have a small overshoot, which decreases at higher
> orders. 2nd    .43%
> 4th    .84%
> 6th    .64%
> 8th    .34%
> 10th    .06%
> note the *very low* value for higher orders. In fact the frequency
> response gets hardly better then.
> The Gauss filter has indeed zero ringing, but a much larger transition
> band. 

Ban,

Thanks for the clarification. In most references, the Bessel is considered 
to have low, negligible, or no overshoot, especially when compared to 
Butterworth, Chebyshev and other types of filters. Your numbers confirm 
this.

In practise, it is difficult to obtain the exact component values needed 
for the theoretical performance. Not only are the values non-standard, but 
it may be difficult to get the inductor "Q" values used in most 
calculations. So we can assume there will be some deviation from the 
theoretical performance, and the overshoot will probably increase slightly. 
However, it is still low enough to be difficult to measure, and the terms 
"low", "neglible" or "no overshoot" are quite descriptive.

Regards,

Mike Monett

Antiviral, Antibacterial Silver Solution:
http://silversol.freewebpage.org/index.htm
SPICE Analysis of Crystal Oscillators:
http://silversol.freewebpage.org/spice/xtal/clapp.htm
Noise-Rejecting Wideband Sampler:
http://www3.sympatico.ca/add.automation/sampler/intro.htm

  miso@sushi.com wrote:

  > You really need to look at theory versus what spice  predicts. The
  > input is  an ideal step. As you do the  convolution,  the negative
  > region of  the impulse response subtracts from the  result, making
  > the signal drop in value, then the postive regions make the result
  > increase in  value, hence ringing.. The Gaussian  impulse response
  > is always positive, hence the convolution output can't decrease as
  > time increases.

  > Linear phase alone is not enough to stop ringing.

  > The discrete time situation is easier to understand, especially if
  > you consider  a finite impulse response filter. The response  of a
  > FIR filter to a step input is the the sum of the  tap coefficients
  > from one to N.

  > That is,  the first output is the first tap. The second  output is
  > the sum  of the first two taps, etc. If no tap  is  negative, then
  > the output always rises, hence no ringing.

  Please see  Ban's  post and my reply. Most  references  describe the
  Bessel as  having  low, negligible, or no  overshoot.  Ban's numbers
  show a theoretical overshoot of less than 1%, decreasing with higher
  order. In  any practical LCR filter, the Bessel will  have  such low
  overshoot as to be difficult or impossible to measure. So it doesn't
  make sense to split hairs between <1% and zero overshoot.

  DSP is a quite different story, and you can realize filters that are
  impossible in real life. But it would be difficult to  implement DSP
  at higher frequencies.

  Regards,

  Mike Monett

  Antiviral, Antibacterial Silver Solution:
  http://silversol.freewebpage.org/index.htm
  SPICE Analysis of Crystal Oscillators:
  http://silversol.freewebpage.org/spice/xtal/clapp.htm
  Noise-Rejecting Wideband Sampler:
  http://www3.sympatico.ca/add.automation/sampler/intro.htm

Jim Thompson wrote:
> On 30 Sep 2006 17:33:25 -0700, miso@sushi.com wrote:
>
> [snip]
> >
> >No circuits were simulated in writing this post. ;-)
>
> Bwahahahaha!  ROTFLMAO!
>
>                                         ...Jim Thompson


Well a few neurons were tortured trying to recall all that theory. No
wait, make that extraordinarily rendered.


> --
> |  James E.Thompson, P.E.                           |    mens     |
> |  Analog Innovations, Inc.                         |     et      |
> |  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
> |  Phoenix, Arizona            Voice:(480)460-2350  |             |
> |  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
> |       http://www.analog-innovations.com           |    1962     |
>
> I love to cook with wine.      Sometimes I even put it in the food.

miso@sushi.com wrote:
>
> You really need to look at theory versus what spice predicts. The
> input is an ideal step. As you do the convolution, the negative
> region of the impulse response subtracts from the result, making the
> signal drop in value, then the postive regions make the result
> increase in value, hence ringing.. The Gaussian impulse response is
> always positive, hence the convolution output can't decrease as time
> increases.
>
> Linear phase alone is not enough to stop ringing.
>
> The discrete time situation is easier to understand, especially if you
> consider a finite impulse response filter. The response of a FIR
> filter to a step input is the the sum of the tap coefficients from
> one to N. That is, the first output is the first tap. The second
> output is the sum of the first two taps, etc. If no tap is negative,
> then the output always rises, hence no ringing.
>
> No circuits were simulated in writing this post. ;-)

There are differences between analog and digital filters. Digital means an 
approximation of the desired characteristic in the passband, but the poles 
and zeros are modified to compensate for the modulation effects. aliasing is 
always happening, but it can be reduced below the noise floor with the 
analog input filter.
Linear phase has a very undesirable side effect, it rings *before and after* 
the step, supposed to be more audible.

And Audio is a very forgiving m�tier, because the ears themselves function 
as reconstruction filters, suppressing all those high frequency artifacts.. 
If you want to display the signal with a digital scope or ECG, you better 
start with 5 to 10 times the upper frequency rolloff, look at the specs 
there, nobody even considers Nyquist adequate, exept programmers having no 
idea of reality.
-- 
ciao Ban
Apricale, Italy 

"Tim Wescott" <tim@seemywebsite.com> wrote in message 
news:UaOdnVhcfetF6IDYnZ2dnUVZ_oudnZ2d@web-ster.com...
> I've seen a lot of posts over the last year or so that 
> indicate a lack of understanding of the implications of 
> the Nyquist theory, and just where the Nyquist rate fits 
> into the design of sampled systems.

Nyquist has a lot to say about how far you *can* go and 
little to say about how far you *should* go.  Those of us 
who are forced to push the Nyquist limits may have a better 
appreciation of this.

For example, compare the frequency response of a 5-pole IIR 
Butterworth low-pass filter designed to roll off at 1 KHz. 
with one designed to roll off at 10 KHz., both filters 
having been designed around a sampling frequency of 50 KHz. 
Things start to get nasty above Fs/10 and the harder you 
push Nyquist, the worse it gets.

Nyquist says you can put a sharp +/- 500 KHz analog filter 
around a 21.4 MHz IF and sample it at 2.14 MHz.  What 
Nyquist doesn't say is what that does to your 
signal-to-noise ratio. TANSTAAFL!

Nyquist is often used by slick, hand-waving charlatans to 
over-sell their capabilities without having a clue about the 
real trade-offs involved.  (And, I'll bet Nyquist didn't say 
*that*, either.)

Ban wrote:


>=20
> And Audio is a very forgiving m=E9tier, because the ears themselves fun=
ction=20
> as reconstruction filters, suppressing all those high frequency artifac=
ts..=20

And audio is a very unforgiving matter, because the distortions of the=20
audio amp are quickly growing towards the high frequencies. You won't=20
hear the high frq artifacts as they are, but you will very well hear the =

result of the nonlinear distortion of those.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

["Followup-To:" header set to sci.electronics.design.]
On Fri, 29 Sep 2006 13:55:32 -0700,
  John Larkin <jjlarkin@highNOTlandTHIStechnologyPART.com> wrote
  in Msg. <2t1rh2d56g4gngogguro04er47ckvrcv0t@4ax.com>

> Don't you go knocking whiteboards. A big board with a nice fresh set
> of markers will multiply my IQ by about 1.3 or so.

But only with the smelly markers. The water-based stuff doesn't do it 
for me.

robert