Digital Signal Processing Reference
In-Depth Information
Q
(
x
)
x
2
(a)
Q
(
x
)
Q
(
x
)
x
x
(b)
(c)
Legend
Quantized
Infinite-precision
Fig. 4.3 Transfer characteristics of a quantizer for (a) rounding; b 1's complement and sign-
magnitude truncation; c 2's complement truncation.True signal is dashed line, quantized signal is
full line
4.3.1.2 Truncation Method
This method is achieved by truncating a fixed-point number of wordlength k ? 1
bits to b ? 1 bits. The quantization error (e
qt
= Q[x] - x) would depend on the
polarity of the number x. For positive x, the error e
qt
will be always less than or
equal to 0 (i.e., e
qt
B 0). Therefore, the range of the error is given as
ð
2
b
2
k
Þ
e
qt
0
:
ð
4
:
7
Þ
On the other hand, for negative number x, the truncation error depends on
the negative number convention used to represent x. Three negative number
conventions are commonly adopted: 1's complement, 2's complement, or sign-
magnitude notation.
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