> I'm looking for a means of phase shifting a square wave clock pulse by
> 90 degrees.
>
>      ______      ______
>     |      |    |      |
>     |      |    |      |
> ----        ----        ----
>         ______      _____
>        |      |    |     |
>        |      |    |     |
>    ----        ----       ----

One possible way (not necessarily the easiest) is to:

1) differentiate the signal by XORing each port reading with the previous
   one:


      ||     ||   ||      ||
      ||     ||   ||      ||
  ---- ------  ---  -----   ----

2) low-pass filter this new signal.  If it is of unknown and variable
   frequency, the easiest way is to:

   a) count the number of samples between two 1s (= period)

   b) output 1/2 that many samples of 1, and 1/2 that many as 0.

   That effectively does generate a new waveform with the desired property:

       ___    __   ___     __
      |   |  |  | |   |   |  |
      |   |  |  | |   |   |  |
  ----    ---   --    ----   ---

  Wow, you have doubled the frequency!

3) XOR the output of 2) with the original input:
           _____       ______
          |     |     |      |
          |     |     |      |
  --------       -----        ----


That's it!! You have shifted phase by 90 degree - on any single frequency
input - no matter which frequency (as long as it is substantially lower
than your sample rate).

Your example waveform is a good example: it is not a pure "square sinus" :)
All frequency deviations were preserved during the processing, and the
output is a 90 degree shift, as good as the ASCII art resolution can
get.


Make sure that you read the port only ONCE per sample, and use the buffered
values for processing. If you read it twice and the calculations base on
two versions of it, the output might become flickery..