[Freetel-codec2] Symbol rate of central sync carrier

Discussion:

Phil Frost

2016-08-17 14:30:10 UTC

I've been working on an independent implementation of the FDMDV modem as
a personal exercise. As I understood the description*, the central BPSK
subcarrier should be at a symbol rate of 50 per second, but looking at
the tone spacing it's too narrow: but a 25 symbols per second seems to
line up. Am I overlooking something or is the sync subcarrier really at
25 sym/sec?

*:
http://freedv.org/tiki-index.php?page=FreeDV+Specification
http://n1su.com/fdmdv/FDMDV_Docs_Rel_1_4b.pdf
http://www.arrl.org/files/file/FDMDV.pdf

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Steve

2016-08-17 16:01:46 UTC

Permalink

The wiki description is pretty dated. I think the original modem had
14 carriers, but the current non-coherent modem has 16 plus the bpsk
sync.

If you work backwards, the modem has to send 64-bits every 40 ms
(vocoder rate). So, 64-bits at 25 Hz.

But since the modem only sends 32-bits (16 carriers) it has to send
two frames every 40 ms, thus, 50 Hz symbol rate, 1600 bit/s.

The bpsk sync carrier being used to identify the starting frame.

Steve

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David Rowe

2016-08-18 00:24:23 UTC

Permalink

Hello Phil,

Good question, and actually took me a while to remember why the two sync
carrier lines are just 25 Hz apart.

FreeDV 1600 uses a symbol rate of Rs=50 symbols/s for each of the 17
carriers, including the central DBPSK sync carrier. Note that we are
using Differential PSK (DPSK) - not PSK.

The start of a 40ms codec frame is indicated by a change in phase in the
DPSK sync carrier, so for example this sequence of phases (in radians)
every 20ms:

... pi pi -pi -pi pi pi -pi -pi .....

Note the _change_ in phase every 2 symbols (40ms), indicating codec
frame sync.

The cosine of the sequence of phases above is ....1 1 -1 -1 1 1 -1 -1
.... which (when up sampled and filtered) approximates a sampled sine
wave of frequency Rs/4 (takes 4 symbols to repeat). So using this Rs/4
frequency sequence to modulate the center carrier at frequency fc we get

s(t) = cos(2*pi*t*fc)*cos(2*pi*t*Rs/4)
s(t) = 0.5*cos(2*pi*t*(fc+Rs/4) + 0.5*cos(2*pi*t(fc-Rs/4)

which is two sine waves Rs/2 = 25Hz apart.

Cheers,

David

The BPSK sync carrier sends alternating ...101010...., this a modulating
signal that takes two symbol periods to repeat. So it's frequency is
Rs/2 or 25Hz.

So when you multiply a Rs/2 signal by the central carrier:

cos(2*pi*fcentre*t)*cos(2*pi*t*Rs/2)
= 0.5*cos(2*pi*t(fcentre+Rs/2) + 0.5*cos(2*pi*t(fcentre-Rs/2)

which should look like two sine waves Rs apart

Post by Phil Frost
I've been working on an independent implementation of the FDMDV modem as
a personal exercise. As I understood the description*, the central BPSK
subcarrier should be at a symbol rate of 50 per second, but looking at
the tone spacing it's too narrow: but a 25 symbols per second seems to
line up. Am I overlooking something or is the sync subcarrier really at
25 sym/sec?
http://freedv.org/tiki-index.php?page=FreeDV+Specification
http://n1su.com/fdmdv/FDMDV_Docs_Rel_1_4b.pdf
http://www.arrl.org/files/file/FDMDV.pdf
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https://lists.sourceforge.net/lists/listinfo/freetel-codec2

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Phil Frost

2016-08-22 20:36:55 UTC

Permalink

Thanks David, that explains so much. I was really scratching my head for a
while trying to figure out why it wouldn't sync :)

If I wanted to update the description after I hash out the details and get
my implementation working, what would be the best way to do that?

Post by David Rowe
Hello Phil,
Good question, and actually took me a while to remember why the two sync
carrier lines are just 25 Hz apart.
FreeDV 1600 uses a symbol rate of Rs=50 symbols/s for each of the 17
carriers, including the central DBPSK sync carrier. Note that we are
using Differential PSK (DPSK) - not PSK.
The start of a 40ms codec frame is indicated by a change in phase in the
DPSK sync carrier, so for example this sequence of phases (in radians)
... pi pi -pi -pi pi pi -pi -pi .....
Note the _change_ in phase every 2 symbols (40ms), indicating codec
frame sync.
The cosine of the sequence of phases above is ....1 1 -1 -1 1 1 -1 -1
.... which (when up sampled and filtered) approximates a sampled sine
wave of frequency Rs/4 (takes 4 symbols to repeat). So using this Rs/4
frequency sequence to modulate the center carrier at frequency fc we get
s(t) = cos(2*pi*t*fc)*cos(2*pi*t*Rs/4)
s(t) = 0.5*cos(2*pi*t*(fc+Rs/4) + 0.5*cos(2*pi*t(fc-Rs/4)
which is two sine waves Rs/2 = 25Hz apart.
Cheers,
David
The BPSK sync carrier sends alternating ...101010...., this a modulating
signal that takes two symbol periods to repeat. So it's frequency is
Rs/2 or 25Hz.
cos(2*pi*fcentre*t)*cos(2*pi*t*Rs/2)
= 0.5*cos(2*pi*t(fcentre+Rs/2) + 0.5*cos(2*pi*t(fcentre-Rs/2)
which should look like two sine waves Rs apart

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Post by Phil Frost
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David Rowe

2016-08-22 21:24:39 UTC

Permalink

Hi Phil,

Sure help with the waveform documentation would be great. We can get
you a password for the wiki and the word processor doc source if you're
keen.

If you want a challenging modem project I'm looking for help on the
cohpsk modem, to support the 700C FreeDV mode I am developing. Much
more fun than re-implementing an existing waveform.

Cheers,

David

Post by Phil Frost
Thanks David, that explains so much. I was really scratching my head for
a while trying to figure out why it wouldn't sync :)
If I wanted to update the description after I hash out the details and
get my implementation working, what would be the best way to do that?
Hello Phil,
Good question, and actually took me a while to remember why the two sync
carrier lines are just 25 Hz apart.
FreeDV 1600 uses a symbol rate of Rs=50 symbols/s for each of the 17
carriers, including the central DBPSK sync carrier. Note that we are
using Differential PSK (DPSK) - not PSK.
The start of a 40ms codec frame is indicated by a change in phase in the
DPSK sync carrier, so for example this sequence of phases (in radians)
... pi pi -pi -pi pi pi -pi -pi .....
Note the _change_ in phase every 2 symbols (40ms), indicating codec
frame sync.
The cosine of the sequence of phases above is ....1 1 -1 -1 1 1 -1 -1
.... which (when up sampled and filtered) approximates a sampled sine
wave of frequency Rs/4 (takes 4 symbols to repeat). So using this Rs/4
frequency sequence to modulate the center carrier at frequency fc we get
s(t) = cos(2*pi*t*fc)*cos(2*pi*t*Rs/4)
s(t) = 0.5*cos(2*pi*t*(fc+Rs/4) + 0.5*cos(2*pi*t(fc-Rs/4)
which is two sine waves Rs/2 = 25Hz apart.
Cheers,
David
The BPSK sync carrier sends alternating ...101010...., this a modulating
signal that takes two symbol periods to repeat. So it's frequency is
Rs/2 or 25Hz.
cos(2*pi*fcentre*t)*cos(2*pi*t*Rs/2)
= 0.5*cos(2*pi*t(fcentre+Rs/2) + 0.5*cos(2*pi*t(fcentre-Rs/2)
which should look like two sine waves Rs apart

Post by Phil Frost
I've been working on an independent implementation of the FDMDV

modem as

Post by Phil Frost
a personal exercise. As I understood the description*, the central

BPSK

Post by Phil Frost
subcarrier should be at a symbol rate of 50 per second, but looking at
the tone spacing it's too narrow: but a 25 symbols per second seems to
line up. Am I overlooking something or is the sync subcarrier

really at

Post by Phil Frost
25 sym/sec?
http://freedv.org/tiki-index.php?page=FreeDV+Specification
http://n1su.com/fdmdv/FDMDV_Docs_Rel_1_4b.pdf
http://www.arrl.org/files/file/FDMDV.pdf

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Post by Phil Frost
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