Revision as of 05:49, 25 October 2013

Homework 9, ECE438, Fall 2013, Prof. Boutin

Harcopy of your solution due in class, Friday October 25, 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.

UNDER CONSTRUCTION. DO NOT BEGIN YET.

Questions 1

A person is pronouncing a phoneme. The pitch of the person's voice is 120Hz. The phoneme has two formants: a large one at 500 Hz and a weak one at 1.5 kHz.

You are given a digital recording of that phoneme. The sampling rate for the recording is 5kHz.

a) From the information given, can you tell the gender of the person?

b) How does the gender of the person influence the location of the formants? Explain.

c) What is the pitch of the digital recording of the phoneme?

d) Sketch the graph of the CT Fourier transform of the phoneme. How does it compare to the graph of the DT Fourier transform of the digital recording of the phoneme?

e) Sketch the graph of the magnitude of the frequency response of the vocal tract of that person. Sketch the graph of the DT equivalent of the vocal tract of the person.

f) Sketch the approximate pole locations of the transfer function H(z) corresponding to the vocal tract of that person.

Question 2

Why do the poles of the transfer function of the vocal tract always come in complex conjugate pairs? Explain.

Question 3

We have seen that the transfer function of the vocal tract for voiced phonemes has poles (which create the formants). a) What does this imply regarding the difference equation representing the system (n discrete-time)? b) Could the vocal tract be modeled using an FIR filter? Explain.

Discussion

Please discuss the homework below.

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