carrier frequency limitations and bandwidth

Hello Forum,

Consider a baseband signal of a certain bandwidth B.
Using analog modulation (either AM, FM or phase modulation), in a single
channel environment(i.e. not worrying about possible interference between
multiple users and channels) can we impress that bandwidth B on carrier of
any frequency f? Does the carrier frequency need to be always much larger
than the bandwidth of the signal it carries (even in a single channel
situation)? Or is there some limitation?

Usually we are in a narrowband situation: B<<f. Would it be ok to have
B>>f?
If not, why not?

Let's think of a  pulse of light of duration T. If the period of the
carrier frequency, which 1/f, is larger than pulse period T, then the pulse
will not even contain a whole cycle of the sinusoid....is that a problem?

thanks
fisico32

fisico32 <marcoscipioni1@n_o_s_p_a_m.gmail.com> wrote:
 
> Consider a baseband signal of a certain bandwidth B.
> Using analog modulation (either AM, FM or phase modulation), in a single
> channel environment(i.e. not worrying about possible interference between
> multiple users and channels) can we impress that bandwidth B on carrier of
> any frequency f? Does the carrier frequency need to be always much larger
> than the bandwidth of the signal it carries (even in a single channel
> situation)? Or is there some limitation?

For AM, the highest frequency, which has to be at least B, should
be lower than the carrier frequency.  Maybe not a lot lower.

For FM, you have to consider both the carrier frequency and
the deviation.   The luminance signal for VHS has bandwidth
plus deviation close to the carrier frequency.

-- glen

On Jun 18, 8:50&#4294967295;pm, "fisico32" <marcoscipioni1@n_o_s_p_a_m.gmail.com>
wrote:
> Hello Forum,
>
> Consider a baseband signal of a certain bandwidth B.
> Using analog modulation (either AM, FM or phase modulation), in a single
> channel environment(i.e. not worrying about possible interference between
> multiple users and channels) can we impress that bandwidth B on carrier of
> any frequency f? Does the carrier frequency need to be always much larger
> than the bandwidth of the signal it carries (even in a single channel
> situation)? Or is there some limitation?

for double-sided AM, f needs to be at least 2B.  for FM, i think there
is something called "Carson's rule" that says what f needs to be.  if
i remember correctly, narrowband FM required the same bandwidth as AM.

>
> Usually we are in a narrowband situation: B<<f. Would it be ok to have
> B>>f?
> If not, why not?
>

aliasing?


> Let's think of a &#4294967295;pulse of light of duration T. If the period of the
> carrier frequency, which 1/f, is larger than pulse period T, then the pulse
> will not even contain a whole cycle of the sinusoid....is that a problem?

it depends on how you define "duration".  if you want a real signal,
for AM,

   x(t) = a(t) * cos(2*pi*f*t)

now, here's the problem, you would have to use only the top sideband
of x(t) to recover a(t), if B < f < 2B.  but it's hopelessly aliased
for 0 < f < B.

or, if you're synched to the cos(2*pi*f*t), are you suggesting to
divide by it?

>
> thanks

i'll send you a bill.

r b-j

robert bristow-johnson <rbj@audioimagination.com> wrote:
(snip0

>> Does the carrier frequency need to be always much larger
>> than the bandwidth of the signal it carries (even in a single channel
>> situation)? Or is there some limitation?
 
> for double-sided AM, f needs to be at least 2B.  for FM, i think there
> is something called "Carson's rule" that says what f needs to be.  if
> i remember correctly, narrowband FM required the same bandwidth as AM.
(snip)
> aliasing?
 
(snip) 
> now, here's the problem, you would have to use only the top sideband
> of x(t) to recover a(t), if B < f < 2B.  but it's hopelessly aliased
> for 0 < f < B.
 
> or, if you're synched to the cos(2*pi*f*t), are you suggesting to
> divide by it?

In other words, a synchronous demodulator?  I believe with the
appropriate demodulator (and appropriate modulator) you can recover
and AM signal at more than 100% modulation.  (That is, when the
amplitude goes negative.)  It seems to me that with a synchronous
demodulator you might also recover for B > carrier.  (If no other
reason, the upper sideband is still there.)

I mentioned the VHS luminance carrier before.  It has to be FM,
as the lower frequency is just about 0Hz.  (That is, completely
uniform picture.)  Magnetic recording doesn't like DC.

-- glen