Rick's 3rd edition is out

On Nov 18, 5:22&#4294967295;pm, rickman <gnu...@gmail.com> wrote:

> Personally, I use this term as the max bandwidth that can be
> represented by a given sample rate, in other words Fs/2. &#4294967295;

Everybody seems to forget that a signal extending from DC to Fs/2 also
extends from DC to -Fs/2, so the bandwidth is actually Fs.  So Fs can
unambiguously represent a bandwidth incrementally less than Fs.

> But then I
> also use it as the minimum sample rate you need to cover a given
> bandwidth signal.

This is actually the same as your first case.

Greg

rickman wrote:

>
>
> Personally, I use this term as the max bandwidth that can be
> represented by a given sample rate, in other words Fs/2.

Wouldn't you name that the "Nyquist bandwidth"? The Nyquist frequency would be
the maximum frequency that can be represented by a given sample rate, in other
words Fs/2.

-jim

On Nov 18, 7:47&#4294967295;pm, Greg Berchin <gjberc...@charter.net> wrote:
> On Nov 18, 5:22&#4294967295;pm, rickman <gnu...@gmail.com> wrote:
>
> > Personally, I use this term as the max bandwidth that can be
> > represented by a given sample rate, in other words Fs/2. &#4294967295;
>
> Everybody seems to forget that a signal extending from DC to Fs/2 also
> extends from DC to -Fs/2, so the bandwidth is actually Fs. &#4294967295;So Fs can
> unambiguously represent a bandwidth incrementally less than Fs.

That is only a way of interpreting the math... there is a reason why
they call them "real" and "imaginary" numbers.  Negative frequency???
Think about what that means in the physical world...  :^)

Actually, there is a discrepancy comparing imaginary number samples
with real number samples.  First only real data can be generated by
sampling a physical signal (or reconstructing it), one data sample
per...  By the time you have complex data you have twice as much data
per sample.  So in a sense with complex numbers you can represent the
signal with half the sample rate, but twice the amount of data per.
In reality, it is just a way of juggling the numbers.


> > But then I
> > also use it as the minimum sample rate you need to cover a given
> > bandwidth signal.
>
> This is actually the same as your first case.

Yes, it is.

Rick (not Lyons)

On Nov 18, 7:08&#4294967295;pm, jim <"sjedgingN0Sp"@m...@mwt.net> wrote:

> rickman wrote:
> Wouldn't you name that the "Nyquist bandwidth"? The Nyquist frequency would be
> the maximum frequency that can be represented by a given sample rate, in other
> words Fs/2.

No, Fs can unambiguously represent an analytic signal (no negative
frequency content) extending from DC to incrementally less than Fs.

Greg

On Nov 18, 7:08=A0pm, jim <"sjedgingN0Sp"@m...@mwt.net> wrote:

> rickman wrote:
> Wouldn't you name that the "Nyquist bandwidth"? The Nyquist frequency wou=
ld be
> the maximum frequency that can be represented by a given sample rate, in =
other
> words Fs/2.

No, Fs can unambiguously represent an analytic signal (no negative
frequency content) extending from DC to incrementally less than Fs.

Greg

On Nov 18, 7:15&#4294967295;pm, rickman <gnu...@gmail.com> wrote:

> That is only a way of interpreting the math... there is a reason why
> they call them "real" and "imaginary" numbers. &#4294967295;Negative frequency???
> Think about what that means in the physical world... &#4294967295;:^)

It is mathematically identical to a signal amplitude-modulated by DC.
Move the carrier frequency away from DC, and the mathematics do not
change.

Greg

Greg Berchin <gjberchin@charter.net> wrote:
> On Nov 18, 5:22&#4294967295;pm, rickman <gnu...@gmail.com> wrote:
 
>> Personally, I use this term as the max bandwidth that can be
>> represented by a given sample rate, in other words Fs/2. &#4294967295;
 
> Everybody seems to forget that a signal extending from DC to Fs/2 also
> extends from DC to -Fs/2, so the bandwidth is actually Fs.  So Fs can
> unambiguously represent a bandwidth incrementally less than Fs.

OK, but how about for the non-baseband case?

Say the signal is from 88.2MHz to 88.4MHz, do you also include
the -88.4MHz to -88.2MHz part?

Even more, how about AM-SSB signals?  

With AM-DSB, you can consider the negative frequencies as the result
of downconverting the lower sideband, but for SSB there is only
one sideband.  When you convert to baseband, are there still positive
and negative frequencies?  (Assume synchronous demodulation, if
that matters.)

-- glen

On Nov 18, 8:01&#4294967295;pm, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote:

> OK, but how about for the non-baseband case?
>
> Say the signal is from 88.2MHz to 88.4MHz, do you also include
> the -88.4MHz to -88.2MHz part?

No.  Baseband is a degenerate case where the positive and negative
images overlap.

The somewhat difficult case is the situation in which the modulation
frequency is not greater than the (single-sided) bandwidth of the
signal.  In that case the positive and negative images overlap, but
not perfectly.

> Even more, how about AM-SSB signals? &#4294967295;

Same as the analytic case I mentioned earlier.  Or you can take it
completely down to baseband, in which case it is a complex signal
extending from -B to +B.  Whatever you do to it, the sampling
frequency required to sample it unambiguously does not change.

Greg

On Nov 18, 8:23&#4294967295;pm, Greg Berchin <gjberc...@charter.net> wrote:
> On Nov 18, 7:15&#4294967295;pm, rickman <gnu...@gmail.com> wrote:
>
> > That is only a way of interpreting the math... there is a reason why
> > they call them "real" and "imaginary" numbers. &#4294967295;Negative frequency???
> > Think about what that means in the physical world... &#4294967295;:^)
>
> It is mathematically identical to a signal amplitude-modulated by DC.
> Move the carrier frequency away from DC, and the mathematics do not
> change.
>
> Greg

So?

On Nov 18, 8:21&#4294967295;pm, Greg Berchin <gjberc...@charter.net> wrote:
> On Nov 18, 7:08&#4294967295;pm, jim <"sjedgingN0Sp"@m...@mwt.net> wrote:
>
> > rickman wrote:
> > Wouldn't you name that the "Nyquist bandwidth"? The Nyquist frequency would be
> > the maximum frequency that can be represented by a given sample rate, in other
> > words Fs/2.
>
> No, Fs can unambiguously represent an analytic signal (no negative
> frequency content) extending from DC to incrementally less than Fs.
>
> Greg

I'm not sure where you are getting that.  It is correct if you are
using complex numbers, but if you are sampling a real signal there is
no imaginary part, so the only signal is real and no negative
frequencies.  But a sample rate of Fs can't represent a real signal
with a wider bandwidth than Fs/2.  Try it, you will see that all
frequencies outside of 0 to Fs/2 get aliased into that frequency
range.

The only way to sample a real signal and end up with complex numbers
is to perform a complex operation to convert the signal.  The real
content can be mixed down to baseband centered at half the bandwidth
or centered at 0 Hz.  If you center it at 0 Hz I have seen the complex
stream reduced so that Fs is equal to the bandwidth and all info
preserved.  The same chip can output the same signal centered at BW/2
and Fs = 2*BW as a real sequence.  The data rate in each case is the
same.

Are we talking about the same thing and just not understanding each
other?

Rick