pulses of duration less than carrier cycle

Hello Forum,

given two carrier signals of different frequencies w1 and w2 with w1>w2.
Is it possible to achieve the same data rate with both carriers or does the
higher frequency carrier w1 allow for higher data rates?
Why?

From the analog perspective, I know that if a message signal has bandwidth
Delta_f<<w1 and Delta_f<<w2, there is no problem with using either carrier
signal (just a choice dictated by application and spectrum
availability).....
But what if Delta_f<<w1 but Delta_f>w2? What type of problems do we run
into?

Can a pulse contain one or a fraction of the carrier cycle? Sure, I think,
it physically possible. But does a sequence of pulses where each pulse
duration is less than carrier cycle duration makes sense from the sending a
message point of view?


thanks
fisico32

Hi,

your message spectrum is convolved with the carrier. A real-valued carrier
has lines at -fc and fc in its spectrum. So the negative frequencies will
be a mirror image of the positive side. In other words, with a real-valued
carrier, you'll get aliasing if your modulated message extends below 0 Hz.
With a complex-valued carrier (for example in DSP processing), this will
not be a problem.

One way to look at the carrier is simply as a tool to shift the message
signal to another frequency (with a single spectral line and its negative
frequency mirror image).
BTW: Conceptually, spreading / scrambling in CDMA aren't that different
from a carrier - they are multiplied with the signal - but I can't remember
anybody ever calling them "carrier".

Thanks you for your message.
so, say the carrier is c(t)=sin(w_c *t)
and we want to send a high data rate signal. Is there a limit of how many
bits/s we can imposed by the carrier frequency w_c?

I understand that multiplication in time domain means convolution in
frequency domain: here we are multiplying c(t) by a periodic squared wave
(the train of zeros and ones). 

The FT of a peridic squared wave is the dicrete sinc function. The period
is T and pulse width 2a.The width 2a of the square peak can be any fraction
of the total period T.
The FT of c(t) is simply two deltas located a +w_c and -w_c.

So, how does the frequency of w_c represent a problem?


thanks!

>Hi,
>
>your message spectrum is convolved with the carrier. A real-valued
carrier
>has lines at -fc and fc in its spectrum. So the negative frequencies will
>be a mirror image of the positive side. In other words, with a
real-valued
>carrier, you'll get aliasing if your modulated message extends below 0
Hz.
>With a complex-valued carrier (for example in DSP processing), this will
>not be a problem.
>
>One way to look at the carrier is simply as a tool to shift the message
>signal to another frequency (with a single spectral line and its negative
>frequency mirror image).
>BTW: Conceptually, spreading / scrambling in CDMA aren't that different
>from a carrier - they are multiplied with the signal - but I can't
remember
>anybody ever calling them "carrier".
>
>

not if I design an asymmetric message spectrum.
Say, I have a carrier at 1 kHz and use quadrature modulation with a signal
that has only an upper sideband, with arbitrary bandwidth.

try to modulate your sinc-spectrum to a very low frequency carrier and see
what happens (earlier mail).

One practical reason why carriers are so popular in RF engineering is that
it is much easier to deal with a bandpass signal than with a baseband
signal of the same bandwidth that extends to DC. 

Hi,

On Saturday, October 1, 2011 11:36:45 PM UTC+5:30, mnentwig wrote:
> not if I design an asymmetric message spectrum.
> Say, I have a carrier at 1 kHz and use quadrature modulation with a signa=
l
> that has only an upper sideband, with arbitrary bandwidth.
>
> try to modulate your sinc-spectrum to a very low frequency carrier and se=
e
> what happens (earlier mail).
>=20
> One practical reason why carriers are so popular in RF engineering is tha=
t
> it is much easier to deal with a bandpass signal than with a baseband
> signal of the same bandwidth that extends to DC.

Theoretically, if the message spectrum is symmetric then the carrier freque=
ncy should be greater than B/2 (where B =3D bandwidth of the message signal=
 that is modulating the carrier). The square wave example quoted above is n=
ot very good as the theoretical bandwidth of such a signal is infinite, but=
 practically it can be limited to some excess %ge of B by using pulse shapi=
ng

I have not used asymetric message spectrum design, but if this were to be u=
sed then any data rate can be transmitted on say a carrier frequency of 1 H=
z. There should be no theoretical issues with data symbol modulating only p=
art of the carrier pulse.

It is not clear if the use of asymetric message spectrum causes some practi=
cal difficulties in system design. I have also not come across these design=
s till now.=20

Thanks,
Sachin 

...snip
> I have not used asymetric message spectrum design, but if this were to be used then any data rate can be transmitted on say a carrier frequency of 1 Hz. There should be no theoretical issues with data symbol modulating only part of the carrier pulse.
>
> It is not clear if the use of asymetric message spectrum causes some practical difficulties in system design. I have also not come across these designs till now.
>
> Thanks,
> Sachin

in the USA, ATSC TV which uses 8VSB modulation is an example of
asymmetric spectrum.

Mark

On 10/1/2011 6:37 AM, fisico32 wrote:
> Hello Forum,
>
> given two carrier signals of different frequencies w1 and w2 with w1>w2.
> Is it possible to achieve the same data rate with both carriers or does the
> higher frequency carrier w1 allow for higher data rates?
> Why?

A decent answer to this would be something like:
If the receive bandwidths are such that the SNR is the same for each 
modulated carrier then the data rate can be the same.

>
>  From the analog perspective, I know that if a message signal has bandwidth
> Delta_f<<w1 and Delta_f<<w2, there is no problem with using either carrier
> signal (just a choice dictated by application and spectrum
> availability).....
> But what if Delta_f<<w1 but Delta_f>w2? What type of problems do we run
> into?

Assuming amplitude modulation then if Delta_f > w2 there will be folding 
of frequencies around zero in the region
-[Delta_f - w2] to +{Delta_f-w2]
So, the original modulating signal will be distored.

Also, this form of modulation has a DC component which may be hard to 
get to propagate depending on the medium.

Also, this form of modulation leaves no opportunity for bandpass 
filtering and thus no SNR improvement with such methods.

>
> Can a pulse contain one or a fraction of the carrier cycle? Sure, I think,
> it physically possible. But does a sequence of pulses where each pulse
> duration is less than carrier cycle duration makes sense from the sending a
> message point of view?
>

No.  Define "carrier" in this case.
Simply compute the Fourier Transform of the pulse.  Does it necessarily 
peak up at some w1 or w2? Not likely.

But one can conjure up a "DC" signalling system made up of pure pulses 
like PAM and then the idea of a carrier has no meaning.  Is that what 
you have in mind?  Sounds like it.
>

I'm sure that someone can come up with a contorted view of how this or 
that can be done but what would be the point in view of the questions asked?

Fred

Here I show my ignorance: 

based on my understanding, QAM modulation involves a carrier (sinusoidal)
signal and we change (modulate) both the amplitude and phase at the same
time to encode more bits per second....

Wikipedia defines quadrature modulation as: 

s(t)=I(t)cos(wt)+ Q(t)sin(t).

So we have two identical carrier waves that are out of phase with each
other by 90° (called quadrature carriers or quadrature components). Each
carrier is amplitude modulated by a different function I(t) and Q(t).
 The two modulated waves are summed, and the resulting waveform is a
combination of both phase modulation (PM) and amplitude modulation.

Why not simply modulating one signal carrier both in phase and amplitude: 

I(t)cos[wt+ theta(t)]?

What do we really gain from considering two carrier waves? It seems that
great advantages show up at the demodulating end where we can easily
extract the two functions I(t) and Q(t). But again, I am missing the
point.
What do we do with the functions I(t) and Q(t)?

Also, where is the "complex" stuff in this case?

thanks
fisico32

On Oct 2, 8:47=A0am, "fisico32" <kavanguj@n_o_s_p_a_m.gmail.com> wrote:
> ...
> based on my understanding, QAM modulation involves a carrier (sinusoidal)
> signal and we change (modulate) both the amplitude and phase at the same
> time to encode more bits per second....

That's true, but not a very useful description in practice.

>
> Wikipedia defines quadrature modulation as:
>
> s(t)=3DI(t)cos(wt)+ Q(t)sin(t).
>
> ...
> Why not simply modulating one signal carrier both in phase and amplitude:
>
> I(t)cos[wt+ theta(t)]?
>
> What do we really gain from considering two carrier waves? It seems that
> great advantages show up at the demodulating end where we can easily
> extract the two functions I(t) and Q(t). But again, I am missing the
> point.

Those great advantages are enough for many people. The advantages also
apply at the modulating end.

> What do we do with the functions I(t) and Q(t)?

Anything you could do with I(t) and theta(t), just more conveniently.

>
> Also, where is the "complex" stuff in this case?

The "complex" stuff just means having two components you can tell
apart and apply certain rules to. You can call them I() and Q() or you
could leave one term unlabeled and label the other with "j" or "i" or
you could use an ordered pair (x,y) as long as you apply the same
rules for operations.

Dale B. Dalrymple

fisico32 wrote:


> Wikipedia defines quadrature modulation as: 
> 
> s(t)=I(t)cos(wt)+ Q(t)sin(t).

Cartesian coordinates.

> Why not simply modulating one signal carrier both in phase and amplitude: 
> 
> I(t)cos[wt+ theta(t)]?

Polar coordinates.

> What do we really gain from considering two carrier waves?

Linearity.

> It seems that
> great advantages show up at the demodulating end where we can easily
> extract the two functions I(t) and Q(t). But again, I am missing the
> point.

Now try to define a filter which works with a signal in polar coordinates.

> What do we do with the functions I(t) and Q(t)? 
> Also, where is the "complex" stuff in this case?

Idiot.