Month: February 2014

http://en.wikipedia.org/wiki/Phasor

Why do you resample the side-tone at 4 times the tone frequency to obtain its envelope? This relates to how you think of the side-tone, or sinusoids (=sine waves) in general. At first glance, the amplitude of a sine wave goes up and down, so depending on the timing you observe the signal, you will get various values as its amplitude. One idea to detect the peak value in an interval greater than its period, somewhat equivalent to an envelope detector using a diode and a CR low-pass filter circuit.

But the truth is that the amplitude of a sinusoid does not vary but is constant, as you see in the bottom half of the figure. The radius of the circle is constant! The amplitude varies because you are looking at the shadow of the rotating bar onto the y-axis.

The problem is how you can estimate the length of the rotating bar by just observing its shadow.

The clue is to observe the shadow not once in its rotating period, the phase of the observation being arbitrary, but observe twice in the period, each separated with the time equal to a quarter of the period. The sampling phase of the observation in this case does not matter with the following reasons.

If the sample rate is 4 times the tone frequency, you will have 4 sampling points (in red) on a circle each separated with 90 degrees. With an arbitrary sampling phase of th, the two adjacent samples are at the phases of th and th+90deg, respectively, which means the two values are x(i)=A*cos(th) and x(i+1)=A*cos(th+90deg), where A is the length of the rotating bar.

Therefore, you will have
sqrt(x(i)^2+x(i+1)^2)
=sqrt(A^2*cos^2(th)+A^2*cos^2(th+90deg))
=A*sqrt(cos^2(th)+sin^2(th))
=A.

Signals with 90 deg phase difference have an important role in signal processing. One example is the SSB generator with a PSN circuit, which is somewhat more complex because you need to give the phase difference not to a sine wave with a fixed frequency but to s signal with some bandwidth, say between 0.3kHz to 2.7kHz.

You can download code practice files from, for example, http://www.arrl.org/code-practice-files. The following is how to make your own practice files.

First, you need to find some text files. I always visit Project Gutenberg, which offers over 42,000 free ebooks in various format including HTML, EPUB, Kindle, and plain text. You will download a book in a plain text format.

% tr -s '[:punct:]' ' ' <original.txt >withoutpunct.txt

You may wish to delete all the punctuations from the text.

% ebook2cw -w 40 -f 600 -s 8000 -b 64 -q 1 -o ChristmasCarol-40wpm ChristmasCarol.txt
% ls
ChristmasCarol-25wpm0000.mp3
ChristmasCarol-30wpm0000.mp3
ChristmasCarol-35wpm0000.mp3
ChristmasCarol-40wpm0000.mp3

ebook2cw is a program to convert ebooks to Morse MP3s/OGGs files. It might be convenient if you add the options -a and -t to add ID3 tags to the file. Or you can import the files into, say, iTunes, and add the tags there.

When you have a side-tone sound file instead of the key’s contact signal, you need to estimate the latter from the former. There are various ways, such as using a Hilbert filter or simply using an envelope detector. Here the audio signal is resampled at 4 times the tone frequency, i.e. at 2400Hz (=4*600Hz), and sqrt(x(i)^2+x(i-1)^2) is computed as signal power, where x(i) is the i-th sample value.

% gawk '{print sqrt($1*$1+b4*b4); b4=$1}' <test2.csv >test3.csv

This is a histogram of the duration of spaces when a space is between two dots. The case happens in a single letter, like in “h”, or between two letters like between “n” and “a”.

Spaces between dot and dash, like in a letter “a”, or between the letters like “n” and “n”.

Spaces between dash and dot, like in a letter “n”, or between the letters “a” and “a”.

Spaces between dash and dash, like in a letter “m”, or between the letters “a” and “n”.

BEGIN {
type="null"
val1b4="null"
val2b4=0
val3b4="null"
val1b44=val1b4
val2b44=val2b4
val3b44=val3b4
}

{
 if(val1b44=="dw" && $1=="dw" ) {
  if(val3b44=="long" && $3=="long")
   type="ll"
  if(val3b44=="long" && $3=="short")
   type="ls"
  if(val3b44=="short" && $3=="long")
   type="sl"
  if(val3b44=="short" && $3=="short")
   type="ss"
  print val2b4, type
 }

 val1b44=val1b4
 val2b44=val2b4
 val3b44=val3b4
 val1b4=$1
 val2b4=$2
 val3b4=$3
}

% gawk -f myprog.awk <w3 >w4
% head w3
dw 20 short
up 34 short
dw 105 long
up 98 long
dw 96 long
up 44 long
dw 22 short
up 26 short
dw 24 short
up 28 short
% head w4
34 sl
98 ll
44 ls
26 ss
28 ss
31 ss
156 sl
42 ls
42 sl
37 ls

%R
> th=seq(0,250,10)
> hist(datass$V1,xlim=c(0,250),ylim=c(0,10),breaks=th,main="Dot-to-Dot",col="green")
> hist(datasl$V1,xlim=c(0,250),ylim=c(0,8),breaks=th,main="Dot-to-Dash",col="blue")
> hist(datals$V1,xlim=c(0,250),ylim=c(0,8),breaks=th,main="Dash-to-Dot",col="yellow")
> hist(datall$V1,xlim=c(0,250),ylim=c(0,8),breaks=th,main="Dash-to-Dash",col="red")

This is a scatter plot considering the dot (or dash) with its directly following space as an entity. The group 1 consists of, say “h”s, in which both dot and space periods are very exact. The group 2 consists of the letters such as “o”s, in which both the periods are controlled manually. The groups 3 and 4 are for the spaces between letters.

% head w2
dw 20
up 34
dw 105
up 98
dw 96
up 44
dw 22
up 26
dw 24
up 28
% cat myprog.awk
{
 if(NR%2 == 0) print b4, $2
 b4=$2
}
% gawk -f myprog.awk <w2 >dw_up
% head dw_up
20 34
105 98
96 44
22 26
24 28
% R
> mydata<-read.table("dw_up")
> mydata
    V1  V2
1   20  34
2  105  98
3   96  44
4   22  26
5   24  28
> plot(mydata$V1,mydata$V2,col="blue",xlim=c(0,250),ylim=c(0,250),main="Dot/Dash vs. Space",xlab="Dot/Dash",ylab="Space")

This is a histogram of key down period (i.e., either dots or dashes). It seems that the dot to dash ratio is around 25:100, or 1:4.

This is a histogram of key up period, or of spaces.

Save Time: 2014-02-02 15:12:44
Units:(mV)
                     CH1
Frequency:      4.564 Hz
Period:       219.091 mS
PK-PK:           3.520 V

1                 400.00
2                   0.00
3                   0.00
4                   0.00
5                  80.00
6                   0.00
7                   0.00
8                 -80.00
9                   0.00
10                  0.00
11                -80.00
12                  0.00
13                  0.00
14                  0.00
15                  0.00
16                160.00
17                  0.00
18                  0.00
19                 80.00
20               1760.00
21               2880.00
22               3280.00
23               3280.00
24               3280.00

The text file obtained from the oscilloscope is something like this.

BEGIN { th=2000; n=10; b4=1 }

/^[0-9]/ {

 if($2>th) out=1
 else
 out=0

 if(b4==1 && out==0)
  i=n

 if(i>0) {
  out=0
  i--
 }

 b4=out

 print out
}

This awk programs gives a “0” and “1” sequence by slicing the voltage.

BEGIN { b4=1; ndown=0; nup=0 }

{
 if(b4==1 && $1==0) {
  ndown=0
  if(nup>0) print "up", nup
 }

 if(b4==0 && $1==1) {
  nup=0
  if(ndown>0) print "dw", ndown
 }

 if($1==0)
  ndown++
 else
  nup++

 b4=$1
}

And this program counts the run of either “0”s or “1”s, and gives:

dw 20
up 34
dw 105
up 98
dw 96
up 44
dw 22
up 26
dw 24
up 28
dw 21
up 31
dw 11
up 156