Note that the reflection coefficients for the junction of two lossless acoustic tubes of areas Ak and A k+1 can be written as either (a) Show that since both A k and A k+1 are positive,  −1 ≤ rk ≤ 1....

Note that the reflection coefficients for the junction of two lossless acoustic tubes of areas Ak and A_k+1
can be written as either

(a) Show that since both A_k
and A_k+1
are positive,  −1 ≤ rk ≤ 1.  (b) Show that if 0
_k
<>_k+1
<>_k

By substituting the appropriate matrices Qˆ₁
and Qˆ₂
into Eq. (5.80), show that the transfer function of a two-tube discrete-time vocal tract model is given by Eq. (5.82).

Eq. (5.80)

Eq. (5.82)