Started by March 19, 2005
```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

```
```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 help

A 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.
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```
```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 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
>
> A 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.
>
=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

```
```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

```
```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,
>
>Prateek

Hi,

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-]

```