# 3.15.hyperbolic.draw
#
# Praat script that creates figure 3.15 of
#    Boersma (1998): Functional Phonology.
# http://fonsg3.hum.uva.nl/paul/
#
Erase all
Times
10

Viewport... 0 3 0 3

Create Sound... frequency 0 0.5 4000 0
Formula... arctan(0.7*sin(2*pi*x)/(1-0.7^2*(1-cos(2*pi*x))))/(2*pi*0.7)
Draw... 0 0 0 0.5 no
Formula... arctan(0.1*sin(2*pi*x)/(1-0.1^2*(1-cos(2*pi*x))))/(2*pi*0.1)
Draw... 0 0 0 0.5 no
Remove
Draw line... 0 0 0.5 0.5

Draw inner box
One mark left... 0 yes yes no
One mark left... 0.5 no yes no %c/2\De%x
Text bottom... yes True frequency %F
One mark bottom... 0 yes yes no
One mark bottom... 0.5 no yes no %c/2\De%x
Text... 0.4 Right 0.4 Bottom %\al = 1
Text... 0.4 Centre 0.25 Top %\al = 0.7
Text... 0.4 Right 0.1 Top %\al = 0.1

Viewport... 0.2 2.9 0 3
Text left... yes Simulated frequency %F\'p

Viewport... 3 6 0 3
Create Sound... q 0 0.5 4000 0
Formula... -ln(1-0.7^2*(1-0.7^2)*(1-cos(2*pi*x))^2)/(2*pi*0.7)
Formula... log10(x/self)
Formula... if self>4 then 4 else self fi
Draw... 0 0.5 -1.001 4 no
Formula... -ln(1-0.1^2*(1-0.1^2)*(1-cos(2*pi*x))^2)/(2*pi*0.1)
Formula... log10(x/self)
Formula... if self>4 then 4 else self fi
Draw... 0 0.5 -1.001 4 no
Remove

Draw inner box
Marks bottom every... 1 1 yes yes no
Text left... yes %Q factor
Logarithmic marks left... 1 yes yes no
Text bottom... yes True frequency %F
One mark bottom... 0 yes yes no
One mark bottom... 0.5 no yes no %c/2\De%x
One mark right... 1 no no no %\al = 0.7
One mark right... -0.5 no no no %\al = 0.1

Viewport... 0.1 6 0.25 3