Digital Signal Processing Reference
In-Depth Information
Fig. 11.1
Structure of the
hybrid code
binary numerical system, in order to implement the filter in a digital hardware plat-
form, such as FPGA, the hybrid coded method [
9
-
11
] is adopted. In this chapter,
a new hybrid coded method, called Accumulated Hybrid Code (AHC), was intro-
duced to improve the precision of the optimal design.
This chapter explores the CSD coded design for FIR and IIR filters. The orga-
nization of this chapter is as follows: Sect.
11.2
introduces the AHC. Then, the
CSD-coded GA is introduced in Sect.
11.3
. Based on the methods in Sect.
11.2
and
Sect.
11.3
, Sect.
11.4
shows the design process and numerical example for an FIR
filter. Subsequently, Sect.
11.5
introduces the design process and numerical example
for an IIR filter.
11.2 The Accumulated Hybrid Code (AHC)
In this chapter, based on the structure of a power-of-two code [
9
-
11
], a hybrid code
is used for the coding of the coefficients in digital filters. In order to reduce design
error and obtain a solution which is closer to the optimal solution, a new hybrid
coded method with better precision is proposed. In this section, the traditional hybrid
code is first introduced, and then a new hybrid code, named Accumulation Hybrid
Code (AHC), is revealed.
11.2.1 The Traditional Hybrid Code Method
The hybrid code is a coding method which improves the signed binary code. It is
similar to the signed binary algorithm. For the signed binary code, the most signifi-
cant bit (MSB) is a sign bit. A positive number is represented with a sign bit '0' and
a negative number is with a sign bit '1'. The structure of the hybrid code is different
to that of a signed binary code. A hybrid code is a composition of several signed
binary codes. Figure
11.1
shows the structure of the hybrid code which comprises
m
signed binary codes [
9
].
In the hybrid code,
k
i
,i
=
1
,
2
,...,m
, are binary codes with
n
bits;
b
ij
,j
=
0
,
1
,
2
,...,n
, denotes the
j
th bit of
k
i
, and
S
k
i
is the sign bit of
k
i
. The magnitude
of
k
i
is calculated as:
n
2
j
,i
∈
k
i
=
b
ij
×
1
,
2
,...,m.
(11.1)
j
=
0
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