EEL6586: Automatic Speech Processing HW#3
EEL 6586: HW#3
Assignment is due Friday, Feb 14, 2003 in class. Late homework
loses e#of days late −1percentage points. See the current late penalty
at http://www.cnel.ufl.edu/hybrid/harris/latepoints.html
This assignment includes both matlab and textbook questions.
PART A: Textbook problems
A1 An infinite train of impulses is created with the following relation
e(n) = X
k
δ(n+kP )
Assume that the sampling frequency is 10kHz.
1. Determine the value of P to create a pitch frequency of 100Hz.
2. The infinite train of impulses is fed through an all-pole model of
H(z) = 1/(1 + .9z−1+.81z−2)
What is the dominant formant frequency in the signal?
3. Is this formant frequency higher or lower than typical first formant
frequencies for humans?
4. How will the formant frequency change if pre-emphasis is applied
to the signal (s(n)−0.95s(n−1))?
A2 Assume that an infinite impulse train
X
k
δ(n+kP )
is filtered by a vocal-tract model given by H(z) = 1/(1+.9z−1+.81z−2)
to produce a speech signal s(n).
1. Derive the difference equation for s(n).
2. Compute the autocorrelation function r(0) for the speech signal
s(n).
3. Compute the autocorrelation function r(1) for the speech signal
s(n).
J.G. Harris January 31, 2003 1
