Digital Signal Processing Reference
In-Depth Information
Compute the difference values of the FCF, i.e.
Decide the appropriate order. If then
P= s-
1 else return
to
Step 5.
Based on our experiments, we have used the threshold
value of
Compute the enhanced speech signal from
If the additive noise
W
is colored, a pre-whitening transformation is applied
to the data matrix. Assuming the sample Hankel matrix of the noise
signal is known, then the corresponding Cholesky factorization or
QR
decomposition is given by or where is
the upper triangular Cholesky factor and has orthonormal
columns The implementation algorithm is exactly the same as
that described in the above procedure except for two extra steps at the
beginning and the end of the procedure. They are described below:
(3).
(7)
.
(8)
.
(9)
.
Compute the QR decomposition of
and
perform a pre-
whitening of
(i.e.
and
The following Steps 4-9 are exactly the same as the above described Steps 3-
8 except that is replaced by
(10).
Perform a de-whitening of
(i.e.
Finally, the reconstructed speech signal,
is computed from
by
arithmetic averaging along its anti-diagonals.
5.
SIMULATION RESULTS
5.1
Order Determination
The performance of the proposed F-norm constrained algorithm is
initially examined using the reconstruction of several voiced and unvoiced
speech signals. The consecutive reconstructions of the signals have been
produced with increasing value of
s
while the corresponding values of the
FCF, as well as the SNRs of the reconstructed signals, are calculated. The
frame length and analysis order of SVD are chosen, based on our
simulations, to be 200 and 21, respectively, i.e.,
M =
180,
N =
21
.
The results of reconstructing a frame of voiced and unvoiced speech
signals embedded in white noise with SNR=0dB are given in Fig. 11-1 and
Fig. 11-2, respectively. As shown in Figs. 11-1 and 11-2, the dots of the FCF
form the convergent curves and the value of
converges to a very
