Mad Man Rambles about Noise Generators

[johns at oei.com]

     I would like to offer my 2 cents on this topic:
     
     My first job out of college was to design a pseodorandom number 
     generator that would serve as a test data source for digital tape 
     recorders.  So naturally I started the project by looking at the basic 
     "shift register with XOR feedback taps" core of the thing.  My 
     analysis convinced me of several things:
     
     1. All pseudorandom number generators (shift registers with XOR 
     feedback) will repeat eventually but the longer ones, generally 
     speaking, will repeat with a longer cycle time (given a constant 
     clock).  The SR repeating in the digital world will sound like "thumpa 
     thumpa" in the audio world.
     
     2. The best way to ensure the longest cycle time is to use the largest 
     prime number less than 2 to the "number of SR bits used" power as your 
     guideline for determining the SR taps for the XOR gate(s).  For 
     example, 13 is largest prime in a 4 bit SR.
     
     3. If you don't use a prime number as a tap guide, you will end up 
     with either a very simple repeating sequence or one that shifts out to 
     all ones or zeros (it dies).
     
     4. I've found that you can minimize the thumpa-thumpa by increasing 
     the SR length (and proper selection of the taps), not the clock 
     frequency.  The clock frequency will control the overall tone of the 
     noise.
     
     5. There are extreme cases where these are not true.  You can do the 
     analysis to verify this.
     
     Refer to the "equivalent circuit" diagram on a MM5837 data sheet.  It 
     shows a very effecient SR with a 2 bit tap which reflects some of my 
     observations.
     
     This is all I could conjure up from my memory of 15 years ago.  Hope 
     I'm not way wrong!
     
     JJS