8
FN3365.10
October 6, 2008
Operational Modes
Decimate By 2 Filter Mode (Mode1-0 = 00)
The concept of operation for Decimate by Two Filter mode is
most easily understood by comparing the 7 tap transversal
filter implementation to the equivalent polyphase
implementation. The transversal implementation is shown in
Figure 5.
By inspecting the sum-of-products for the decimated output
in Figure 5, it is seen that even indexed input samples are
always multiplied by the even filter coefficients and the odd
samples are always multiplied by the odd coefficients. This
computational partitioning is realized in the polyphase
implementation shown in Figure 6.
In the polyphase implementation, the input data is broken into
even and odd sample streams which are processed by a set
of polyphase filters running at one half of the input data rate.
These filters are designated as even or odd tap filters
depending upon whether the coefficients were derived from
the even or odd indexed coefficients of the original transversal
filter. This architecture only produces the outputs which are
not discarded by the decimation process. NOTE: Since the
only non-zero tap for a halfband filter is the center tap,
the Odd Tap Filter reduces to a delay and multiply
operation.
The operation of the HSP43216 in Decimate by Two mode is
analogous to the polyphase implementation in Figure 6. In
this mode, the internal data paths are routed as shown in
Figure 7A and Figure 7B. The different data flows depend on
whether internal or external multiplexing has been selected
using the INT/EXT control input. In either case, an input data
stream is decomposed into even and odd sample streams
which are then routed to the even and odd tap polyphase
filters. The output of each polyphase filter is summed and
output via AOUT0-15.
TABLE 5. OUTPUT ROUNDING CONTROL
RND
2-0
ROUND FUNCTION
000
Round output to 8-bits, AOUT15-8 and BOUT15-8, zero
lower bits.
001
Round output to 9-bits, AOUT15-7 and BOUT15-7, zero
lower bits.
010
Round output to 10-bits, AOUT15-6 and BOUT15-6,
zero lower bits.
011
Round output to 11-bits, AOUT15-5 and BOUT15-5,
zero lower bits.
100
Round output to 12-bits, AOUT15-4 and BOUT15-4,
zero lower bits.
101
Round output to 14-bits, AOUT15-2 and BOUT15-2,
zero lower bits.
110
Round output to 16-bits, AOUT15-0 and BOUT15-0.
111
Zero all outputs.
C0 C1 C2 C3 C4 C5 C6
X3,X2,X1,X0
Y(0) = X0(C0)+X1(C1)+X2(C2)+X3(C3)+X4(C4)+X5(C5)+X6(C6)
Y(1) = X1(C0)+X2(C1)+X3(C2)+X4(C3)+X5(C4)+X6(C5)+X7(C6)
Y(2) = X2(C0)+X3(C1)+X4(C2)+X5(C3)+X6(C4)+X7(C5)+X8(C6)
Y(3) = X3(C0)+X4(C1)+X5(C2)+X6(C3)+X7(C4)+X8(C5)+X9(C6)
...,Y1,Y0
2
..,Y4,Y2,Y0
Indicates samples discarded by decimation process
FIGURE 5. TRANSVERSAL IMPLEMENTATION OF
DECIMATE BY 2 HALFBAND FILTER
C0 C2 C4 C6
...,X4,X2,X0
Y(0) = X0(C0)+X1(C1)+X2(C2)+X3(C3)+X4(C4)+X5(C5)+X6(C6)
Y(1) = X2(C0)+X3(C1)+X4(C2)+X5(C3)+X6(C4)+X7(C5)+X8(C6)
..,Y2,Y1,Y0
C1 C3 C5
R
E
G
ODD TAP FILTER
EVEN TAP FILTER
...,X5,X3,X1
+
FIGURE 6. POLYPHASE IMPLEMENTATION OF DECIMATE
BY 2 HALFBAND FILTER
HSP43216