4.9 Modeling the speech signal  (Page 3/4)

Speech spectrum

These peaks are known as formants . Thus, speech signal processors would say that the sound "oh" has a higherfirst formant frequency than the sound "ee," with $\mathrm{F2}$ being much higher during "ee." $\mathrm{F2}$ and $\mathrm{F3}$ (the second and third formants) have more energy in "ee" than in "oh." Rather than serving as a filter, rejecting high or lowfrequencies, the vocal tract serves to shape the spectrum of the vocal cords. In the time domain, we have a periodic signal, the pitch, serving as the input to alinear system. We know that the output—the speech signal we utter and that is heard by others and ourselves—willalso be periodic. Example time-domain speech signals are shown in [link] , where the periodicity is quite apparent.

Since speech signals are periodic, speech has a Fourier series representation given by a linear circuit's response to a periodic signal . Because the acoustics of the vocal tract are linear, we knowthat the spectrum of the output equals the product of the pitch signal's spectrum and the vocal tract's frequency response. Wethus obtain the fundamental model of speech production .

Voice spectrum

Pulse

Voice spectrum

The model spectrum idealizes the measured spectrum, and captures all the important features. The measured spectrum certainlydemonstrates what are known as pitch lines , and we realize from our model that they are due to the vocal cord'speriodic excitation of the vocal tract. The vocal tract's shaping of the line spectrum is clearly evident, but difficultto discern exactly, especially at the higher frequencies. The model transfer function for the vocal tract makes the formants much more readily evident.