Quadrature low pass filter question
in [DSP]
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From: maury on 11 May 2010 15:55 On May 11, 4:09 am, Rune Allnor <all...(a)tele.ntnu.no> wrote: > On 10 Mai, 22:11, maury <maury...(a)core.com> wrote: > > > On May 10, 11:24 am, "jacobfenton" > > > <jacob.fenton(a)n_o_s_p_a_m.gmail.com> wrote: > > >............ Is that the only way to do this, > > > What you are getting into is multidimensional (n-dimensional filter) > > MIMO (I and Q channels) signal processing. > > I would agree with your suggestion that one gets into MIMO stuff > if one accepts the quadrature filter as *both* an implementation > of the complex-valued arithmetics of a complex-valued filter, *and* > that the I and Q components are independent. In that case one needs > to handle the cross terms between the 'real' and 'imaginary' > components > to emulate the complex-valued filter, which means one need to get > into some sort of MIMO structure. Or use complex-valued arithmetics. > > But the quadrature filter contains two real-valued sequences that > usually (always?) are not independent, but have been derived as > (emulations for) the real and imaginary components of a Hibert > transform of one real-valued signal. Each of these real-valued > signals must then be processed under the conditions of a real- > valued signals. > > So far so good. > > As I understand it, the fact that the I and Q component are > related through the HT, implicitly takes care of the cross-terms > in the complex-valued arithmetics. Which means that one, simple, > SISO real-valued filter is sufficient to handle the 'complex'- > valued quadrature signal. > > The fact that the I and Q channels are processed individually as > real-valued data, also have some implictaions. Quadrature filters > are actually restricted by Nyquist's limit, Fs > 2B, whereas > complex-valued filters are restricted by the far more forgiving > Fs > B. > > Or have I misunderstood or missed out on something? > > Rune Rune, I was answering the specific question "is there anothe way?". And, as I said in the last line, he just might want to implement two separate filters rather than using the alternative :). Maurice
From: John O'Flaherty on 11 May 2010 18:25 On Tue, 11 May 2010 17:30:30 +0000 (UTC), glen herrmannsfeldt <gah(a)ugcs.caltech.edu> wrote: >Randy Yates <yates(a)ieee.org> wrote: >> Jerry Avins <jya(a)ieee.org> writes: >>> [...] >>> It's the same thing. > >> So, e.g., using complex sampling doesn't allow you to gather >> more bandwidth using today's technology in ADCs than real >> sampling does? > >There are many tricks that could be used to sample faster >than ADC technology allows. You could, for example, use >two ADCs and the appropriate sample and hold such that each >one received every other sample (and correct for any >differences in the two ADCs later). > >Though the system I still remember from many years ago >(likely still used, but with different numbers): > >Sample at high speed but at reduced resolution, such as only >four bits per sample. Convert the result back to analog >with an equivalent speed DAC. Analog subtract from the >original (possibly delayed through sample and hold type >circuitry). Send the analog difference to another ADC, >to get the low bits of the result. This works if the >threshold levels of the first ADC are accurate enough, yet >allows for a much faster conversion. > >Otherwise, it reminds me of stories from the early days of >CD players, using one ADC for both stereo channels, alternating >between the two. The resulting half sample period delay was >said to be audible by some people. That would correspond to a stereo speaker positioning error of 0.15 inches. Maybe they were hearing something else. -- John
From: Jerry Avins on 11 May 2010 18:40 On 5/11/2010 6:25 PM, John O'Flaherty wrote: > On Tue, 11 May 2010 17:30:30 +0000 (UTC), glen herrmannsfeldt > <gah(a)ugcs.caltech.edu> wrote: > >> Randy Yates<yates(a)ieee.org> wrote: >>> Jerry Avins<jya(a)ieee.org> writes: >>>> [...] >>>> It's the same thing. >> >>> So, e.g., using complex sampling doesn't allow you to gather >>> more bandwidth using today's technology in ADCs than real >>> sampling does? >> >> There are many tricks that could be used to sample faster >> than ADC technology allows. You could, for example, use >> two ADCs and the appropriate sample and hold such that each >> one received every other sample (and correct for any >> differences in the two ADCs later). >> >> Though the system I still remember from many years ago >> (likely still used, but with different numbers): >> >> Sample at high speed but at reduced resolution, such as only >> four bits per sample. Convert the result back to analog >> with an equivalent speed DAC. Analog subtract from the >> original (possibly delayed through sample and hold type >> circuitry). Send the analog difference to another ADC, >> to get the low bits of the result. This works if the >> threshold levels of the first ADC are accurate enough, yet >> allows for a much faster conversion. >> >> Otherwise, it reminds me of stories from the early days of >> CD players, using one ADC for both stereo channels, alternating >> between the two. The resulting half sample period delay was >> said to be audible by some people. > > That would correspond to a stereo speaker positioning error of 0.15 > inches. Maybe they were hearing something else. Not even. For speakers 5 feet apart, it would merely rotate the stereo axis 1/400th of a radian, about a degree and a half. Jerry -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." --Barbara Smuts, U. Mich. �����������������������������������������������������������������������
From: Randy Yates on 11 May 2010 21:49 Jerry Avins <jya(a)ieee.org> writes: > On 5/11/2010 12:46 PM, Randy Yates wrote: >> Jerry Avins<jya(a)ieee.org> writes: >>> [...] >>> It's the same thing. >> >> So, e.g., using complex sampling doesn't allow you to gather >> more bandwidth using today's technology in ADCs than real >> sampling does? > > Numbers will clarify what I mean. Sampling I and Q each at 1 KHz > suffices for a (nearly) 1 KHz bandwidth. You should expect no less > from the 2000 samples/second that you are collecting. I understand that, and I agree that the number of "samples" per second is the same in either case. However, there are other metrics besides "samples" per second that make your statement "It's the same thing" inaccurate, e.g., "samples per second per A/D converter". -- Randy Yates % "I met someone who looks alot like you, Digital Signal Labs % she does the things you do, mailto://yates(a)ieee.org % but she is an IBM." http://www.digitalsignallabs.com % 'Yours Truly, 2095', *Time*, ELO
From: Jerry Avins on 11 May 2010 23:12
On 5/11/2010 9:49 PM, Randy Yates wrote: > Jerry Avins<jya(a)ieee.org> writes: > >> On 5/11/2010 12:46 PM, Randy Yates wrote: >>> Jerry Avins<jya(a)ieee.org> writes: >>>> [...] >>>> It's the same thing. >>> >>> So, e.g., using complex sampling doesn't allow you to gather >>> more bandwidth using today's technology in ADCs than real >>> sampling does? >> >> Numbers will clarify what I mean. Sampling I and Q each at 1 KHz >> suffices for a (nearly) 1 KHz bandwidth. You should expect no less >> from the 2000 samples/second that you are collecting. > > I understand that, and I agree that the number of "samples" per second > is the same in either case. However, there are other metrics besides > "samples" per second that make your statement "It's the same thing" > inaccurate, e.g., "samples per second per A/D converter". As long as we both know what we mean and have the same operations in mind, straightening out the semantics os secondary to me. There are even circumstances where one converter suffices, simply using odd numbered samples for one stream and even numbered samples for the other, interpolating zeroes into each stream. That simulates a multiplication by sine in one channel and cosine in the other. Jerry -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." --Barbara Smuts, U. Mich. ����������������������������������������������������������������������� |