I'm relatively new to signal processing, so please excuse me if this is a trivial question. Why is the spectrum of a frame of speech samples periodic? What is the meaning of a periodic spectrum? And if a spectrum is periodic, doesn't that mean that it is not band-limited (i.e. it goes on to infinity)? How is the spectrum of a speech frame affected by the windowing function (does it change the amplitude or period of the periodic spectrum)? This is mostly out of curiosity, and to help me get a better qualitative understanding of cepstral analysis. Thanks in advance.
The spectrum of a vowel sound typically contains many harmonics. These harmonics are of course evenly spaced in the frequency domain (i.e. you see peaks at f0, 2*f0, 3*f0, 4*f0, etc). The spectrum can therefore be considered to be "periodic", with a "period" equal to f0. (This is usually called quefrency in the cepstral analysis literature).