EEL6586: Automatic Speech Processing HW#3
EEL 6586: HW#3
Assignment is due Friday, February 22, 2008 in class. Late home-
work loses e#of days late −1percentage points.
PART A: Short Answer (No more than a few sentences each)
A1 Assume that a speech signal was framed with a 25ms rectangular win-
dow. What is the main lobe width in Hz due to the rectangular window?
Recall that the main lobe width appears in the Fourier magnitude spec-
trum of speech as the width of each pitch harmonic. Assume a 20KHz
sampling rate.
A2 A common algorithm for pitch determination is to perform autocorre-
lation on the LPC residual (error) and look for peaks. Why does this
algorithm work better than performing autocorrelation on the original
speech signal and looking for peaks?
A3 The following synthetic sound is created:
s(t) = sin(2π(200Hz)t)+0.5 sin(2π(400Hz)t)+0.25 sin(2π(500Hz)t)
What is the likely pitch frequency we would perceive in listening to this
sound? Explain.
A4 Compute the complex cepstrum of
H(z) = 1/(1 + az−1)
Assume |a|<1.
A5 In class, the cepstrum was defined as the inverse Fourier Transform
of the log of the Fourier Transform. However, some people define the
cepstrum as the Fourier Transform of the log of the Fourier Transform
(without the inverse). Which version do you expect to perform better
in actual applications? Explain.
J.G. Harris February 11, 2008 1
