Quardrature Direct Fourier Transform

[Bill Sloman]

I cannot speak for the 1982 era SH's- but they are no longer a
limitation in modern times- with sampling apertures at under 100ps and
much faster than the actual A/D pipelined conversion rate.

In the 1980's you could build something quite quick using a diode
bridge to do the sampling - an approach that I'd used at EMI Central
Research back in about 1978 when sampling 2MHz ultrasound, where we
really didn't need much in the way of speed - and Burr-Brown were
selling their 12- and 14-bit accurate sample and holds, which - IIRR -
were good for a few tens of nanoseconds.

None of this answers my question, which is what the digital circuitry
contributed to the phase and amplitude precision, since both depended
on the accuracy of the analog sample and hold. Or are you using
"digital" in the very broad sense of "switching"?

 

[Fred Bloggs]

In the 1980's you could build something quite quick using a diode
bridge to do the sampling - an approach that I'd used at EMI Central
Research back in about 1978 when sampling 2MHz ultrasound, where we
really didn't need much in the way of speed - and Burr-Brown were
selling their 12- and 14-bit accurate sample and holds, which - IIRR -
were good for a few tens of nanoseconds.

None of this answers my question, which is what the digital circuitry
contributed to the phase and amplitude precision, since both depended
on the accuracy of the analog sample and hold. Or are you using
"digital" in the very broad sense of "switching"?

The digital quadrature sampling came into its own when the advantages
complex- phase and amplitude- signal processing were realized in
wideband communications and pulse measurement systems. Since the phase
measurement is largely ratiometric, the requirement is on the I/Q
channels to undergo identical phase/amplitude frequency transformations
and this is realized with the quadrature digital sampling technique
using a single analog channel -the S/H and A/D phase and amplitude error
is identical for both I and Q sample sequences.

 

[Bill Sloman]

The digital quadrature sampling came into its own when the advantages
complex- phase and amplitude- signal processing were realized in
wideband communications and pulse measurement systems. Since the phase
measurement is largely ratiometric, the requirement is on the I/Q
channels to undergo identical phase/amplitude frequency transformations
and this is realized with the quadrature digital sampling technique
using a single analog channel -the S/H and A/D phase and amplitude error
is identical for both I and Q sample sequences.

You get the same advantage by putting an analog multiplexer after a
single sample and hold and using it to feed four parallel box-car
integrators - the multiplexer doesn't have to be up to much.

I repeat - where is the digital advantage?

My copy of Floyd M. Gardner's "Phaselock Techniques" is the second
edition, published in 1979 (ISBN 0-471-04294-3) but the first edition
dates back to 1966, and the introduction refers back to Bellescize's
paper in the French "L'Onde Electrique" vol. 11, pp 230-240 (1932) on
synchronous/homodyne radio receivers. Your heroes seem to have
performed the not-unfamiliar trick of stuffing an A/D converter into a
well-known system and then making exaggerated claims about the
improvement in performance they got.

 

[Frank Raffaeli]

Wow, only 22 years! Looks like I'm catching up.

I'm not sure you are 22 years behind the "curve". There is still a lot
of room for development in this area. A demodulator only begins with
digital sampling. There is symbol detection, frequency shift
compensation, phase and amplitude detection to name a few. IMO it's
getting easier and faster with newer MCU's (I only understand Atmel
and TI). Algorithms similar to what you have done will become more
instrumental in mod-demod applications because it saves money. FPGA's
provide even more design flexibility. Once the input signal is
sampled, you can decimate and filter into two vectors that define
instantaneous amplitude and phase. Here is an intro in MS Word:

http://www.aomwireless.com/dif/docs/fm_vr6.doc

or html: http://www.aomwireless.com/dif/fm_vr4.htm

Frank Raffaeli
http://www.aomwireless.com/

 

[gwhite]

You get the same advantage by putting an analog multiplexer after a
single sample and hold and using it to feed four parallel box-car
integrators - the multiplexer doesn't have to be up to much.

I repeat - where is the digital advantage?

My copy of Floyd M. Gardner's "Phaselock Techniques" is the second
edition, published in 1979 (ISBN 0-471-04294-3) but the first edition
dates back to 1966, and the introduction refers back to Bellescize's
paper in the French "L'Onde Electrique" vol. 11, pp 230-240 (1932) on
synchronous/homodyne radio receivers. Your heroes seem to have
performed the not-unfamiliar trick of stuffing an A/D converter into a
well-known system and then making exaggerated claims about the
improvement in performance they got.

As Mr. Bloggs stated, the amplitude error of the quadrature demodulation
approaches zero, since only one sampler is used. No analog circuitry
follows to add DC offsets or any amplitude errors. Also, a very precise
90 degrees can be acquired digitally, so the "LO" phase error will be
quite low too. Of course, a digital 90 degree phase splitter could also
be applied to an analog IQ decoder/demultiplexer, and sometimes is. I
think the digital advantage, so to speak, is eventually to be had in
high integration and low cost -- the detector/demultiplxer/decoder and
entire BB analog section can be eliminated. In truth, both methods are
still used, and conventional superhet designs can largely mitigate DC
offset problems.

At my previous employer, we used bandpass-quadrature sampling at 5/4
wavelength. As a result, we had no DC, amplitude, or phase error
issues. The conversion to digital (which has to happen anyway), the
downconversion, and the IQ decoding, is done in one fell swoop. Analog
I/Q demodulators always have some measure of DC, amplitude, and phase
issues.

 

[Bill Sloman]

At my previous employer, we used bandpass-quadrature sampling at 5/4
wavelength. As a result, we had no DC, amplitude, or phase error
issues. The conversion to digital (which has to happen anyway), the
downconversion, and the IQ decoding, is done in one fell swoop. Analog
I/Q demodulators always have some measure of DC, amplitude, and phase
issues.

Analog I/Q demodulators always have some measure of DC, amplitude and
phase error, but so do systems that include an A/D converter. If you
could use a low frequency sigma-delta A/D converter, you could get the
digitisation error level down to the same sorts of of error levels you
can achieve with precision analog design (as practiced at national
standards laboratories, amongst other places). The faster methods of
A/D conversion have higher error levels, and bottle-neck the process,
unless you can end up digitising a difference signal.

Like I said, there is no magic advantage to be gained by including A/D
conversion in the signal processing, though it can often make life
easier.

In the last project I worked on, the proof of principle prototype used
analog demodulation and the production machine used an A/D converter
to do the same job, and it didn't make any difference to the
performance of the system, which was limited by other considerations,
as usually seems to be the case.

 

[gwhite]

The faster methods of
A/D conversion have higher error levels, and bottle-neck the process,
unless you can end up digitising a difference signal.

Can you describe the product and quantify the amplitude, phase, and DC
errors?

Like I said, there is no magic advantage to be gained by including A/D
conversion in the signal processing, though it can often make life
easier.

"Make life easier" is a good enough reason itself.

In the last project I worked on, the proof of principle prototype used
analog demodulation and the production machine used an A/D converter
to do the same job, and it didn't make any difference to the
performance of the system, which was limited by other considerations,
as usually seems to be the case.

Obviously if some other error swamps it out, and the system can tolerate
it, it doesn't matter. That just says the _system_ sensitivity is low.
(I'm not disagreeing with you that the net answer is that it often
doesn't matter from a performance perspective.)

 

[Bill Sloman]

Can you describe the product and quantify the amplitude, phase, and DC
errors?

Only for a specific situation.

"Make life easier" is a good enough reason itself.

It certainly can be. Designing equipment involves juggling a number of
very different constraints, and every design job has a different set
of weighing factors, which can include a idiot boss claiming that he
couldn't sell anything which has a sampling jitter of more than 10psec
when the minimum width sampling pulse had a full width at half maximum
of 500psec.

Obviously if some other error swamps it out, and the system can tolerate
it, it doesn't matter. That just says the _system_ sensitivity is low.
(I'm not disagreeing with you that the net answer is that it often
doesn't matter from a performance perspective.)

Agreed.