Block filtering in amplitude-continuous time-discrete channels (Corresp.)

A linear amplitude-continuous (LAC) block filter is a real-valued rectangular matrix transformation
A
of a vector of real-valued zero-mean signal samples with covariance matrix
R_x
, such that
tr(A R_x A ^ T)
is invariant with
A
. The matrix
A
adds redundancy to the signal by having more rows than columns. A special class of LAC filters, called orthogonal LAC filters, is constrained by
A^T A \propto I
. For a channel containing zero-mean additive noise, independent of the signal, it is shown that optimum orthogonal LAC filters reduce error by diagonalizing the covariance matrices in the error expression, but are as ineffective as transmission without prefiltering against stationary white noise. On the other hand, this correspondence describes a class of LAC filters that are effective against stationary white noise.