Formant: List formant slope...


A command available in the Query submenu if you select a Formant object. The Info window will show the characteristics of the slope of the chosen interval as a vector with a number of values.
Settings

Formant number,

defines the formant whose slope characteristics you want.

Time range (s),

defines the start time and the end time of the segment on which the slope should be determined.

Slope curve

defines the kind of curve you want to fit on the formant points to determine the slope characteristics. The options available are Exponential plus constant, Parabolic and Sigmoid plus constant.
The vector result
The vector values are determined from the fit of the formant track with a an exponential plus constant function F(t) = a+b·exp(c·t), or a parabolic function F(t) = a+b·t+c·t^{2}, or a sigmoid plus constant function F(t) = a+b / (1 + exp( (t c) / d)) on the chosen interval [t_{min}, t_{max}].

1. Average slope (Hz / s)

defined as (F_{start}  F_{end}) / (t_{max}  t_{min}), where F_{start} and F_{end} are the start and end values of the fitted function F(t) and t_{max} and t_{min} are the start and end times of the interval.

2. R^{2}

The R^{2} value of the fit defined as R^{2} = 1  varianceAfter / varianceBefore.

3. F_{start}

the frequency in hertz of the function F(t_{min}).

4. F_{end}

the frequency in hertz of the function F(t_{max}).

5. a

the parameter a (hertz) of the function F(t).

6. b

the parameter b of the function F(t).

7. c

the parameter c ( / s) of the function F(t).

8. d

the parameter d of the function F(t), if the sigmoid plus constant function was chosen.
Remarks about the interpretation of the fit parameters.
The returned average slope parameter is reliable only if the formant trajectory is clearly not constant and there is a large difference between the F_{start} and the F_{end} values. In cases where the formant trajectory shows a noisy pattern all return values have a large error margin and the determined average slope can also be unreliable.
Algorithm
The algorithm to fit the nonlinear exponential plus constant and the sigmoid plus constant functions to a series of (time, frequency) values by a noniterative algorithm is described in Jacquelin (2009).
© djmw 20210813