Contents
Homework 10, ECE438, Fall 2013, Prof. Boutin
Harcopy of your solution due in class, Friday November 8, 2013
Presentation Guidelines
- Write only on one side of the paper.
- Use a "clean" sheet of paper (e.g., not torn out of a spiral book).
- Staple the pages together.
- Include a cover page.
- Do not let your dog play with your homework.
Question 1
Consider a model of the vocal tract consisting of three tubes of equal length l connected to a first tube that is infinitely thin. Assume that l=Tc where c is the speed of sound and T is the period at which you sample the airflow throughout the model.
a) Obtain the transfer function of this model of the vocal tract. (You may use the matrix equations for the tube junction/time delay obtained in class without justification.)
b) How many formants could one create with such a model? Explain.
c) Explain how one would control the location of the formants with such a model.
That's it!
Discussion
Please discuss the homework below.
- Comment/question here
- answer here
Looking further into this problem, I am confused as to why we are using three separate tubes here? Shouldn't we be using 2 tubes since L = T*c. According to some notes posted on Rhea [1], the number of tube segments equals (2*L)/(c*T). Since we are given L = c*T, I believe two tubes is the correct number to model here. Thoughts?
Not to mention, this would change the transfer function as well as the number of formants.
