Jerry Wolf wrote:
> Rick Lyons wrote:
> 
>>On Fri, 19 May 2006 18:21:39 +0800, Steve Underwood <steveu@dis.org>
>>wrote:
>>
>>
>>>Rick Lyons wrote:
>>
>>  (snipped)
>>
>>>>I just learned of a new (new to me) efficient
>>>>I/Q sampling scheme proposed twenty years
>>>>ago by DSP pioneer Charles Rader.
>>>>He uses two all-pass filters that have
>>>>a 90-degree phase shift between them.  Rader's
>>>>paper is:
> 
> .> >> [C. M. Rader, "A Simple Method for Sampling In-
> 
>>>>Phase and Quadrature Components," IEEE Trans. Aerospace
>>>>and Electronic Syst.,vol. 20, no. 6, pp. 821-824,
>>>>Nov. 1984.]
> 
> 
> <snip>
> 
>>Now Steve, if you've just won the Lottery then you
>>can afford to sign up for the IEEE Explore program
>>and download a copy of Rader's paper.
> 
> 
> Sadly, not even the Lottery will help.  I just tried IEEE Explore and
> was puzzled not to succeed in finding it there.  Finally a peek at
> their FAQ explains that it provides only:
>     * IEEE journals, transactions, letters, and magazines from 1988
> with select content back to 1952
>     * IEEE conference proceedings from 1988 with select content back to
> 1953
>     * IEEE standards from 1988
>     * IEE journals, letters, and magazines from 1988
>     * IEE conference proceedings from 1988
> 
Darned good thing I kept the lottery money in my Swiss bank accounts, 
then. :-)

Steve

Rick Lyons wrote:
> On Fri, 19 May 2006 18:21:39 +0800, Steve Underwood <steveu@dis.org>
> wrote:
>
> >Rick Lyons wrote:
>   (snipped)
> >>
> >> I just learned of a new (new to me) efficient
> >> I/Q sampling scheme proposed twenty years
> >> ago by DSP pioneer Charles Rader.
> >> He uses two all-pass filters that have
> >> a 90-degree phase shift between them.  Rader's
> >> paper is:
.> >> [C. M. Rader, "A Simple Method for Sampling In-
> >> Phase and Quadrature Components," IEEE Trans. Aerospace
> >> and Electronic Syst.,vol. 20, no. 6, pp. 821-824,
> >> Nov. 1984.]

<snip>

> Now Steve, if you've just won the Lottery then you
> can afford to sign up for the IEEE Explore program
> and download a copy of Rader's paper.

Sadly, not even the Lottery will help.  I just tried IEEE Explore and
was puzzled not to succeed in finding it there.  Finally a peek at
their FAQ explains that it provides only:
    * IEEE journals, transactions, letters, and magazines from 1988
with select content back to 1952
    * IEEE conference proceedings from 1988 with select content back to
1953
    * IEEE standards from 1988
    * IEE journals, letters, and magazines from 1988
    * IEE conference proceedings from 1988

Dmitry Utyansky wrote:

> Jerry Avins wrote:
> 
>>Steve Underwood wrote:
>>
>>  ...
>>A pair of matched-amplitude all-pass filters whose outputs are in
>>quadrature (but neither of which is linear phase) can be computationally
>>cheaper than a low-ripple broadband Hilbert transformer. I know how to
>>make the filter pair with analog circuits (three op-amps each for a
>>decade bandwidth), I've never even heard of an analog HT.
>>
> 
> 
> I am not an expert in analog circuits, but thinking/looking for this
> I've just come across some tutorial/paper at
> http://members.tripod.com/michaelgellis/mixerscom.html by Michael
> Ellis, which shows some rather frighteningly-looking analog networks
> for phase splitting/shifting.
> 
> I wonder if such things are/were really used (and work(ed)
> adequately)...

Yes. Three all-passes in each leg give a 90-degree relative shift over a
decade with about a quarter-degree peak error. I've designed them and
you may find on in the ARRL handbook. It was there several years ago.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Dmitry Utyansky wrote:
> Jerry Avins wrote:
> 
>>Steve Underwood wrote:
>>
>>  ...
>>A pair of matched-amplitude all-pass filters whose outputs are in
>>quadrature (but neither of which is linear phase) can be computationally
>>cheaper than a low-ripple broadband Hilbert transformer. I know how to
>>make the filter pair with analog circuits (three op-amps each for a
>>decade bandwidth), I've never even heard of an analog HT.
>>
> 
> 
> I am not an expert in analog circuits, but thinking/looking for this
> I've just come across some tutorial/paper at
> http://members.tripod.com/michaelgellis/mixerscom.html by Michael
> Ellis, which shows some rather frighteningly-looking analog networks
> for phase splitting/shifting.

None of them look very frightening, but maybe I'm just more fearless 
than I realise :-) Figure 14 looks fun, though.
> 
> I wonder if such things are/were really used (and work(ed)
> adequately)...

They were certainly used, and I'm sure still are in many places.

Steve

Jerry Avins wrote:
> Steve Underwood wrote:
>
>   ...
> A pair of matched-amplitude all-pass filters whose outputs are in
> quadrature (but neither of which is linear phase) can be computationally
> cheaper than a low-ripple broadband Hilbert transformer. I know how to
> make the filter pair with analog circuits (three op-amps each for a
> decade bandwidth), I've never even heard of an analog HT.
>

I am not an expert in analog circuits, but thinking/looking for this
I've just come across some tutorial/paper at
http://members.tripod.com/michaelgellis/mixerscom.html by Michael
Ellis, which shows some rather frighteningly-looking analog networks
for phase splitting/shifting.

I wonder if such things are/were really used (and work(ed)
adequately)...

Regards,
Dmitry.

On Fri, 19 May 2006 18:21:39 +0800, Steve Underwood <steveu@dis.org>
wrote:

>Rick Lyons wrote:
  (snipped)
>> 
>> I just learned of a new (new to me) efficient 
>> I/Q sampling scheme proposed twenty years 
>> ago by DSP pioneer Charles Rader.  
>> He uses two all-pass filters that have 
>> a 90-degree phase shift between them.  Rader's 
>> paper is:
>> [C. M. Rader, "A Simple Method for Sampling In-
>> Phase and Quadrature Components," IEEE Trans. Aerospace
>> and Electronic Syst.,vol. 20, no. 6, pp. 821-824,
>> Nov. 1984.]
>
>I haven't seen the paper, but can you explain the novelty in a couple of 
>sentances? You said all-pass, but surely if they are all pass you only 
>need one filter - a hilbert transformer. In comms systems I and Q and 
>often created by using a pair of filters to pulse shape the signal, and 
>provide 90 degree different phase shifts at the same time. That's neat, 
>because you kill two birds with one stone. Is that the kind of thing you 
>mean, because I think the cavemen were using that technique?

Hi Steve,

  Rader's scheme uses just one A/D converter and 
two filters having a 90-degree phase difference 
(as you said).
What made Rader's method neat was that he had a 
way to provide built-in decimation at no 
computational cost.

[When I get the time, I want to model Rader's 
idea with MATLAB to see how well it works.]

I searched the Web for an electronic copy of 
Rader's paper, but failed to find any website 
where you can download a copy of his paper.

Now Steve, if you've just won the Lottery then you 
can afford to sign up for the IEEE Explore program 
and download a copy of Rader's paper.

Regards,
[-Rick-]

Eric Jacobsen wrote:
> On Fri, 19 May 2006 08:30:07 -0700, Tim Wescott <tim@seemywebsite.com>
> wrote:
> 
> 
>>John Monro wrote:
>>
>>
>>>Tim Wescott wrote:
>>>
>>>
>>>>Jerry Avins wrote:
>>>>
>>>>
>>>>>Tim Wescott wrote:
>>>>>
>>>>>
>>>>>
>>>>>>MikeEdmans wrote:
>>>>>>
>>>>>>
>>>>>>
>>>>>>>Hello out there,
>>>>>>>
>>>>>>>
>>>>>>>I am confused about hardware implementation of complex sampling. Can I
>>>>>>>just set up two ADCs sampling at the same rate, but with their clock
>>>>>>>signals 90 degrees out of phase, or do I actually need to multiply my
>>>>>>>input signal by a sine-wave?
>>>>>>>
>>>>>>>I assume that by sampling with 2 ADCs with out-of-phase clocks, 
>>>>>>>this is
>>>>>>>the equivalent of multiplying by complex sine wave which is in 
>>>>>>>phase with
>>>>>>>the sampling clock. Does this work?
>>>>>>>
>>>>>>>Thanks for your help!
>>>>>>>
>>>>>>>
>>>>>>
>>>>>>Yes you can just sample with two ADCs with clocks that are 90 degrees
>>>>>>out of phase.  I've never done it this way; I'd look for problems 
>>>>>>having
>>>>>>to do with dealing with DC bias and mismatch between the ADCs, but it
>>>>>>should work.
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>How is that different from sampling at twice the rate with a single ADC
>>>>>and assigning alternate samples to I and Q? If the scheme works in
>>>>>general -- there are special cases where it does work -- every normal
>>>>>sampling at 2k*f_max (k>1) is identical to complex sampling at k*f_max.
>>>>>Intuition says no.
>>>>>
>>>>>Jerry
>>>>
>>>>
>>>>
>>>>With 90 degrees between clocks you're sampling like this:  
>>>>IQ..IQ..IQ..IQ..
>>>>
>>>>Your method is essentially 180 degrees between clocks, like this: 
>>>>IQIQIQIQIQIQIQIQ.
>>>>
>>>>Not only is it harder to pronounce, but your method doesn't give you 
>>>>that essential 90 degrees of phase difference.
>>>>
>>>>Were I doing this sort of thing, and had I a fast enough ADC, I'd 
>>>>sample  like ABabABabABab, and I'd keep I = A - a and Q = B - b (which 
>>>>is really just a dead-simple digital quadrature mix-and-sample).
>>>>
>>>
>>>Tim,
>>>I can't see that having a 90 degree offset between clocks does you much 
>>>good.   The signal samples from the  'Q' channel will have a phase of 45 
>>>degrees at Fs/2, decreasing towards a phase of zero degrees at DC.  As 
>>>far as I can see there are no analytic signals present at any frequency 
>>>in the 'IQ' sample stream that is produced, and so you would not obtain 
>>>the benefit of 'normal' IQ sampling in respect to alias suppression.  It 
>>>would seem to be more productive to simply sample at twice the rate *as 
>>>with Jerry's 'IQIQIQIQ...' suggestion.
>>>
>>>Maybe I am missing something.  Has anyone actually tried this method and 
>>>got it to work?  In particular, can you sample signals with components 
>>>up to Fs using this method, without producing aliases below Fs?
>>>
>>>Regards,
>>>John
>>
>>Look at any of the IQ demodulators out there from Maxim, Linear, 
>>whoever.  They multiply the signal by cos(wt) for the I channel, and 
>>sin(wt) for the Q channel.  This scheme does exactly that.
> 
> 
> No, I think it doesn't.
> 
> Picking a sampling instant doesn't equate to multiplication by a
> sinusoid.  One can post-multiply digitally in many cases (e.g., a
> synchronous demodulator) and that's best done with a single ADC in
> order to avoid gain/balance mismatches between two ADCs (even though
> some "single" ADCs are actually implemented with multiple converters
> these days).
> 
> I don't see how just changing the phases between two sampling clocks
> equates to downconversion, which seems to be what was implied by this
> discussion.
> 
> 
>>Now, I did assume that this guy is interested in sampling an IF signal 
>>to get a baseband complex signal -- if that's what he's trying, his 
>>scheme will work (but probably with flaws).
> 
> 
> I don't think it will.

Ignore mismatched ADCs for the moment (which is one of the difficulties 
I was alluding to in my original post).

Consider the inphase ADC as multiplying the signal by a train of impulses:

sum from {k = -infinity} to infinity {delta(t - kT)}

This impulse train has the Fourier series

sum from {p = -infinity} to infinity {exp(i * p 2 pi t / T))},

whose fundamental is just cos(2 pi t / T)

Now consider the quadrature ADC as multiplying the signal by a train of 
impulses:

sum from {k = -infinity} to infinity {delta(t - kT - T/4)}

This impulse train has the Fourier series

sum from {p = -infinity} to infinity {exp(i * p pi (2t - 1/2) / T ))},

whose fundamental is just sin(2 pi t / T).

So _at the sampling rate_ you are effectively doing quadrature 
downsampling.  Everywhere else you're either magnifying or at least not 
suppressing all the ADC peculiarities, but _at the sampling rate_ its 
quadrature downsampling.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google?  See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

On Fri, 19 May 2006 14:47:30 -0400, Jerry Avins <jya@ieee.org> wrote:

>Eric Jacobsen wrote:
>
>  ...
>
>> Picking a sampling instant doesn't equate to multiplication by a
>> sinusoid.  One can post-multiply digitally in many cases (e.g., a
>> synchronous demodulator) and that's best done with a single ADC in
>> order to avoid gain/balance mismatches between two ADCs (even though
>> some "single" ADCs are actually implemented with multiple converters
>> these days).
>
>In some cases it can. If the multiplying sinusoids are 1/4 the sampling
>frequency, the sine is [0 1 0 -1 ...] and the cosine [1 0 -1 0 ...].
>Those samples can all be taken by a single DAC, alternating I and Q
>channels.

>Jerry

Yes, that's the "synchronous demodulator" that I mentioned, and it
still requires post-multiplication by +/-1, as well as eventual
realignment by filtering.   In other words, you can't just get
downconversion by picking sampling points.   You can possibly reduce
some computation (like with synchronous demodulation) by judiciously
picking sampling instances, but the tradeoff isn't always
straightforward or obvious.

Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org

Eric Jacobsen wrote:

  ...

> Picking a sampling instant doesn't equate to multiplication by a
> sinusoid.  One can post-multiply digitally in many cases (e.g., a
> synchronous demodulator) and that's best done with a single ADC in
> order to avoid gain/balance mismatches between two ADCs (even though
> some "single" ADCs are actually implemented with multiple converters
> these days).

In some cases it can. If the multiplying sinusoids are 1/4 the sampling
frequency, the sine is [0 1 0 -1 ...] and the cosine [1 0 -1 0 ...].
Those samples can all be taken by a single DAC, alternating I and Q
channels.

  ...

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

On Fri, 19 May 2006 08:30:07 -0700, Tim Wescott <tim@seemywebsite.com>
wrote:

>John Monro wrote:
>
>> Tim Wescott wrote:
>> 
>>> Jerry Avins wrote:
>>>
>>>> Tim Wescott wrote:
>>>>
>>>>
>>>>> MikeEdmans wrote:
>>>>>
>>>>>
>>>>>> Hello out there,
>>>>>>
>>>>>>
>>>>>> I am confused about hardware implementation of complex sampling. Can I
>>>>>> just set up two ADCs sampling at the same rate, but with their clock
>>>>>> signals 90 degrees out of phase, or do I actually need to multiply my
>>>>>> input signal by a sine-wave?
>>>>>>
>>>>>> I assume that by sampling with 2 ADCs with out-of-phase clocks, 
>>>>>> this is
>>>>>> the equivalent of multiplying by complex sine wave which is in 
>>>>>> phase with
>>>>>> the sampling clock. Does this work?
>>>>>>
>>>>>> Thanks for your help!
>>>>>>
>>>>>>
>>>>>
>>>>> Yes you can just sample with two ADCs with clocks that are 90 degrees
>>>>> out of phase.  I've never done it this way; I'd look for problems 
>>>>> having
>>>>> to do with dealing with DC bias and mismatch between the ADCs, but it
>>>>> should work.
>>>>
>>>>
>>>>
>>>>
>>>> How is that different from sampling at twice the rate with a single ADC
>>>> and assigning alternate samples to I and Q? If the scheme works in
>>>> general -- there are special cases where it does work -- every normal
>>>> sampling at 2k*f_max (k>1) is identical to complex sampling at k*f_max.
>>>> Intuition says no.
>>>>
>>>> Jerry
>>>
>>>
>>>
>>> With 90 degrees between clocks you're sampling like this:  
>>> IQ..IQ..IQ..IQ..
>>>
>>> Your method is essentially 180 degrees between clocks, like this: 
>>> IQIQIQIQIQIQIQIQ.
>>>
>>> Not only is it harder to pronounce, but your method doesn't give you 
>>> that essential 90 degrees of phase difference.
>>>
>>> Were I doing this sort of thing, and had I a fast enough ADC, I'd 
>>> sample  like ABabABabABab, and I'd keep I = A - a and Q = B - b (which 
>>> is really just a dead-simple digital quadrature mix-and-sample).
>>>
>> 
>> Tim,
>> I can't see that having a 90 degree offset between clocks does you much 
>> good.   The signal samples from the  'Q' channel will have a phase of 45 
>> degrees at Fs/2, decreasing towards a phase of zero degrees at DC.  As 
>> far as I can see there are no analytic signals present at any frequency 
>> in the 'IQ' sample stream that is produced, and so you would not obtain 
>> the benefit of 'normal' IQ sampling in respect to alias suppression.  It 
>> would seem to be more productive to simply sample at twice the rate *as 
>> with Jerry's 'IQIQIQIQ...' suggestion.
>> 
>> Maybe I am missing something.  Has anyone actually tried this method and 
>> got it to work?  In particular, can you sample signals with components 
>> up to Fs using this method, without producing aliases below Fs?
>> 
>> Regards,
>> John
>
>Look at any of the IQ demodulators out there from Maxim, Linear, 
>whoever.  They multiply the signal by cos(wt) for the I channel, and 
>sin(wt) for the Q channel.  This scheme does exactly that.

No, I think it doesn't.

Picking a sampling instant doesn't equate to multiplication by a
sinusoid.  One can post-multiply digitally in many cases (e.g., a
synchronous demodulator) and that's best done with a single ADC in
order to avoid gain/balance mismatches between two ADCs (even though
some "single" ADCs are actually implemented with multiple converters
these days).

I don't see how just changing the phases between two sampling clocks
equates to downconversion, which seems to be what was implied by this
discussion.

>Now, I did assume that this guy is interested in sampling an IF signal 
>to get a baseband complex signal -- if that's what he's trying, his 
>scheme will work (but probably with flaws).

I don't think it will.
Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org