Confusion on bandwidth

I am confused by the relation between �data rate�, �frequency� and
�bandwidth�.
Let me explain my confusion with the following cases.
Case 1.  bandwidth is fixed, say �M�. There�re two frequency ranges. One
is from 0-M, the other is from M to 2M. Assume that all other conditions
such as modulation are the same. Who�s data rate is higher? 
Case 2. Assume that the second is from M to M+N where M/2 < N < M , then
who&#4294967295;s data rate is higher?

mathrookie wrote:
> I am confused by the relation between "data rate", "frequency" and
> "bandwidth".
> Let me explain my confusion with the following cases.
> Case 1.  bandwidth is fixed, say "M". There're two frequency ranges. One
> is from 0-M, the other is from M to 2M. Assume that all other conditions
> such as modulation are the same. Who's data rate is higher?

"Bandwidth" is a property of the channel. It is usually determined by
the physics of the problem. Or these days, some political document
stating how much bandwidth any one user is allowed to play with.

"Modulation" is how you encode information into your signal. Different
modulation schemes encode different amounts of information into the
same bandwidth.

"Data rate": The amount of information (bits or bytes per second)
carried by a channel. This number is a function of both bandwidth
and modulation scheme.

So in your example, both channels have the same data rate.

> Case 2. Assume that the second is from M to M+N where M/2 < N < M , then
> who's data rate is higher?

Since M+N < 2M then, according to the arguments above... ?

Rune

mathrookie wrote:

> I am confused by the relation between �data rate�, �frequency� and
> �bandwidth�.

> Let me explain my confusion with the following cases.

> Case 1.  bandwidth is fixed, say �M�. There�re two frequency ranges. One
> is from 0-M, the other is from M to 2M.

There is a factor of two that comes in, in some cases, which comes
from the Fourier description as negative frequencies.  When you
say 0 to M some might say you mean -M to +M.  At baseband the
bandwidth is M, but upconverted it is 2M.

> Assume that all other conditions such as modulation are the same.
 > Who�s data rate is higher?

I would say it depends on the modulation method.  Many modulation
methods are practical today that weren't 20 or 50 years ago.

AM radio, modulated with an audio signal, uses twice the necessary
bandwidth to make demodulation easier.

FM radio takes a 20kHz audio signal and expands it to 200kHz,
among other reasons for better S/N ratio.

AM doesn't make sense at baseband (your 0 to M example),
though possibly if you mean M/2 +/- M/2.

> Case 2. Assume that the second is from M to M+N where M/2 < N < M , then
> who&#4294967295;s data rate is higher?

Filtering is much easier with the carrier much higher than the
bandwidth.  Asking data rate questions without specifying a
modulation method doesn't really make sense.

-- glen

glen herrmannsfeldt wrote:
> mathrookie wrote:
>
> > I am confused by the relation between "data rate", "frequency" and
> > "bandwidth".

"bandwidth" is real-estate on the electromagnetic spectrum.

> FM radio takes a 20kHz audio signal and expands it to 200kHz,
> among other reasons for better S/N ratio.

current FM radio in the North America (87.9 -> 107.9 MHz) takes a 15
kHz bandlimited audio signal and expands it as you say (because FM is
not linear modulation).  FM-stereo has a big monster pilot signal (for
L/R synchronization) at 19 kHz (and the baseband is as high as 53 kHz).
 dunno what it is in Europia or other parts of the world.

r b-j

robert bristow-johnson wrote:
> glen herrmannsfeldt wrote:
>> mathrookie wrote:
>>
>>> I am confused by the relation between "data rate", "frequency" and
>>> "bandwidth".
> 
> "bandwidth" is real-estate on the electromagnetic spectrum.
> 
>> FM radio takes a 20kHz audio signal and expands it to 200kHz,
>> among other reasons for better S/N ratio.
> 
> current FM radio in the North America (87.9 -> 107.9 MHz) takes a 15
> kHz bandlimited audio signal and expands it as you say (because FM is
> not linear modulation).  FM-stereo has a big monster pilot signal (for
> L/R synchronization) at 19 kHz (and the baseband is as high as 53 kHz).
>  dunno what it is in Europia or other parts of the world.

The 19 KHz is doubled to 38 to become the actual pilot. Don't forget the 
SCA channel that's there too. (Sometimes two.)

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

>
>mathrookie wrote:
>> I am confused by the relation between "data rate", "frequency" and
>> "bandwidth".
>> Let me explain my confusion with the following cases.
>> Case 1.  bandwidth is fixed, say "M". There're two frequency ranges.
One
>> is from 0-M, the other is from M to 2M. Assume that all other
conditions
>> such as modulation are the same. Who's data rate is higher?
>
>"Bandwidth" is a property of the channel. It is usually determined by
>the physics of the problem. Or these days, some political document
>stating how much bandwidth any one user is allowed to play with.
>
>"Modulation" is how you encode information into your signal. Different
>modulation schemes encode different amounts of information into the
>same bandwidth.
>
>"Data rate": The amount of information (bits or bytes per second)
>carried by a channel. This number is a function of both bandwidth
>and modulation scheme.
>
>So in your example, both channels have the same data rate.
>
>> Case 2. Assume that the second is from M to M+N where M/2 < N < M ,
then
>> who's data rate is higher?
>
>Since M+N < 2M then, according to the arguments above... ?
>
>Rune
>
>

May I argue like this? According to your definition of "Data rate",
firstly we fix a simple phase-keying as modulation method, one sine wave
represent bit "1" and the sine wave of the opposite phase stands for bit
"0". However, we send the signal in different frequecies, first in  "M"
herz, while secondly in "1" herz. Starting from time 0, in one second, the
first signal can carry theoretically as much as "M" bits. However, the
second can only carry 1 bit. 

robert bristow-johnson wrote:

> glen herrmannsfeldt wrote:
(snip)

>>FM radio takes a 20kHz audio signal and expands it to 200kHz,
>>among other reasons for better S/N ratio.

> current FM radio in the North America (87.9 -> 107.9 MHz) takes a 15
> kHz bandlimited audio signal and expands it as you say (because FM is
> not linear modulation).  FM-stereo has a big monster pilot signal (for
> L/R synchronization) at 19 kHz (and the baseband is as high as 53 kHz).
>  dunno what it is in Europia or other parts of the world.

If I remember it right, mono FM allows up to 20kHz.  Stereo limited
it to 15kHz into the multiplexer.  Mono FM stations are rare these
days, so it probably doesn't matter much.  I thought the pilot was
10% modulation index, so it isn't that big.

The amplitude limits on subcarriers approximately keep the overall
bandwidth the same as for a 20kHz audio signal with no subcarriers.
(Not counting that an FM signal theoretically has sidebands to
infinity.)

-- glen

mathrookie wrote:
> I am confused by the relation between "data rate", "frequency" and
> "bandwidth".
> Let me explain my confusion with the following cases.
> Case 1.  bandwidth is fixed, say "M". There're two frequency ranges. One
> is from 0-M, the other is from M to 2M. Assume that all other conditions
> such as modulation are the same. Who's data rate is higher?
> Case 2. Assume that the second is from M to M+N where M/2 < N < M , then
> who's data rate is higher?

I will try to remove your confusion by defining each term you have
stated above. Also, for the sake of comprehensiveness, I will have to
introduce another term called "symbol rate". I think the introduction
of this term will increase your understanding on these terms and the
relation between them.

Bandwidth of a signal : The band width of any signal is defined as the
range of frequencies where the signal strength is "appreciable". The
exact interpretation of this "appreciable" strength various depending
on the context where this signal is used and the commercial standards
which this signal has to meet.

Bandwidth of a channel: The band width of a channel is defined as the
range of frequencies it can transmit without "apprecialbe" attenuation.
The "appreciable" here holds the same meaning as above.

Symbol: In any digital Communication scheme, data is sent in the form
of symbols. Each symbol may represent one or more data elements ( this
number can also be in fractions). The rate at which these symobols are
sent is called the SYMBOL RATE and the rate at which the resulting data
is sent is called the DATA RATE. Another important factor is the way
the transition is made from one symbol to another. This method of
transiton is called signal shaping or wave shaping. Both the symbol
rate and the signal shape influence the bandwidth of a signal. (gradual
transitions result in low bandwidth and low symbol rate result in low
bandwidth).

Carrier frequency: This is the frequency which is modulated by the
sumbols. The bandwidth of the signal does not depend on this frequency.


I hope this clears your confusion. Please feel free to contact me if
there is any thing you don't understand in the above discussion or if
you feel something is incorrect.

HarishKumar.Ch@gmail.com wrote:

   ...

> I hope this clears your confusion. Please feel free to contact me if
> there is any thing you don't understand in the above discussion or if
> you feel something is incorrect.

I would add to the fine explanation that "bandwidth" is often used 
erroneously to mean information-carrying capacity, and that is the 
source of much confusion. Even though the proverbial "boy on a bicycle" 
transporting a box of memory cards can move information across town as 
quickly as a microwave link, a bicycle is not a high-bandwidth device.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

HarishKumar.Ch@gmail.com wrote:
> mathrookie wrote:
> > I am confused by the relation between "data rate", "frequency" and
> > "bandwidth".
> > Let me explain my confusion with the following cases.
> > Case 1.  bandwidth is fixed, say "M". There're two frequency ranges. One
> > is from 0-M, the other is from M to 2M. Assume that all other conditions
> > such as modulation are the same. Who's data rate is higher?
> > Case 2. Assume that the second is from M to M+N where M/2 < N < M , then
> > who's data rate is higher?
>
> I will try to remove your confusion by defining each term you have
> stated above. Also, for the sake of comprehensiveness, I will have to
> introduce another term called "symbol rate". I think the introduction
> of this term will increase your understanding on these terms and the
> relation between them.
>

> Bandwidth of a signal : The band width of any signal is defined as the
> range of frequencies where the signal strength is "appreciable". The
> exact interpretation of this "appreciable" strength various depending
> on the context where this signal is used and the commercial standards
> which this signal has to meet.

Sometimes this is specifically constrained. The signal bandwidth of
carrier grade voice is 3.4kHz, even though the original microphone will
pick up a far wider bandwidth than this.
The bandwidth of a signal is also sometimes stated as the required
bandwidth for less than 3dB attenuation of the information signal.

Much depends on the specifics of the signal you wish to deal with. It
relates directly to the next item:

>> Bandwidth of a channel: The band width of a channel is defined as the
> range of frequencies it can transmit without "apprecialbe" attenuation.
> The "appreciable" here holds the same meaning as above.
>

The bandwidth of a physical channel is _defined_ (for hardware) as the
range of frequencies it can pass with less than 3dB attenuation. (Half
power point). This can give rise to multiple transmission bands in a
phyical channel. For a proper appreciation of channel characteristics,
S parameters should be used.

> Symbol: In any digital Communication scheme, data is sent in the form
> of symbols. Each symbol may represent one or more data elements ( this
> number can also be in fractions). The rate at which these symobols are
> sent is called the SYMBOL RATE and the rate at which the resulting data
> is sent is called the DATA RATE. Another important factor is the way
> the transition is made from one symbol to another. This method of
> transiton is called signal shaping or wave shaping. Both the symbol
> rate and the signal shape influence the bandwidth of a signal. (gradual
> transitions result in low bandwidth and low symbol rate result in low
> bandwidth).

The symbol rate of a channel is also the baud rate (surely one of the
most abused terms in the history of electronics). Trivia: a 2400 bps
telephone line modem (using 16 QAM) has a baud rate of 600 (600 symbols
/ sec).


>
> Carrier frequency: This is the frequency which is modulated by the
> sumbols. The bandwidth of the signal does not depend on this frequency.


>
>
> I hope this clears your confusion. Please feel free to contact me if
> there is any thing you don't understand in the above discussion or if
> you feel something is incorrect.

Cheers

PeteS