On Fri, 08 Jul 2005 09:12:27 -0400, David Kirkland <spam@netscape.net>
wrote:
(snipped)
>>
>Hi Guys,
>
>I wasn't able to look able to find the source for this that I was
>thinking of. I was able to find adescription of the technique in
>Crochiere and Rabiner's book "Multirate Digital Signal Processing".
>There is also a similar section in Whalen's Book "Detection of Signals
>in Noise"
>
>First, by related I meant in terms of computational savings. The
>technique I mentioned doesn't give the full I/Q samples - the signal
>still stays real (if it started that way). Essentially the left edge of
>the +ve freq components are moved down close to the right side of zero,
>and the right edge of the -ve freq components are moved down close to
>the left side of 0. Moving them close to 0 prevents them from overlaping
>and causing corruption.
Hi David,
Ah, I misunderstood you.
When I first learned about it, I thought the freq translation
method that you descibe was pretty neat.
Neat enough that I covered that topic in the
2nd edition of my DSP book.
Thanks David,
[-Rick-]
(snipped)
>> Then I thought, "If we have a narrowband real signal
>> centered at Fs/3, what happens when I decimate that signal
>> by 3?"
>>
>> I believe the answer is that the signal's
>> positive freq components get shifted to be centered at
>> zero Hz, and its negative freq components also get
>> shifted to be centered at zero Hz. Then I was
>> wondering, off the top of my head, under what conditions
>> will that decimation of a real signal by 3 give me a
>> useable (no alising errors) signal whose spectrum is
>> centered at zero Hz.
>
>I'm not very sure of my answer but I think the condition where you would get
>a useable signal centered at zero Hz is when the real signal has a symmetric
>spectrum around it's carrier (fs/3)
Hi Bhaskar,
I willing to bet one bottle of beer that
you are correct.
>> Am ashamed to say but I don't have a solid answer,
>> in which I'm confident, just by thinking about
>> this.
>>
>> I sure wish I knew more about DSP.
>
>Don't we all...but I think you say such things to make the rest of us feel
>small.
Ha ha Bhaskar, you're a good guy.
But please know, I am unable to count the number
of times when someone asked me a fairly simple
DSP question and I was forced to admit to myself,
"Sheece Rick! Why don't you *KNOW* the answer to
such a simple question(!!)?"
See Ya,
[-Rick-]
Reply by David Kirkland●July 8, 20052005-07-08
Bhaskar Thiagarajan wrote:
> "Rick Lyons" <R.Lyons@_BOGUS_ieee.org> wrote in message
> news:42cd109b.834470500@news.sf.sbcglobal.net...
>
>>On Wed, 06 Jul 2005 21:15:57 GMT, Randy Yates <yates@ieee.org> wrote:
>>
>>
>>>R.Lyons@_BOGUS_ieee.org (Rick Lyons) writes:
>>>
>>>
>>>>On Mon, 04 Jul 2005 14:02:20 -0400, David Kirkland <spam@netscape.net>
>>>>wrote:
>>>>
>>>> (snipped)
>>>>
>>>>>A related technique - If your sampling frequency and decimation factor
>>>>>are chosen appropriately you avoid the multiplication / frequency
>
> shift
>
>>>>>and just filter and decimate. Essentially one of the aliased images
>
> ends
>
>>>>>up appearing in the baseband.
>>>>>
>>>>>Cheers,
>>>>>David
>>>>
>>>>Hi David,
>>>>
>>>> You make a really good point here.
>>>>I can see that your method always works fine
>>>>if the time sequence is complex, but I'm wondering
>>>>under what conditions will it work for real-valued
>>>>time samples.
>>>>
>>>>Humm, ... I'll have to model this sometime.
>>>>
>>>>See Ya',
>>>>[-Rick-]
>>>
>>>Hey Rick,
>>>
>>>I think David means that you start out with a real sequence, then
>>>when you "decimate," one sample becomes real and one imaginary.
>>>
>>>I think I see the technique - the trick (in addition to carefully
>>>choosing your sampling frequencies and bandwidths) is to downsample
>>>by four by keeping samples 0 and 1 every 8 instead of samples 0 and
>>>4. I think - shooting from the hip (and probably missing).
>>>--
>>>% Randy Yates % "Maybe one day I'll feel her cold
>
> embrace,
>
>>Hi Randy,
>>
>> Ah, here we go with our ever-present symantics
>>problems. When David said "... one of the aliased images
>>ends up appearing in the baseband",
>>I ASSUMED he meant a signal image ends up centered at zero Hz.
>>
>>Next I thought, "Yep, if a narrowband complex signal
>>(a signal with only positive freq components)
>>is centered at Fs/3, then I can decimate that signal
>>by 3. The resulting decimated sequence's spectrum will
>>be centered at zero Hz."
>>
>>That way, we've performed down-conversion with no
>>multiplication. A fairly neat trick.
>>
>>Then I thought, "If we have a narrowband real signal
>>centered at Fs/3, what happens when I decimate that signal
>>by 3?"
>>
>>I believe the answer is that the signal's
>>positive freq components get shifted to be centered at
>>zero Hz, and its negative freq components also get
>>shifted to be centered at zero Hz. Then I was
>>wondering, off the top of my head, under what conditions
>>will that decimation of a real signal by 3 give me a
>>useable (no alising errors) signal whose spectrum is
>>centered at zero Hz.
>
>
> I'm not very sure of my answer but I think the condition where you would get
> a useable signal centered at zero Hz is when the real signal has a symmetric
> spectrum around it's carrier (fs/3)
>
>
>
>>Am ashamed to say but I don't have a solid answer,
>>in which I'm confident, just by thinking about
>>this.
>>
>>I sure wish I knew more about DSP.
>
>
> Don't we all...but I think you say such things to make the rest of us feel
> small.
>
> Cheers
> Bhaskar
>
>
>>See Ya' Randy,
>>[-Rick-]
>>
>
>
>
Hi Guys,
I wasn't able to look able to find the source for this that I was
thinking of. I was able to find adescription of the technique in
Crochiere and Rabiner's book "Multirate Digital Signal Processing".
There is also a similar section in Whalen's Book "Detection of Signals
in Noise"
First, by related I meant in terms of computational savings. The
technique I mentioned doesn't give the full I/Q samples - the signal
still stays real (if it started that way). Essentially the left edge of
the +ve freq components are moved down close to the right side of zero,
and the right edge of the -ve freq components are moved down close to
the left side of 0. Moving them close to 0 prevents them from overlaping
and causing corruption.
Compared to full I/Q, the sample rate is ~ twice, but the samples are
still real because the complex conjugate symmetry is still preserved. I
hope that helps clear things up. I also apologize for not including any
rigourous mathematics - I hate putting math into plain text formats such
as this.
If more detail is required then let me know and I will put it in. For
those looking for a reference, in the previously mentioned C&R book see
section 2.4.2, pg 43, "Integer Band Decimation and Interpolation"
Copyright 1983.
I'm glad to see guys like Randy, Rick and Bhaskar reading my posts :) I
know I'm in good company!
All the best.
Cheers,
David
Reply by Bhaskar Thiagarajan●July 7, 20052005-07-07
"Rick Lyons" <R.Lyons@_BOGUS_ieee.org> wrote in message
news:42cd109b.834470500@news.sf.sbcglobal.net...
> On Wed, 06 Jul 2005 21:15:57 GMT, Randy Yates <yates@ieee.org> wrote:
>
> >R.Lyons@_BOGUS_ieee.org (Rick Lyons) writes:
> >
> >> On Mon, 04 Jul 2005 14:02:20 -0400, David Kirkland <spam@netscape.net>
> >> wrote:
> >>
> >> (snipped)
> >>>>
> >>>
> >>>A related technique - If your sampling frequency and decimation factor
> >>>are chosen appropriately you avoid the multiplication / frequency
shift
> >>>and just filter and decimate. Essentially one of the aliased images
ends
> >>>up appearing in the baseband.
> >>>
> >>>Cheers,
> >>>David
> >>
> >> Hi David,
> >>
> >> You make a really good point here.
> >> I can see that your method always works fine
> >> if the time sequence is complex, but I'm wondering
> >> under what conditions will it work for real-valued
> >> time samples.
> >>
> >> Humm, ... I'll have to model this sometime.
> >>
> >> See Ya',
> >> [-Rick-]
> >
> >Hey Rick,
> >
> >I think David means that you start out with a real sequence, then
> >when you "decimate," one sample becomes real and one imaginary.
> >
> >I think I see the technique - the trick (in addition to carefully
> >choosing your sampling frequencies and bandwidths) is to downsample
> >by four by keeping samples 0 and 1 every 8 instead of samples 0 and
> >4. I think - shooting from the hip (and probably missing).
> >--
> >% Randy Yates % "Maybe one day I'll feel her cold
embrace,
>
> Hi Randy,
>
> Ah, here we go with our ever-present symantics
> problems. When David said "... one of the aliased images
> ends up appearing in the baseband",
> I ASSUMED he meant a signal image ends up centered at zero Hz.
>
> Next I thought, "Yep, if a narrowband complex signal
> (a signal with only positive freq components)
> is centered at Fs/3, then I can decimate that signal
> by 3. The resulting decimated sequence's spectrum will
> be centered at zero Hz."
>
> That way, we've performed down-conversion with no
> multiplication. A fairly neat trick.
>
> Then I thought, "If we have a narrowband real signal
> centered at Fs/3, what happens when I decimate that signal
> by 3?"
>
> I believe the answer is that the signal's
> positive freq components get shifted to be centered at
> zero Hz, and its negative freq components also get
> shifted to be centered at zero Hz. Then I was
> wondering, off the top of my head, under what conditions
> will that decimation of a real signal by 3 give me a
> useable (no alising errors) signal whose spectrum is
> centered at zero Hz.
I'm not very sure of my answer but I think the condition where you would get
a useable signal centered at zero Hz is when the real signal has a symmetric
spectrum around it's carrier (fs/3)
> Am ashamed to say but I don't have a solid answer,
> in which I'm confident, just by thinking about
> this.
>
> I sure wish I knew more about DSP.
Don't we all...but I think you say such things to make the rest of us feel
small.
Cheers
Bhaskar
>
> See Ya' Randy,
> [-Rick-]
>
Reply by Rick Lyons●July 7, 20052005-07-07
On Wed, 06 Jul 2005 21:15:57 GMT, Randy Yates <yates@ieee.org> wrote:
>R.Lyons@_BOGUS_ieee.org (Rick Lyons) writes:
>
>> On Mon, 04 Jul 2005 14:02:20 -0400, David Kirkland <spam@netscape.net>
>> wrote:
>>
>> (snipped)
>>>>
>>>
>>>A related technique - If your sampling frequency and decimation factor
>>>are chosen appropriately you avoid the multiplication / frequency shift
>>>and just filter and decimate. Essentially one of the aliased images ends
>>>up appearing in the baseband.
>>>
>>>Cheers,
>>>David
>>
>> Hi David,
>>
>> You make a really good point here.
>> I can see that your method always works fine
>> if the time sequence is complex, but I'm wondering
>> under what conditions will it work for real-valued
>> time samples.
>>
>> Humm, ... I'll have to model this sometime.
>>
>> See Ya',
>> [-Rick-]
>
>Hey Rick,
>
>I think David means that you start out with a real sequence, then
>when you "decimate," one sample becomes real and one imaginary.
>
>I think I see the technique - the trick (in addition to carefully
>choosing your sampling frequencies and bandwidths) is to downsample
>by four by keeping samples 0 and 1 every 8 instead of samples 0 and
>4. I think - shooting from the hip (and probably missing).
>--
>% Randy Yates % "Maybe one day I'll feel her cold embrace,
Hi Randy,
Ah, here we go with our ever-present symantics
problems. When David said "... one of the aliased images
ends up appearing in the baseband",
I ASSUMED he meant a signal image ends up centered at zero Hz.
Next I thought, "Yep, if a narrowband complex signal
(a signal with only positive freq components)
is centered at Fs/3, then I can decimate that signal
by 3. The resulting decimated sequence's spectrum will
be centered at zero Hz."
That way, we've performed down-conversion with no
multiplication. A fairly neat trick.
Then I thought, "If we have a narrowband real signal
centered at Fs/3, what happens when I decimate that signal
by 3?"
I believe the answer is that the signal's
positive freq components get shifted to be centered at
zero Hz, and its negative freq components also get
shifted to be centered at zero Hz. Then I was
wondering, off the top of my head, under what conditions
will that decimation of a real signal by 3 give me a
useable (no alising errors) signal whose spectrum is
centered at zero Hz.
Am ashamed to say but I don't have a solid answer,
in which I'm confident, just by thinking about
this.
I sure wish I knew more about DSP.
See Ya' Randy,
[-Rick-]
Reply by Randy Yates●July 6, 20052005-07-06
R.Lyons@_BOGUS_ieee.org (Rick Lyons) writes:
> On Mon, 04 Jul 2005 14:02:20 -0400, David Kirkland <spam@netscape.net>
> wrote:
>
> (snipped)
>>>
>>
>>A related technique - If your sampling frequency and decimation factor
>>are chosen appropriately you avoid the multiplication / frequency shift
>>and just filter and decimate. Essentially one of the aliased images ends
>>up appearing in the baseband.
>>
>>Cheers,
>>David
>
> Hi David,
>
> You make a really good point here.
> I can see that your method always works fine
> if the time sequence is complex, but I'm wondering
> under what conditions will it work for real-valued
> time samples.
>
> Humm, ... I'll have to model this sometime.
>
> See Ya',
> [-Rick-]
Hey Rick,
I think David means that you start out with a real sequence, then
when you "decimate," one sample becomes real and one imaginary.
I think I see the technique - the trick (in addition to carefully
choosing your sampling frequencies and bandwidths) is to downsample
by four by keeping samples 0 and 1 every 8 instead of samples 0 and
4. I think - shooting from the hip (and probably missing).
--
% Randy Yates % "Maybe one day I'll feel her cold embrace,
%% Fuquay-Varina, NC % and kiss her interface,
%%% 919-577-9882 % til then, I'll leave her alone."
%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr
Reply by Rick Lyons●July 6, 20052005-07-06
On Mon, 04 Jul 2005 14:02:20 -0400, David Kirkland <spam@netscape.net>
wrote:
(snipped)
>>
>
>A related technique - If your sampling frequency and decimation factor
>are chosen appropriately you avoid the multiplication / frequency shift
>and just filter and decimate. Essentially one of the aliased images ends
>up appearing in the baseband.
>
>Cheers,
>David
Hi David,
You make a really good point here.
I can see that your method always works fine
if the time sequence is complex, but I'm wondering
under what conditions will it work for real-valued
time samples.
Humm, ... I'll have to model this sometime.
See Ya',
[-Rick-]
Reply by EfiimoFunk●July 5, 20052005-07-05
Thanks for all your help guys. For those of you who wish to take a closer
look at exactly what I was talking about check out a paper called "Digital
I/Q Demodulator" by C. Ziomek and P Corredoura which can be found on IEEE
Xplore. It gives a pretty gove overview of the technique as well as some
good examples. Of course it just glances over what we were talking about
here. The best method I have found to demonstrate this method is to input
a DC "1" multiplied by the sine and cosine and added to give you your
outgoing signal. If you sample this at 4 times the frequency of the
carriers then you get exactly what Tim has previously shown. Or you get
back a DC "1" signal. It is a bit harder to show that it works with sine
input because of the oversampling that is created. Thanks again for all
your help. I now have a new love for this website.
--Ryan
--------------------------
SPAWAR
>EfiimoFunk wrote:
>>>>The quadrature demodulator drops out:
>>>>
>>>>For the I channel multiply by
>>>>
>>>>1, 0, -1, 0, 1, 0, -1, ...
>>>>
>>>>For the Q channel multiply by
>>>>
>>>>0, 1, 0, -1, 0, 1, 0, ...
>>
>> Tim,
>> I understand the +1/-1 after the multiplexing of the input samples
but
>> I am trying to prove that it works (to my boss) and he wants to see it
as
>> a sin and cosine wave added/subtracted and then sampled to give us
back
>> the correct signal. My problem is that when I do this I get the sine
wave
>> multiplied by one and the cosine wave multiplied by -1 (instead of the
>> every other sample type). Any idea on how to visually construct a
signal
>> that will show how this process is fundamentally working. It is easy
>> enough to visuallize using a real/imag plot and samples in the four
needed
>> places but this is not extremely intuitive for a non-DSP person. I
would
>> like to be able to show a signal and show how sampling it at the
correct
>> frequency yields the I and Q components. Thanks a bunch for all your
guys
>> help. It is great they have a site like this around to help all of us
out.
>>
>>
>> --Ryan
>>
>>
>>
>>
>> This message was sent using the Comp.DSP web interface on
>> www.DSPRelated.com
>
>Sample a sine wave at a rate four times its frequency, taking care that
>half the sample instants fall on zero crossings. You get 0, +1, 0, -1,
>repeat. Do the same with a cosine. You get +1, 0, -1, 0, repeat. Sp by
>multiplying by those pulse trains, you are multiplying by sampled sine
>and cosine waveforms.
>
>Jerry
>--
>Engineering is the art of making what you want from things you can get.
>�����������������������������������������������������������������������
>
This message was sent using the Comp.DSP web interface on
www.DSPRelated.com
Reply by Jerry Avins●July 5, 20052005-07-05
EfiimoFunk wrote:
>>>The quadrature demodulator drops out:
>>>
>>>For the I channel multiply by
>>>
>>>1, 0, -1, 0, 1, 0, -1, ...
>>>
>>>For the Q channel multiply by
>>>
>>>0, 1, 0, -1, 0, 1, 0, ...
>
> Tim,
> I understand the +1/-1 after the multiplexing of the input samples but
> I am trying to prove that it works (to my boss) and he wants to see it as
> a sin and cosine wave added/subtracted and then sampled to give us back
> the correct signal. My problem is that when I do this I get the sine wave
> multiplied by one and the cosine wave multiplied by -1 (instead of the
> every other sample type). Any idea on how to visually construct a signal
> that will show how this process is fundamentally working. It is easy
> enough to visuallize using a real/imag plot and samples in the four needed
> places but this is not extremely intuitive for a non-DSP person. I would
> like to be able to show a signal and show how sampling it at the correct
> frequency yields the I and Q components. Thanks a bunch for all your guys
> help. It is great they have a site like this around to help all of us out.
>
>
> --Ryan
>
>
>
>
> This message was sent using the Comp.DSP web interface on
> www.DSPRelated.com
Sample a sine wave at a rate four times its frequency, taking care that
half the sample instants fall on zero crossings. You get 0, +1, 0, -1,
repeat. Do the same with a cosine. You get +1, 0, -1, 0, repeat. Sp by
multiplying by those pulse trains, you are multiplying by sampled sine
and cosine waveforms.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Tim Wescott●July 5, 20052005-07-05
Randy Yates wrote:
> Tim Wescott <tim@seemywebsite.com> writes:
>
>>[...]
>>The quadrature demodulator drops out:
>>
>>For the I channel multiply by
>>
>>1, 0, -1, 0, 1, 0, -1, ...
>>
>>For the Q channel multiply by
>>
>>0, 1, 0, -1, 0, 1, 0, ...
>
>
> So you mean that _if_ the original signal were sampled at
> the carrier frequency, and _then_ the signal was oversampled
> by four and the said mixing performed, and _then_ the result
> was decimated (including filtering) back down to the original
> sample rate, you'd have a quadrature demodulator? Yes, I
> agree with that, and perhaps this is what the OP meant, but
> if he did he was quite terse.
I was taking the term "IQ Demod" in the sense used by the semiconductor
companies when they sell quadrature demodulators which go straight from
RF to baseband.
--
-------------------------------------------
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com