First, take a simple signal (e.g., one
period of a sinusoid at some frequency) and plot its
autocorrelation sequence for appropriate values of
l
l. You may wish to use the xcorr MATLAB
function to compare with your own version of this function.
At what time shift
l
l is
r
s
s
l
r
s
s
l
maximized and why? Is there any symmetry in
r
s
s
l
r
s
s
l
? What does
r
s
s
l
r
s
s
l
look like for periodic signals?
Next, write your own version of the Levinson-Durbin algorithm
in MATLAB. Note that MATLAB uses indexing from
1
1 rather than
0
0. One way to resolve this problem is to start the
loop with
i=2
i
2
, then shift the variables
k
k,
E
E,
α
α, and
r
s
s
r
s
s
to start at
i=1
i
1
and
j=1
j
1
. Be careful with indices such as
i−j
i
j
, since these could
still be
0
0.
Apply your algorithm to a
20
20-
30
30 ms segment of a speech signal. Use a microphone to
record .wav audio files on the PC using Sound
Recorder or a similar application. Typically, a sample rate
of
8
8 kHz is a good choice for voice signals, which are
approximately bandlimited to
4
4
kHz. You will use these audio files to test algorithms in
MATLAB. The functions wavread,
wavwrite, sound will help you read,
write and play audio files in MATLAB:
The output of the algorithm is the prediction coefficients
a
k
a
k
(usually about
P=10
P
10
coefficients is sufficient), which represent the
speech segment containing significantly more samples. The LPC
coefficients are thus a compressed representation of the
original speech segment, and we take advantage of this by
saving or transmitting the LPC coefficients instead of the
speech samples. Compare the coefficients generated by your
function with those generated by the levinson or
lpc functions available in the MATLAB toolbox.
Next, plot the frequency response of the IIR model represented
by the LPC coefficients (see Speech Processing: Theory of LPC Analysis and
Synthesis). What is the fundamental frequency of the
speech segment? Is there any similarity in the prediction
coefficients for different
20
20-
30
30
ms segments of the same vowel sound? How could the prediction
coefficients be used for recognition?
"Doug course at UIUC using the TI C54x DSP has been adopted by many EE, CE and CS depts Worldwide "