Electro-acoustic control of radiation impedance for brass instrument timbre shaping: design of a vocalizing mute

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Table D.1.

Expressions of the transfer functions A,B,Cand D defined in (D.5) for the mouthpiece (left-hand column) and the vocal tract (right-hand column). These transfer functions give the pressure travelling waves at the inlet to the first tube of the Kelly-Lochbaum structure in Figure 14, with respect to the input pressure and flow.

	Mouthpiece (Sect. D)	Vocal Tract (Sect. 3.2)
A	$\frac{1}{β + (1 + α β) Y_{1}}$ $\frac {1}{\beta + (1 +\alpha \beta )Y_1}$	Z₁
B	$- \frac{β - (1 + α β) Y_{1}}{β + (1 + α β) Y_{1}}$ $-\frac {\beta - (1 + \alpha \beta )Y_1}{\beta + (1 +\alpha \beta )Y_1}$	1
C	$\frac{2 Y_{1}}{β + (1 + α β) Y_{1}}$ $\frac {2Y_1}{\beta + (1 +\alpha \beta )Y_1}$	2
D	$\frac{1 + α Y_{1}}{β + (1 + α β) Y_{1}}$ $\frac {1 +\alpha Y_1}{\beta + (1 +\alpha \beta )Y_1}$	Z₁

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