Digital Signal Processing Reference
In-Depth Information
1
+
X[k]
ROM
2
n
N
X
0
1
W
2
addr
0
clk
h
1
h
2
h
3
h
4
h
5
h
6
h
7
h
0
X
X
X
X
X
X
X
X
rst_n
+
+
+
+
+
+
+
+
x[n]
0
1
clk
mux_zero
2
−
n
mux_n
demux_out
2
h
[
n
]
=
W
8
controller
Figure 6.24
DFT implementation using circular convolution
The following example optimizes the implementation of DFT architecture.
Example: Redesign the architecture of Figure 6.24 using a TDF FIR filter structure. Optimize the
multiplications using the CSE technique.
The filter coefficients for N
2
W
n
=
2
¼
8 are computed by evaluating the expression
for n
¼
0
...
7.
N
The values of the coefficients are:
h½n¼½
1
;
0
:
92
þ
0
:
38
j; j
0
:
92
0
:
38
j;
1
0
:
92
0
:
38
j; j
0
:
92
þ
0
:
38
j
These values of coefficients require just one multiplier and swapping of real and imaginary
components of x[n] for realizingmultiplication by j. The FIRfilter structure of Figure 6.24 is given in
Figure 6.25.
x[n]
0.92+0.38j
X
I
j
I
I
j
j
x
n
h
7
x
n
h
4
-
x
n
h
6
x
n
h
5
x
n
h
3
x
n
h
2
x
n
h
1
x
n
h
0
-
+
+
+
+
+
+
+
y[n]
Figure 6.25
Optimized TDF implementation of the DF implementation in Figure 6.24
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