Interesting technical question with solution

What is the bandwidth of a Morse code radio signal if the Morse code is being sent at a speed is 20 words/minute?


Solved by using  L. W. Couch, Digital and Analog Communication Systems, 7th Edition, Prentice Hall, 2007

The usual assumption is that the typical word is 5 characters in length. Morse Code characters have a variable width. However, assume that a Morse code character C is typical or slightly longer than the width of the average characters sent in English text, so that if a C is used, the maximum "average" bandwidth will be evaluated.  The C is  _ ._.  and there are three bits for each dash and one bit for each dit with a spacing of one bit between dashes and dits. Assume that there is a spacing of one dash (three bits) between characters and three dashes (nine bits) between words.  

Consequently the number of bits in a word is

         (14 bits/C character)(5 C characters/word) + 9 bits for word spacing = 79 bits/word


Thus for code being sent at a rate of 20 words/minute,  the maximum "average" bit rate, R, for a word (including the spacing after it) is

R= (20 words/min)(79 Bits/word)(1 min/60 sec) = 26 bits/sec

The Morse code signal is an On Off Keyed (OOK) signal since a dash is three bits on and a dit is one bit on and during other times the bits are off. Referring to Figure 5-20 of L. W. Couch, Digital and Analog Communication Systems, 7th Edition, Prentice Hall, 2007, the null-to-null bandwidth of an OOK signal is

B=2R=2(26)=52 Hz.

Thus the bandwidth for a 20 word/minute Morse code signal is around 50 Hz

Note: This result agrees with the results shown in Figure 9.11 of the 2005 ARRL Handbook, The American Radio Relay League, Inc, Newington, CT, 2004 (which gives the result, but not how to calculate it.)

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