Digital Signal Processing Reference
In-Depth Information
where and We make three
assumptions here: (1) The signal is orthogonal to the noise in the sense that
(2) The noise is white: (3) The smallest
singular value of is larger than the largest singular value of i.e.,
Generally, the minimum variance (MV) estimate is used in noise
reduction [7].
Given the matrices
and
as in (1), There exists a matrix
which
minimizes
where
Under these three assumptions, the MV estimated of
can be derived as,
The last expression can also be denoted as
using the following
PxP
matrix filter,
Since of does not have the Hankel structure, it is necessary to
make a Hankel matrix approximation to A simple procedure, as
described in [7], for restoring the Hankel structure is to average along the
anti-diagonals of and put each average value as a common element in
the corresponding diagonal of a new Hankel structured matrix with the same
dimension. In the meantime, it is noted that the choice of
P
takes an
important role in the whole speech enhancement scheme in that a small value
