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Python implementation of Liljencrants-Fant (LF) model of the glottal flow

The implementation uses (Gobl 2017). Also from that paper is this diagram:

LF-model

NOTE: The LF-model has two implicit equations that need to be solved due to the continuity constraint for $U_g(t)$ and the constraint that the integral over $U_g'(t)$ must be zero. It seems that the numerical routines are very sensitive to the five LF-model parameters listed below. When debugging, set visual=True to help in the process.

LF model parameters

The five time-domain parameters (denoted collectively by $P$) describing the GFM derivative are (@Doval2006 p. 5):

  1. $E_e$: maximum amplitude of the excitation (i.e. $U_g'(t)$)
  2. $T_0$
  3. $T_e$: instant of maximum excitation (GCI)
  4. $T_p$: instant of the maximum of $U_g(t)$
  5. $T_a$: time constant of the return phase (see picture above)

Alternative parameters

Alternative definitions for the last three parameters are (Fant1995, The LF model revisited):

  • $R_k = (T_e-T_p)/T_p$
  • $R_g = T_0/(2T_p)$
  • $F_a=1/(2πT_a)$ (as an alternative to $R_a=T_a/T_0$)

This conversion is implemented in the conv_R_param() function in LF.py.

Typical values

Typical values for male vowels are $F_a$ = 700 Hz, $R_k$ = 0.30, $R_g$ = 1.20.

Typical values for female vowels are $F_a$ = 400 Hz, $R_k$ = 0.30, $R_g$ = 1.00.

These are implemented in gen_param() in LF.py.

Files

LF.py implements the model and helper routines.

The two notebooks show use cases. Good luck!