Question about Continuous Phase FSK

On Sep 3, 4:04&#4294967295;pm, brent <buleg...@columbus.rr.com> wrote:
> On Sep 3, 3:35&#4294967295;pm, dvsarwate <dvsarw...@gmail.com> wrote:
>
>
>
>
>
> > On Sep 3, 11:23&#4294967295;am, Randy Yates <ya...@ieee.org> wrote:
>
> > > To my way of
> > > thinking, the easiest is this: if we consider an FSK signal is in the
> > > form
>
> > > &#4294967295; x(t) = A*cos(phi(t)),
>
> > > then a _continuous-phase FSK signal requires phi(t) to be continuous.
>
> > More strongly, phi(t) should be a piecewise linear function as well
> > as being continuous. &#4294967295;That is, the graph of phi(t) should be a series
> > of straight-line segments with the segments joining at their
> > endpoints.
>
> > > Most of the time the term "phase" refers to the function theta
> > > in the argument:
>
> > > &#4294967295; cos(w*t + theta).
>
> > In such cases, theta is perhaps better referred to as the phase
> > offset, but it is true that "phase" is very commonly used. &#4294967295;In
> > fact, for FSK perhaps it is best to write the signal as
>
> > cos(w*t + phi(t))
>
> > where w is the nominal or average frequency (sum of Mark and
> > Space frequencies divided by 2) and take phi(t) to be a
> > piecewise linear continuous function where the line segments
> > have positive or negative slopes (of equal magnitude). &#4294967295;If
> > phi(t) increases (or decreases) by pi/2 over a signaling
> > interval, we have MSK; if the change is plus/minus pi, we
> > have Sunde's FSK etc.
>
> > Hope this helps
>
> > --Dilip Sarwate
>
> The modulation is for UAT (aviation system used to broadcast aircraft
> locations and weather info) system that I am looking into. &#4294967295;It is at
> 978 MHz and it has a bit interval of .96 usec and the frequency shifts
> up or down by 312 KHz from 978 depending upon 1 or 0.
>
> As I think about this, the bit interval only has about 1/3 of a cycle
> in it, so while it is called FSK it seems like I need to think of it
> more in terms of phase shift than frequency shift.- Hide quoted text -
>
> - Show quoted text -

if the bit interval is about 1us, and the carrier frequency is about
1GHz, then there are about 1000 cycles of the carrier in each bit
interval..

Mark

On Sep 3, 4:30&#4294967295;pm, Mark <makol...@yahoo.com> wrote:
> On Sep 3, 4:04&#4294967295;pm, brent <buleg...@columbus.rr.com> wrote:
>
>
>
> > On Sep 3, 3:35&#4294967295;pm, dvsarwate <dvsarw...@gmail.com> wrote:
>
> > > On Sep 3, 11:23&#4294967295;am, Randy Yates <ya...@ieee.org> wrote:
>
> > > > To my way of
> > > > thinking, the easiest is this: if we consider an FSK signal is in the
> > > > form
>
> > > > &#4294967295; x(t) = A*cos(phi(t)),
>
> > > > then a _continuous-phase FSK signal requires phi(t) to be continuous.
>
> > > More strongly, phi(t) should be a piecewise linear function as well
> > > as being continuous. &#4294967295;That is, the graph of phi(t) should be a series
> > > of straight-line segments with the segments joining at their
> > > endpoints.
>
> > > > Most of the time the term "phase" refers to the function theta
> > > > in the argument:
>
> > > > &#4294967295; cos(w*t + theta).
>
> > > In such cases, theta is perhaps better referred to as the phase
> > > offset, but it is true that "phase" is very commonly used. &#4294967295;In
> > > fact, for FSK perhaps it is best to write the signal as
>
> > > cos(w*t + phi(t))
>
> > > where w is the nominal or average frequency (sum of Mark and
> > > Space frequencies divided by 2) and take phi(t) to be a
> > > piecewise linear continuous function where the line segments
> > > have positive or negative slopes (of equal magnitude). &#4294967295;If
> > > phi(t) increases (or decreases) by pi/2 over a signaling
> > > interval, we have MSK; if the change is plus/minus pi, we
> > > have Sunde's FSK etc.
>
> > > Hope this helps
>
> > > --Dilip Sarwate
>
> > The modulation is for UAT (aviation system used to broadcast aircraft
> > locations and weather info) system that I am looking into. &#4294967295;It is at
> > 978 MHz and it has a bit interval of .96 usec and the frequency shifts
> > up or down by 312 KHz from 978 depending upon 1 or 0.
>
> > As I think about this, the bit interval only has about 1/3 of a cycle
> > in it, so while it is called FSK it seems like I need to think of it
> > more in terms of phase shift than frequency shift.- Hide quoted text -
>
> > - Show quoted text -
>
> if the bit interval is about 1us, and the carrier frequency is about
> 1GHz, then there are about 1000 cycles of the carrier in each bit
> interval..
>
> Mark

yes, you are correct.

 I was thinking in terms of demodulating it down to video.

On 09/03/2010 01:04 PM, brent wrote:
> On Sep 3, 3:35 pm, dvsarwate<dvsarw...@gmail.com>  wrote:
>> On Sep 3, 11:23 am, Randy Yates<ya...@ieee.org>  wrote:
>>
>>> To my way of
>>> thinking, the easiest is this: if we consider an FSK signal is in the
>>> form
>>
>>>    x(t) = A*cos(phi(t)),
>>
>>> then a _continuous-phase FSK signal requires phi(t) to be continuous.
>>
>> More strongly, phi(t) should be a piecewise linear function as well
>> as being continuous.  That is, the graph of phi(t) should be a series
>> of straight-line segments with the segments joining at their
>> endpoints.
>>
>>> Most of the time the term "phase" refers to the function theta
>>> in the argument:
>>
>>>    cos(w*t + theta).
>>
>> In such cases, theta is perhaps better referred to as the phase
>> offset, but it is true that "phase" is very commonly used.  In
>> fact, for FSK perhaps it is best to write the signal as
>>
>> cos(w*t + phi(t))
>>
>> where w is the nominal or average frequency (sum of Mark and
>> Space frequencies divided by 2) and take phi(t) to be a
>> piecewise linear continuous function where the line segments
>> have positive or negative slopes (of equal magnitude).  If
>> phi(t) increases (or decreases) by pi/2 over a signaling
>> interval, we have MSK; if the change is plus/minus pi, we
>> have Sunde's FSK etc.
>>
>> Hope this helps
>>
>> --Dilip Sarwate
>
> The modulation is for UAT (aviation system used to broadcast aircraft
> locations and weather info) system that I am looking into.  It is at
> 978 MHz and it has a bit interval of .96 usec and the frequency shifts
> up or down by 312 KHz from 978 depending upon 1 or 0.
>
> As I think about this, the bit interval only has about 1/3 of a cycle
> in it, so while it is called FSK it seems like I need to think of it
> more in terms of phase shift than frequency shift.

Well, there's 2/3 of a cycle _difference_ between a mark and a space. 
This is the same ratio as was used for one of the modem schemes -- I 
_think_ it was Bell 206, 1200 baud.

I know what the advantages are for MSK (where the total shift = 1/2 the 
bit frequency); I don't know if there's any advantages to be had from 
the total shift = 2/3, although I do recall that it has an 
autocorrelation function that takes an infinite amount of time to settle 
compared to MSK whose autocorrelation function goes to zero at one bit 
time in either direction of tau = 0.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

Tim Wescott <tim@seemywebsite.com> wrote:
(snip)
 
> Well, there's 2/3 of a cycle _difference_ between a mark and a space. 
> This is the same ratio as was used for one of the modem schemes -- I 
> _think_ it was Bell 206, 1200 baud.

Bell 103, the favorite of many of use from years ago, uses a 200Hz
shift, and commonly worked at 300 baud.  As I remember it, though,
it was said to be good to 600, though I never saw it done.

In any case, that is again 2/3 of a cycle difference.
(1270Hz-1070Hz, or 2225Hz-2025Hz)

Later modems that I knew used PLL ICs, I don't know how they
did it in 1962.

The wikipedia page Audio_frequency-shift_keying  seems to indicate
that a half cycle is required, but I am not convinced.

It seems to me that what is really needed is for the first sideband
at the modulation frequency to be reasonably within the passband of
the transmission medium.  Well, that isn't quite as obvious as it
would be for AM, but it seems to me that the cycle fraction isn't
so obviously the determining factor.
 
> I know what the advantages are for MSK (where the total shift = 1/2 the 
> bit frequency); I don't know if there's any advantages to be had from 
> the total shift = 2/3, although I do recall that it has an 
> autocorrelation function that takes an infinite amount of time to settle 
> compared to MSK whose autocorrelation function goes to zero at one bit 
> time in either direction of tau = 0.

-- glen

On 09/03/2010 02:30 PM, glen herrmannsfeldt wrote:
> Tim Wescott<tim@seemywebsite.com>  wrote:
> (snip)
>
>> Well, there's 2/3 of a cycle _difference_ between a mark and a space.
>> This is the same ratio as was used for one of the modem schemes -- I
>> _think_ it was Bell 206, 1200 baud.
>
> Bell 103, the favorite of many of use from years ago, uses a 200Hz
> shift, and commonly worked at 300 baud.  As I remember it, though,
> it was said to be good to 600, though I never saw it done.
>
> In any case, that is again 2/3 of a cycle difference.
> (1270Hz-1070Hz, or 2225Hz-2025Hz)
>
> Later modems that I knew used PLL ICs, I don't know how they
> did it in 1962.
>
> The wikipedia page Audio_frequency-shift_keying  seems to indicate
> that a half cycle is required, but I am not convinced.
>
> It seems to me that what is really needed is for the first sideband
> at the modulation frequency to be reasonably within the passband of
> the transmission medium.  Well, that isn't quite as obvious as it
> would be for AM, but it seems to me that the cycle fraction isn't
> so obviously the determining factor.
>
>> I know what the advantages are for MSK (where the total shift = 1/2 the
>> bit frequency); I don't know if there's any advantages to be had from
>> the total shift = 2/3, although I do recall that it has an
>> autocorrelation function that takes an infinite amount of time to settle
>> compared to MSK whose autocorrelation function goes to zero at one bit
>> time in either direction of tau = 0.
>
> -- glen

Dangit, I should have double checked.  Bell 103 is a modem protocol. 
The Bell 206 is a helicopter that I used to use as a standard for 
"shakes a lot" when designing control loops for things that hung off of 
aircraft.

So I guess there's a bit of difference there.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

Tim Wescott <tim@seemywebsite.com> wrote:
(snip, I wrote)

>> Bell 103, the favorite of many of use from years ago, uses a 200Hz
>> shift, and commonly worked at 300 baud.  As I remember it, though,
>> it was said to be good to 600, though I never saw it done.
(snip)
 
> Dangit, I should have double checked.  Bell 103 is a modem protocol. 
> The Bell 206 is a helicopter that I used to use as a standard for 
> "shakes a lot" when designing control loops for things that hung off of 
> aircraft.

There are many Bell modems in the 2xx series, so it didn't seem
at all strange to me when you wrote 206.  I believe there are
Bell 202, 208, and 212, and probably more than that.
 
> So I guess there's a bit of difference there.

-- glen 

Tim Wescott <tim@seemywebsite.com> wrote:

> Dangit, I should have double checked.  Bell 103 is a modem protocol. 
> The Bell 206 is a helicopter that I used to use as a standard for 
> "shakes a lot" when designing control loops for things that hung off of 
> aircraft.

Um, not the same "Bell" is it?


Steve

On Sep 4, 1:10�am, spop...@speedymail.org (Steve Pope) wrote:
> Tim Wescott <t...@seemywebsite.com> wrote:
> > Dangit, I should have double checked. &#4294967295;Bell 103 is a modem protocol.
> > The Bell 206 is a helicopter that I used to use as a standard for
> > "shakes a lot" when designing control loops for things that hung off of
> > aircraft.
>
> Um, not the same "Bell" is it?
>
> Steve

The helicopter "Bell" is Larry Bell : aviation pioneer from Buffalo,
NY. His company got into helicopters in Buffalo then moved the
operation to TX at some point.

 We all know the other Bell :-)

dvsarwate <dvsarwate@gmail.com> writes:

> On Sep 3, 11:23&nbsp;am, Randy Yates <ya...@ieee.org> wrote:
>> To my way of
>> thinking, the easiest is this: if we consider an FSK signal is in the
>> form
>>
>> &nbsp; x(t) = A*cos(phi(t)),
>>
>> then a _continuous-phase FSK signal requires phi(t) to be continuous.
>
> More strongly, phi(t) should be a piecewise linear function as well
> as being continuous.  

True, but "piecewise linearity" would have come from phi(t) being
an FSK signal. 

> That is, the graph of phi(t) should be a series
> of straight-line segments with the segments joining at their
> endpoints.

The "joining at their endpoints" is what makes it continuous. 

>> Most of the time the term "phase" refers to the function theta
>> in the argument:
>>
>> &nbsp; cos(w*t + theta).
>>
>
> In such cases, theta is perhaps better referred to as the phase
> offset, but it is true that "phase" is very commonly used.  In
> fact, for FSK perhaps it is best to write the signal as
>
> cos(w*t + phi(t))
>
> where w is the nominal or average frequency (sum of Mark and
> Space frequencies divided by 2) and take phi(t) to be a
> piecewise linear continuous function where the line segments
> have positive or negative slopes (of equal magnitude).  

I have seen that form in at least a couple of books. 

> If phi(t) increases (or decreases) by pi/2 over a signaling interval,
> we have MSK; if the change is plus/minus pi, we have Sunde's FSK etc.

That form is convenient for these reasons (to see these relationships).

Back to Brent, I suggest you go to your local university library and
check out (literally or figuratively) the following books:

@BOOK{couch,
  title = "{Digital and Analog Communication Systems}",
  author = "{Leon~W.~Couch}",
  publisher = "Prentice Hall",
  edition = "fifth",
  year = "1993"}

@BOOK{leeandmesserschmitt3,
  title = "{Digital Communication}",
  author = "{John R. Barry and Edwared A. Lee and David G. Messerschmitt}",
  publisher = "Springer",
  edition = "third",
  year = "2004"}

@BOOK{proakiscomm,
  title = "{Digital Communications}",
  author = "John~G.~Proakis",
  publisher = "McGraw-Hill",
  edition = "fourth",
  year = "2001"}

-- 
Randy Yates                      % "With time with what you've learned, 
Digital Signal Labs              %  they'll kiss the ground you walk 
mailto://yates@ieee.org          %  upon."
http://www.digitalsignallabs.com % '21st Century Man', *Time*, ELO

On 09/03/2010 10:10 PM, Steve Pope wrote:
> Tim Wescott<tim@seemywebsite.com>  wrote:
>
>> Dangit, I should have double checked.  Bell 103 is a modem protocol.
>> The Bell 206 is a helicopter that I used to use as a standard for
>> "shakes a lot" when designing control loops for things that hung off of
>> aircraft.
>
> Um, not the same "Bell" is it?

Bell 103 is a modem standard named after the American Bell Telephone 
company, founded by noted inventor and aviation pioneer Alexander Graham 
Bell.

The Bell 206 Jetranger is built by the Bell Aircraft Corporation (now, 
like almost half of everything aviation a division of Textron), which 
was founded by Lawrence Dale Bell.

It is of note, however, that while Bell may have founded the company 
that makes the helicopters, it was Bell that was instrumental in helping 
to birth the second aviation company in the United States, and arguably 
the first really commercially successful one.

So Bell may be the "name" in aviation he was only in his teens when Bell 
was supporting Glenn Curtis in the development of his line of early 
planes (and superlative aviation engines).

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html