Hi, I have read the chapter on "Quadrature Sampling" from Rick Lyons book. The point where it is said that the quadrature samplers can work at half the Nyquist rate (Fs/2) seems a little confusing to me. In SSB or VSB signals, where the spectrum when centred around zero after downconversion is not symmetric around zero Hz, this looks obvious. But for double sideband spectrum (say AM) where the spectrum is symmetric around zero Hz, I do not see how the quadrature samplers can work at rate half that of any other normal samplers. Am I missing something ?? If you can point to some examples it will really help Regards, Prateek

# Quadrature Sampling

Started by ●March 19, 2005

Reply by ●March 19, 20052005-03-19

PMD wrote:> Hi, > > I have read the chapter on "Quadrature Sampling" from Rick Lyons book. > The point where it is said that the quadrature samplers can work at > half the Nyquist rate (Fs/2) seems a little confusing to me. > > In SSB or VSB signals, where the spectrum when centred around zero > after downconversion is not symmetric around zero Hz, this looks > obvious. But for double sideband spectrum (say AM) where the spectrum > is symmetric around zero Hz, I do not see how the quadrature samplers > can work at rate half that of any other normal samplers. Am I missing > something ?? If you can point to some examples it will really helpA quadrature sample is a complex number. As such, it contains twice as much information as the real samples you're accustomed to thinking about. Since each complex sample counts for two real samples, you need only half as many of them. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������

Reply by ●March 19, 20052005-03-19

Hi, Thanks .... actually I was having trouble interpreting the complex samples and how phase information can be extracted out of them. I read some previous posts on the stuff and also read on "Hilbert transforms". I realized that analytic signal's complex samples (having single sided fourier transforms) give phase and magnitude information. Am I correct in my understanding that 1=2E Quadrature sampling and hilbert transforms are two different ways of achieving the same thing. I/Q sampling is easier to implement. 2=2E I/Q sampling and hilbert tranform give the same analytic representation for any signals. Regards, Prateek Jerry Avins wrote:> PMD wrote: > > Hi, > > > > I have read the chapter on "Quadrature Sampling" from Rick Lyonsbook.> > The point where it is said that the quadrature samplers can work at > > half the Nyquist rate (Fs/2) seems a little confusing to me. > > > > In SSB or VSB signals, where the spectrum when centred around zero > > after downconversion is not symmetric around zero Hz, this looks > > obvious. But for double sideband spectrum (say AM) where thespectrum> > is symmetric around zero Hz, I do not see how the quadraturesamplers> > can work at rate half that of any other normal samplers. Am Imissing> > something ?? If you can point to some examples it will really help > > A quadrature sample is a complex number. As such, it contains twiceas> much information as the real samples you're accustomed to thinking > about. Since each complex sample counts for two real samples, youneed> only half as many of them. > > Jerry > -- > Engineering is the art of making what you want from things you canget.>=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF

Reply by ●March 19, 20052005-03-19

Hi Prateek : 1. Quadrature sampling and hilbert transforms are two different ways of achieving the same thing. - I think that you probably can achieve the same thing if your filtering is right so yes. I/Q sampling is easier to implement. - who can say? easier than what? 2. I/Q sampling and hilbert tranform give the same analytic representation for any signals. - I'm not sure what the difference is between this statement and statement 1/ , if they are two ways of doing the same thing then you can arrange for them to give the same analytic representation, no? Best of Luck - Mike

Reply by ●March 20, 20052005-03-20

On 19 Mar 2005 08:44:14 -0800, "PMD" <prateek@iitg.ac.in> wrote:>Hi, > >Thanks .... actually I was having trouble interpreting the complex >samples and how phase information can be extracted out of them. I read >some previous posts on the stuff and also read on "Hilbert transforms". >I realized that analytic signal's complex samples (having single sided >fourier transforms) give phase and magnitude information. > >Am I correct in my understanding that > >1=2E Quadrature sampling and hilbert transforms are two different ways of >achieving the same thing. I/Q sampling is easier to implement. > >2=2E I/Q sampling and hilbert tranform give the same analytic >representation for any signals. > >Regards, > >PrateekHi, To add to the other replies, the goal of that Quad Sampling scheme (also very often called "complex down-conversion") was to obatin a complex sequence of time samples whose spectrum was centered at zero Hz. Another way to achieve the same goal is to apply the analog bandpass signal to an A/D converter. Next, pass the A/D's output through a Hilbert tranformer to obtain the "Q" sequence (the quadrature part) of a complex bandpass signal sequence. The A/D's output samples would then be considered the "real" part of the complex bandpass sequence. Finally that complex bandpass sequence can be multiplied by e^(-j2*pi*Fc*t) to translate its center frequency down to zero Hz. Hope that helps, Good Luck, [-Rick-]