Fast fourier transforms of random binary data

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I am a physicist who is trying to make sense of FFTs and binary data.

Say I have a series of random binary data, which is measured with a repetition rate of 400Hz (interval time of 0.0025s). I have a total of 12489 points, which corresponds to a total measurement time of about 31 seconds.

I would like to be able to learn more about what I would expect an FFT of this data to look like.

Some things I would like to understand the significance of:

  • What should be the average amplitude of the data, post-FFT?
  • what is the significance of the maximum amplitude of binary data that is not random, but consists of 1,0,1,0,1,0 data (12489 points). How can this help me find my y-scale?