Digital Signal Processing Reference
In-Depth Information
(at the receiver). This method of proceeding has a cost: the prediction is made on the
reconstructed signal
x
(
n
) rather than on the original signal
x
(
n
). This is not serious
as long as
x
(
n
) is a good approximation of
x
(
n
), when the intended compression rate
is slightly increased.
We can now turn to the problem of determining the coefficients for the polynomial
A
(
z
). The signals to be quantized are not time-invariant and the coefficients must be
determined at regular intervals. If the signals can be considered to be locally stationary
over
N
samples, it is enough to determine the coefficients for every
N
sample. The
calculation is generally made from the signal
x
(
n
). We say that the prediction is
calculated
forward
. Although the information must be transmitted to the decoder, this
transmission is possible as it requires a slightly higher rate. We can also calculate
the filter coefficients from the signal
x
(
n
). In this case, we say that the prediction is
calculated
backward
. This information does not need to be transmitted. The adaptation
can even be made at the arrival of each new sample
x
(
n
) by a gradient algorithm
(adaptive method).
Let us compare the details of the advantages and disadvantages of these two
methods separately.
Fo r w a rd
prediction uses more reliable data (this is particularly
important when the statistical properties of a signal evolve rapidly), but it requires
the transmission of
side information
and we must wait until the last sample of the
current frame before starting the encoding procedure on the contents of the frame.
We therefore have a reconstruction delay of at least
N
samples. With a
backward
prediction, the reconstruction delay can be very short but the prediction is not as good
because it is produced from degraded samples. We can also note that, in this case,
the encoding is more sensitive to transmission errors. This choice comes down to a
function of the application.
We have yet to examine the problem of decoder filter stability because it is
autoregressive. We cannot, in any case, accept the risk of instability. We have seen
that if the autocovariance matrix estimate is made so as to maintain its definite-positive
character, the filter stability is assured, and the poles of the transfer function are inside
the unit circle.
