mirror of
https://github.com/f4exb/sdrangel.git
synced 2024-11-20 07:11:46 -05:00
562 lines
21 KiB
Markdown
562 lines
21 KiB
Markdown
# Digital Speech Decoder 1.7.0-dev
|
|
Copyright (C) 2010 DSD Author
|
|
GPG Key ID: 0x3F1D7FD0 (74EF 430D F7F2 0A48 FCE6 F630 FAA2 635D 3F1D 7FD0)
|
|
|
|
Permission to use, copy, modify, and/or distribute this software for any
|
|
purpose with or without fee is hereby granted, provided that the above
|
|
copyright notice and this permission notice appear in all copies.
|
|
|
|
THE SOFTWARE IS PROVIDED "AS IS" AND ISC DISCLAIMS ALL WARRANTIES WITH
|
|
REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY
|
|
AND FITNESS. IN NO EVENT SHALL ISC BE LIABLE FOR ANY SPECIAL, DIRECT,
|
|
INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM
|
|
LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE
|
|
OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR
|
|
PERFORMANCE OF THIS SOFTWARE.
|
|
|
|
DSD is able to decode several digital voice formats from discriminator
|
|
tap audio and synthesize the decoded speech. Speech
|
|
synthesis requires mbelib, which is a separate package.
|
|
|
|
|
|
### Supported formats
|
|
|
|
#### P25 Phase 1
|
|
|
|
Widely deployed radio standard used in public safety and amateur radio.
|
|
|
|
Support includes decoding and synthesis of speech,
|
|
display of all link control info, and the ability to save
|
|
and replay .imb data files
|
|
|
|
#### ProVoice
|
|
|
|
EDACS Digital voice format used by public safety and amateur radio.
|
|
|
|
Support includes decoding and synthesis of speech and
|
|
the ability to save and replay .imb data files.
|
|
|
|
Note: not enabled by default, use `-fp` to enable.
|
|
|
|
#### X2-TDMA
|
|
|
|
Two slot TDMA system currently being deployed by several
|
|
public safety organizations. Based on the DMR
|
|
standard with extensions for P25 style signaling.
|
|
|
|
Support includes decoding and synthesis of speech,
|
|
display of all link control info, and the ability to save
|
|
and replay .amb data files
|
|
|
|
#### DMR/MOTOTRBO
|
|
|
|
"Digital Mobile Radio" Eurpoean two slot TDMA standard.
|
|
MOTOTRBO is a popular implementation of this standard.
|
|
|
|
Support includes decoding and synthesis of speech and
|
|
the ability to save and replay .amb data files.
|
|
|
|
#### NXDN
|
|
|
|
Digital radio standard used by NEXEDGE and IDAS brands.
|
|
Supports both 9600 baud (12.5 kHz) and
|
|
4800 baud (6.25 kHz) digital voice.
|
|
|
|
Support includes decoding and synthesis of speech and
|
|
the ability to save and replay .amb data files.
|
|
|
|
#### D-STAR
|
|
|
|
Amateur radio digital voice standard
|
|
|
|
This is an earlier version of the AMBE codec than the one
|
|
used by most of the protocols. Support for this was added by
|
|
various developers.
|
|
|
|
### Unsupported formats in version 1.6 considered for future development:
|
|
|
|
#### P25 Phase 2
|
|
|
|
This is not yet a published standard. Full support is
|
|
expected once the standard is published and there are
|
|
systems operating to test against. Phase 2 will use
|
|
a vocoder supported by mbelib.
|
|
|
|
#### OpenSKY
|
|
|
|
It is possible that the four slot version uses a vocoder
|
|
supported by mbelib. The two slot version does not.
|
|
|
|
### Supported demodulation optimizations in version 1.6:
|
|
|
|
#### C4FM
|
|
|
|
Continuous envelope 2 or 4 level FSK with relatively
|
|
sharp transitions between symbols. Used by most P25
|
|
systems.
|
|
|
|
Optimizations include calibrating decision points only
|
|
during sync, 4/10 sample window per symbol, and symbol
|
|
edge timing calibration.
|
|
|
|
#### GFSK
|
|
|
|
Continuous envelope 2 or 4 level FSK with a narrower
|
|
Gaussian/"raised cosine" filter that affects transitions
|
|
between symbols. Used by DMR/MOTOTRBO, NXDN and many
|
|
others. Noisy C4FM signals may be detected as GFSK
|
|
|
|
but this is ok, the optimization changes will help with
|
|
noisy signals.
|
|
|
|
Optimizations are similar to C4FM except symbol transitions
|
|
are only kept out of the middle 4 samples and only the
|
|
middle two samples are used.
|
|
|
|
#### QPSK
|
|
|
|
Quadrature Phase Shift Keying (and variants) used in
|
|
some P25 systems and all known X2-TDMA systems. May be
|
|
advertised under the marketing term "LSM"
|
|
|
|
Optimizations include continuous decision point
|
|
calibration, using middle two samples, and using the
|
|
symbol midpoint "spike" for symbol timing.
|
|
|
|
## Installation
|
|
|
|
DSD should easily compile on any Linux or *BSD system with gcc.
|
|
There are some debugging/development options in `config.h` that
|
|
normal users will want to leave disabled as they can severely
|
|
impact performance.
|
|
|
|
### Requirements
|
|
* cmake
|
|
* mbelib
|
|
* sndfile
|
|
|
|
### Example building instructions on Ubuntu:
|
|
|
|
````
|
|
sudo apt-get update
|
|
sudo apt-get install git make cmake # Update packages
|
|
git clone <URL of git repository> # Something like: git@github.com:USERNAME/dsd.git
|
|
cd dsd # Move into source folder
|
|
mkdir build # Create build directory
|
|
cd build # Move to build directory
|
|
cmake .. # Create Makefile for current system
|
|
make # Compiles DSD
|
|
sudo make install # Installs DSD to the system
|
|
````
|
|
|
|
## Operation
|
|
|
|
There are two main operating modes, "Live scanner" and "Play files"
|
|
|
|
Usage: dsd [options] Live scanner mode
|
|
|
|
Live Scanner mode takes 48KHz/16 bit mono audio samples from a
|
|
sound card input and decodes speech in real time. Options are provided
|
|
for controling information display and saving mbe data files.
|
|
|
|
The synthesized speech can be output to a soundcard and/or a
|
|
.wav file.
|
|
|
|
Usage: dsd [options] -r <files> Read/Play saved mbe data from file(s)
|
|
|
|
|
|
Play files mode reads mbe data from files specified on the command
|
|
line (including wildcards) and synthesizes speech from those files.
|
|
The synthesized speech can be output to a soundcard and/or a
|
|
.wav file. The `-r` command line options is used to activate Play files
|
|
mode.
|
|
|
|
### Display modes
|
|
|
|
There are two main display modes in Live scanner mode. "Errorbars"
|
|
and "Datascope".
|
|
|
|
Errorbars mode output for P25 Phase 1 looks like this:
|
|
|
|
````
|
|
Sync: -P25p1 mod: C4FM inlvl: 39% nac: 5C2 src: 0 tg: 32464 TDULC
|
|
Sync: -P25p1 mod: C4FM inlvl: 39% nac: 5C2 src: 0 tg: 32464 TDULC
|
|
Sync: -P25p1 mod: C4FM inlvl: 39% nac: 5C2 src: 0 tg: 32464 TDULC
|
|
Sync: -P25p1 mod: C4FM inlvl: 39% nac: 5C2 src: 0 tg: 32464 TDULC
|
|
Sync: -P25p1 mod: C4FM inlvl: 38% nac: 5C2 src: 0 tg: 32464 TDU
|
|
Sync: -P25p1 mod: C4FM inlvl: 38% nac: 5C2 src: 0 tg: 32464 HDU
|
|
Sync: -P25p1 mod: C4FM inlvl: 42% nac: 5C2 src: 0 tg: 32464 LDU1 e:
|
|
Sync: (-P25p1) mod: C4FM inlvl: 39% nac: 5C2 src: 52610 tg: 32464 (LDU2) e:
|
|
Sync: -P25p1 mod: C4FM inlvl: 38% nac: 5C2 src: 52610 tg: 32464 LDU1 e:
|
|
Sync: -P25p1 mod: C4FM inlvl: 39% nac: 5C2 src: 52610 tg: 32464 LDU2 e:
|
|
Sync: -P25p1 mod: C4FM inlvl: 39% nac: 5C2 src: 52610 tg: 32464 LDU1 e:
|
|
Sync: -P25p1 mod: C4FM inlvl: 39% nac: 5C2 src: 52610 tg: 32464 LDU2 e:
|
|
Sync: -P25p1 mod: C4FM inlvl: 39% nac: 5C2 src: 52610 tg: 32464 LDU1 e:
|
|
````
|
|
|
|
* "Sync" indicates the frame type detected and whether the polarity is
|
|
positive or negative. DSD automatically detects and handles either
|
|
polarity except for DMR/MOTOTRBO/X2-TDMA which unfortunatley use both
|
|
sync polarities.
|
|
|
|
* Most combinations of transmitter, receiver and soundcard show netagive
|
|
(-) polarity for X2-TDMA signals and (+) polarity for DMR/MOTOTRBO so
|
|
those are the defaults.
|
|
|
|
* You may need to use the `-x` option to select non-inverted polarity if
|
|
you are not getting usable X2-TDMA/MOTOTRBO/DMR speech. As they use both
|
|
normal and inverted sync it is not possible to detect polariy
|
|
automatically.
|
|
|
|
* "mod" indicates the current demodulation optimizations.
|
|
|
|
* "inlvl" indicates the audio input level. QPSK signals tend to appear
|
|
much "wider" than C4FM from a discriminator tap so it is important
|
|
to set your input gain using a QPSK signal if you plan to montir them.
|
|
It is not necessary nor desirable to get to 100%, in fact your sound
|
|
card may max out below 100%. It is best to use the Datascope mode for
|
|
setting input gain (see below). Typical values with good results are
|
|
40% for C4FM and 66% for QPSK.
|
|
|
|
* "nac" is the P25 Phase 1 Network Access Code. This is a 12 bit field
|
|
in each P25 Phase 1 header. It should not be confused with the 16
|
|
bit System ID used in non-P25 trunking control channels.
|
|
|
|
* "src" is the radio id of the trasmitting subscriber unit.
|
|
|
|
* "tg" is the talkgroup derived from link control information.
|
|
|
|
* "HDU/LDU1/LDU2/TDU/TDULC" are P25 Phase 1 frame types, referred to as
|
|
frame subtype within DSD.
|
|
|
|
* "e:" is the beginning of the errorbars display. Each "=" indicates a
|
|
detected error within the voice data. "R" and "M" indicat that a voice
|
|
frame was repeated or muted due to excessive errors.
|
|
|
|
* Values in parentheses () indicate an assumption (soft decision) was
|
|
made based on the previous frame.
|
|
|
|
Errorbars mode output for X2-TDMA looks like this:
|
|
````
|
|
Sync: -X2-TDMA mod: QPSK inlvl: 59% src: 17211 tg: 197 [SLOT0] slot1 VOICE e:
|
|
Sync: -X2-TDMA mod: QPSK inlvl: 47% src: 17211 tg: 197 [SLOT0] slot1 VOICE e:
|
|
Sync: -X2-TDMA mod: QPSK inlvl: 43% src: 17211 tg: 197 [SLOT0] slot1 VOICE e:
|
|
Sync: (-X2-TDMA) mod: QPSK inlvl: 28% src: 17211 tg: 197 [SLOT0] slot1 VOICE e:
|
|
````
|
|
|
|
DMR/MOTOTRBO display is similar except it does not yet show source
|
|
and talkgroup information.
|
|
|
|
As of version 1.2 DSD shows which specific TDMA slots are active (with
|
|
capital SLOT letters) and which slot is currently being monitored (with
|
|
square brackets []. Noisy/degraded signals will affect the accuracy
|
|
of this display.
|
|
|
|
The frame subtypes (Voice/LC etc) are shown based on the DMR standard
|
|
types.
|
|
|
|
Datascope mode output looks like this:
|
|
|
|
````
|
|
Demod mode: C4FM Nac: 8C3
|
|
Frame Type: P25 Phase 1 Talkgroup: 16528
|
|
Frame Subtype: LDU1 Source: 0
|
|
TDMA activity: slot0 slot1 Voice errors:
|
|
+----------------------------------------------------------------+
|
|
| # ^ !| ^ # |
|
|
| * | * |
|
|
| * | * |
|
|
| * | * * |
|
|
| * * | * * |
|
|
| * * | ** * |
|
|
| * ** | ** * |
|
|
| ** ** | ** * |
|
|
| ** ** | ** * |
|
|
| ** ** | ** * |
|
|
+----------------------------------------------------------------+
|
|
C4FM Example
|
|
````
|
|
````
|
|
Demod mode: C4FM Nac: 126
|
|
Frame Type: P25 Phase 1 Talkgroup: 25283
|
|
Frame Subtype: LDU2 Source: 0
|
|
TDMA activity: slot0 slot1 Voice errors:
|
|
+----------------------------------------------------------------+
|
|
| # ^ ! ^ # |
|
|
| * | |
|
|
| * | |
|
|
| ** | |
|
|
| ** | * |
|
|
| * ** | * * |
|
|
| ** ** | * * |
|
|
| *** ** | ** * |
|
|
| *** ** | *** * |
|
|
| *** **** | **** * * |
|
|
+----------------------------------------------------------------+
|
|
QPSK Example
|
|
````
|
|
|
|
At the top is various information about the signal, similar to the
|
|
information provided in Errorbars mode. The large box is similar to
|
|
a spectrum analyzer viewing the channel bandwidth.
|
|
|
|
The horizontal axis is the input audio level, minimum on the left and
|
|
maximum on the right. The vertical axis is the number of samples
|
|
seend at each audio level.
|
|
|
|
The "*" symbols represent the number of audio
|
|
samples that were at each level during the aggregation period.
|
|
(default = 36 symbols) The `-S` options controls the aggregation period
|
|
as well as the QPSK tracking symbol buffer, so changing that will affect
|
|
QPSK performance as well as the Datascope display.
|
|
|
|
As you can see from the figures above, clean C4FM signals tend to have
|
|
four very sharply defined audio levels. The datascope pattern also
|
|
tends to be faily stable with minor shifts left and right as the
|
|
receiver tries to frequency track any DC offset.
|
|
|
|
QPSK signals on the other hand tend to appear much broader (and artifact
|
|
of how they are distored by FM PLL discriminators). They also tend
|
|
to vary wildly in width and centering. This is especially true when
|
|
monitoring simulcast systems. Muliple QPSK signals interfere much more
|
|
dramatically with an FM discriminator than C4FM signals.
|
|
|
|
For this reason it is important to isolate your receiver to one
|
|
transmitter tower, _especially_ for QPSK signals.
|
|
|
|
The "#" symbols indicate the detected min/max values that are used
|
|
to calibrate the symbol decision points. These are indicated by
|
|
"!" for the center decision point and "^" for the mid decision points.
|
|
|
|
### Display Options
|
|
|
|
There are several options to control the type and quantity of
|
|
information displayed in Errorbars mode:
|
|
|
|
````
|
|
-e Show Frame Info and errorbars (default)
|
|
-pe Show P25 encryption sync bits
|
|
-pl Show P25 link control bits
|
|
-ps Show P25 status bits and low speed data
|
|
-pt Show P25 talkgroup info
|
|
-q Don't show Frame Info/errorbars
|
|
-s Datascope (disables other display options)
|
|
-t Show symbol timing during sync
|
|
-v <num> Frame information Verbosity
|
|
-z <num> Frame rate for datascope
|
|
````
|
|
|
|
Most of these options are self explanitory. Symbol timing is a noisy
|
|
option that allows you to view the quality of the frame sync samples
|
|
and accuracy of the symbol timing adjustments.
|
|
|
|
Symbol Timing display looks like this:
|
|
````
|
|
Symbol Timing:
|
|
----------
|
|
----------
|
|
----------
|
|
----------
|
|
----------
|
|
-+++++++++ 1
|
|
+---------- 0
|
|
----------
|
|
++++++++++ 0
|
|
++++++++++
|
|
---------- 0
|
|
----------
|
|
++++++++++ 0
|
|
++++++++++
|
|
++++++++++
|
|
++++++++++
|
|
---------- 0
|
|
++++++++++ 0
|
|
---------- 0
|
|
++++++++++ 0
|
|
++++++++++
|
|
++++++++++
|
|
++++++++++
|
|
++++++++++
|
|
C4FM example
|
|
````
|
|
````
|
|
Symbol Timing:
|
|
+---------
|
|
----------
|
|
----------
|
|
----------
|
|
-----X---- 5
|
|
--+++O++++- 4
|
|
----------
|
|
----X----- 4
|
|
++++O++--- 4
|
|
--++O++++- 4
|
|
----X----- 4
|
|
----------
|
|
++++O+++-- 4
|
|
-+++O+++-- 4
|
|
--++O+++-- 4
|
|
--++O+++-- 4
|
|
----------
|
|
++++O++++- 4
|
|
----------
|
|
++++O+++-- 4
|
|
-+++O++++- 4
|
|
-+++O+++++ 4
|
|
-+++O++--- 4
|
|
--++O+++-- 4
|
|
QPSK example
|
|
````
|
|
|
|
Symbol timing is only displayed for symbols during the frame sync
|
|
period. Each horizontal line represents the 10 audio samples for each
|
|
symbol. "-" indicates an audio sample below the center reference level
|
|
and "+" represents a sample above center. "X" indicates a low spike
|
|
below a reference threshold (reference minimum for C4FM and 80%
|
|
of reference minimum for QPSK). "O" represents a high spike above
|
|
the high reference threshold. The numbers to the right indicate which
|
|
sample position the targeted transition occurred (+/- for C4FM or
|
|
spike high/low for QPSK). The number of audio samples for the next
|
|
symbol are adjusted to get this value closer to the target (0 for
|
|
C4FM and 4 for QPSK). This shows how DSD maintains accurate symbol
|
|
timing. Symbol timing adjustments are only made during sync, which
|
|
is the only time reliable transitions can be observed.
|
|
|
|
In both examples above the symbol timing was off by one sample at
|
|
the beginning of the frame sync period and was adjusted. Generally
|
|
if you see any spike values "X/O" in C4FM mode, or lots of them in
|
|
QPSK mode it indicates noise on the input signal.
|
|
|
|
### Input/Output Options
|
|
|
|
````
|
|
-i <device/file> Audio input device/file (default is /dev/audio)
|
|
-o <device> Audio output device (default is /dev/audio)
|
|
-d <dir> Create mbe data files, use this directory
|
|
-r <files> Read/Play saved mbe data from file(s)
|
|
-g <num> Audio output gain (default = 0 = auto)
|
|
-n Do not send synthesized speech to audio output device
|
|
-w <file> Output synthesized speech to a .wav file
|
|
````
|
|
|
|
The audio in device can be a sound card OR a .wav file if the file
|
|
is in the exact format 48k/16bits/mono/pcm. Audio in should be an
|
|
unfilterd discriminator tap signal.
|
|
|
|
The audio out device should be a sound card (use the `-w` options to
|
|
output to a .wav file).
|
|
|
|
If the audio in device is the same as the audio out device, the
|
|
synthesized speech has to be upsampled to the 48k sample rate required
|
|
for input. A fast upsample function is provided but still leaves some
|
|
artifacts.
|
|
|
|
The best sound and minimum cpu usage is achieved with separate sound
|
|
cards for input and output
|
|
|
|
If you specify different input/output devices DSD will use 8k as the
|
|
output sample rate and the lack of resampling results in much better
|
|
audio as well as lowe cpu consumption.
|
|
|
|
If you are using onboard "AC97" sound device you may find that DSD uses
|
|
much more cpu than expected, in some cases more than is available.
|
|
This is because many AC97 sound devices are designed to rely on CPU
|
|
processing power instead of hardware. You may also find that 8k sample
|
|
rate output is upsampled in the driver using a very basic algorithim
|
|
resulting in severe distortion. The solution is to use a real hardware
|
|
sound device (pci card, usb device etc).
|
|
|
|
As of version 1.2 DSD now automatically levels the output audio. This
|
|
greately improves readability and eliminates the painful effects of
|
|
noise bursts. You can specify a fixed audio output gain with the -g
|
|
option.
|
|
|
|
### Scanner control options:
|
|
````
|
|
-B <num> Serial port baud rate (default=115200)
|
|
-C <device> Serial port for scanner control (default=/dev/ttyUSB0)
|
|
-R <num> Resume scan after <num> TDULC frames or any PDU or TSDU
|
|
````
|
|
|
|
On some P25 systems Packet Data Units (PDU) are sent on the same
|
|
frequencies used for voice traffic. If done constantly this can
|
|
be a severe hinderance to scanning the system in conventional
|
|
mode. The -R option enables sending a "resume scan" command to
|
|
a scanner connected to a serial port. Use `-B` and `-C` to set the baud
|
|
rate and serial port device if necessary.
|
|
|
|
### Decoder options
|
|
````
|
|
-fa Auto-detect frame type (default)
|
|
-f1 Decode only P25 Phase 1
|
|
-fd Decode only D-STAR*
|
|
-fi Decode only NXDN48* (6.25 kHz) / IDAS*
|
|
-fn Decode only NXDN96 (12.5 kHz)
|
|
-fp Decode only ProVoice*
|
|
-fr Decode only DMR/MOTOTRBO
|
|
-fx Decode only X2-TDMA
|
|
-l Disable Filters (not recommended)
|
|
-ma Auto-select modulation optimizations (default)
|
|
-mc Use only C4FM modulation optimizations
|
|
-mg Use only GFSK modulation optimizations
|
|
-mq Use only QPSK modulation optimizations
|
|
-pu Unmute Encrypted P25
|
|
-u <num> Unvoiced speech quality (default=3)
|
|
-xx Expect non-inverted X2-TDMA signal
|
|
-xr Expect inverted DMR/MOTOTRBO signal
|
|
````
|
|
\* denotes frame types that cannot be auto-detected.
|
|
|
|
ProVoice and NXDN48 not auto-detected as use different symbol
|
|
rates (9600 and 2400) than most formats (4800).
|
|
|
|
MBE speech synthesis is broken down into two main types of sounds,
|
|
"Voiced" and "Unvoiced". Voiced speech bands are synthesized with
|
|
a single sine wave centered in the frequency band with the appropriate
|
|
phase and amplitude.
|
|
|
|
Unvoiced speech is supposed to be generated with a noise source, 256
|
|
point DFT a number of band filters, followed by a 256 point inverse DFT.
|
|
For computational simplicity mbelib uses a different method. For each
|
|
unvoiced speech band, a number of sine waves are generated, each with a
|
|
different random initial phase. The number of waves used per band is
|
|
controlled by the `-u` option. A setting of 4 would approximate the
|
|
performance of the 256 point DFT method as the maximum number of voice
|
|
bands is 56, and very low frequencies are not synthesized. Values less
|
|
than 3 have a noticable lack of unvoiced speech and/or artifacts. The
|
|
defualt of 3 provides good speech quality with reasonable cpu use.
|
|
Increasing the quality above the default rapidly consumes more CPU for
|
|
increasingly diminishing returns.
|
|
|
|
|
|
#### Advanced decoder options
|
|
````
|
|
-A <num> QPSK modulation auto detection threshold (default=26)
|
|
-S <num> Symbol buffer size for QPSK decision point tracking
|
|
(default=36)
|
|
-M <num> Min/Max buffer size for QPSK decision point tracking
|
|
(default=15)
|
|
````
|
|
|
|
### Encryption
|
|
|
|
Decryption of speech is **NOT** supported, even if you lawfully posess the
|
|
encryption keys. Decryption support will not be added in the future as
|
|
the authors wish to steer as far away from the legal issues associated
|
|
with encryption as possible.
|
|
|
|
|
|
We realize that there are many legitemate and lawful uses of decryption
|
|
software including system/interoperability testing and lawful monitoring.
|
|
This software is distributed under a liberal BSD license so there is
|
|
nothing to stop others from supplying patches, forking this project or
|
|
incorporating it into a commercial product and adding decryption support.
|
|
|
|
There is support for displaying the encryption sync bits transmitted in
|
|
the clear on P25 Phase 1 systems. These bits do not allow for the
|
|
decryption of signals without the secret encryption keys. The
|
|
encryption sync bits are useful for determining whether a signal is
|
|
encrypted vs merely noisy or degraded. As the encryption sync bits
|
|
typically include long strings of zeros when a transmission is not
|
|
encrypted they can also be used to visually estimate bit error rates.
|