I've read that the reflection coefficients in speech processing (as computed by the Levinson-Durbin algorithm for solving the Yule-Walker equations) "represent the fraction of energy reflected back" at each tube junction,[1] assuming the speaker's vocal tract is modeled as a series of uniform lossless acoustic tubes (see Figure 1). Now, I've seen that statement from multiple PDFs online, but did not see it mentioned in my textbook (Rabiner, Schafer - Digital Processing of Speech Signals).

Does this mean we can do autoregressive modeling of electrical transmission lines as well? In other words, does a series of lossless transmission lines form an all-pole filter whose (magnitude) reflection coefficients (one for each junction) and linear-prediction coefficients can be estimated by inputting white noise to the system and then analyzing the output with the Levinson-Durbin algorithm? (Figure 2.)

Figure 1. Approximating a time-varying acoustic tube using a series of short tubes of uniform cross-section

Figure 1. Approximating a non-uniform acoustic tube using a series of short tubes of uniform cross-section. (Source: Rabiner, Schafer - Digital Processing of Speech Signals p.83.)

Figure 2. A series of lossless transmission lines.

Figure 2. A series of lossless transmission lines. (Source: Pozar - Microwave Engineering 4th Ed. p.251.)

[1] http://research.cs.tamu.edu/prism/lectures/sp/l7.pdf


1 Answer 1


This is a neat idea and could probably be made to work - it seems like a variant on time-domain reflectometry, which exploits correlations of this kind https://en.wikipedia.org/wiki/Time-domain_reflectometry. However, there's an important difference between your two use cases: we can normally inject a test signal onto an electrical transmission line, while we normally can't do that in the vocal tract. Measuring the cross-correlation of the injected and reflected signals is generally going to be more reliable than measuring the cross-correlation of noise.


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