Hi, you are correct. When you are referring to the noise parts of a speech waveform, you are most likely talking about sounds like 's' or 'sh' as in say or sheep. These are called fricatives in speech and the energy in these fricatives is isolated in higher frequencies than the enery in the voiced, periodic sounds (vowels).
There is a Fourier theory for random processes.
By the way, for analyzing speech, you'll want to learn about the spectrogram, so you can visualize how the spectrum changes over time.
