# Rick's 3rd edition is out

Started by November 16, 2010
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