1
Amplitude Quantisation
Sampling of an analog signal, such as voice, will produce signal samples,
which have continuous range of amplitudes. In other words, each signal
sample is represented by an infinite number of amplitude levels. However,
human hearing can detect only finite intensity differences. As a result, it is
only necessary to approximate the original analog signal with signal samples
of finite number of amplitude levels.
The process of transforming the sample amplitude
)
(
s
nT
m
of an analog
message signal
)
(
t
m
at time
s
nT
t
=
into a discrete amplitude
)
(
s
nT
y
taken
from a finite set of possible amplitudes is called
amplitude quantisation.
The
device used for quantisation is often referred to as the quantiser.
Here, it is assumed that the quantisation process is
memoryless
and
instantaneous
. This means that the transformation of the sample amplitude at
time
s
nT
t
=
is not affected by earlier or later samples of the message signal.
Consider a memoryless quantiser as shown:
The signal amplitude
m
is specified by the index
k
if it lies inside the
amplitude interval
L
k
m
m
m
Q
k
k
k
,...,
2
,
1
},
{
:
1
=
≤
<
+
, where
L
is the total
number of amplitude levels used in the quantiser.
The amplitudes
m
k
, k=1,2,…,L
, are called decision levels or decision
thresholds.
The output amplitudes
y
k
k=1,2,…,L
are called the representation levels or
reconstruction levels.
The interval between two adjacent representation levels is called a
quantum or step size.
Quantiser
g
(
m
)
Continuous sample
m
(
nT
s
)
Discrete sample
y
(
nT
s
)
m
k-1
m
k
y
k
m
k+1
m
k+2
Q
k

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