Digital Signal Processing Reference
In-Depth Information
Step 1: Dynamic range and normalizing the sampled signal
Fix the dynamic range of the sampled signal -
x
M
x
M
. Normalize the
sampled signal
x
(
n
) by its peak amplitude
x
M
, to yield the normalized signal
s
(
n
):
≤
x
(
n
)
≤
xn
x
M
()
sn
()
=
with a dynamic range -1
≤
s
(
n
)
≤
1.
Step 2: Signal compression
This step basically pre-processes the sampled signal, to provide more ampli-
fication to the lower amplitude samples and less amplification to the higher
amplitude samples. The compression function is given below:
(
)
ln
ln(
1
1
+
µ
µ
s
Fs
()
=
sgn( )
s
(4.7)
µ
+
)
where
s
is the normalized sampled signal and
µ
is the compression param-
eter, usually taken as 255.
Step 3: Processing by uniform quantizer
The compressed output,
F
(
s
), is input to a uniform
L
-level quantizer, which
has been described in detail in the previous section.
µ
Step 4: Signal expanding
The output of the uniform quantizer, , is passed through the inverse
expanding function, in order to re-synthesize the input signal. The expand-
ing function is given below:
ˆ
()
sn
1
()
=
()
⎡
⎢
ˆ
⎤
⎥
s
−
1
ˆ
s n
ˆ
Fs
(
1
+
µ
)
−
1
s
(4.8)
µ
µ
where
ˆ
()
.
−≤
1
sn
≤
1
Step 5: Signal de-normalization
The final step in the nonuniform quantization process is the de-normaliza-
tion of the signal,
ˆ
()
, to yield the final quantized signal:
sn
ˆ
()
ˆ
()
xn
=
snx
M
