The two most popular methods of time-domain pitch shifting used in sound effects processors are the chopping method, as J.Guy suggested, and the 'Vocoder' tecnique, using FFT as suggested by Kunal.

Both methods have their disadvantages and advantages. Firstly, the chopping method is easy to implement, not requiring much in the way of processing power. The results are fairly passable if you are only shifting the original sound a couple of semi-tones or less, however after that, the processed sound takes on a 'robotic sounding' quality, as the chopping becomes more apparent. The voices of the Darleks from Dr. Who sounded the way they did because they were chopped, although not shifted. Also, this method tends to work better when lowering the pitch. It should be noted that although the chopping should occur at an almost constant rate, each 'chunk' of sound should start and end at zero-crossing point in the audio data.

The FFT or Vocoder method produces by far the best results, it does however require a pretty powerful DSP to pull it off successfully. Some of you in the know, may want to mention at this point, that early Vocoders were implemented totally in analog. Yes, they were, and although they sounded good as an effect in their own right (ELO proved that! ;-) ), as a serious pitch-shifter, they sounded rubbish! I won't go in to great depth about how they work, accept to say, it involves filtering the original sound through several band-pass filters (the more the better), obtaining the amplitude of the signals from all the filters, and then modulating each of these amplitudes with a set of sine-wave osciallators with frequencies set to multiples of the band-pass filter frequencies respectivley. If you were doing this digitally, a real-time FFT could be used in place of the filters. Me thinks an 8052 is not up to the task!

Matt.