HSP43216 Datasheet, PDF (15/19 Pages) Intersil Corporation – Halfband Filter

INPUT SIGNAL SPECTRUM
-f_S
0
f_S
2f_S
INTERPOLATED SIGNAL
FILTER PASSBAND
-f^’S/2
0
f^’S/2
f^’S
UPCONVERTED SIGNAL
-f^’S/2
0
f^’S/2
f^’S
REAL OUTPUT
HSP43216
HALFBAND FILTER
..R1,R0
2
..R1,0,R0,0
C0 C1 C2 C3 C4 C5 C6
HALFBAND FILTER
COS((n+1)π/2)
0,1,0,-1...
..,Y2,Y1,Y0
+
..I1,I0
..I1,0,I0,0
2
C0 C1 C2 C3 C4 C5 C6
-1,0,1,0...
SIN(-(n+1)π/2)
Y(0) = 0(0(C0)+R0(C1)+0(C2)+R1(C3)+0(C4)+R2(C5)+0(C6))+
-1(0(C0)+I0(C1)+0(C2)+I1(C3)+0(C4)+I2(C5)+0(C6))
Y(1) = 1(R0(C0)+0(C1)+R1(C2)+0(C3)+R2(C4)+0(C5)+R3(C6))+
0(I0(C0)+0(C1)+I1(C2)+0(C3)+I2(C4)+0(C5)+I3(C6))
Y(2) = 0(0(C0)+R1(C1)+0(C2)+R2(C3)+0(C4)+R3(C5)+0(C6))+
1(0(C0)+I1(C1)+0(C2)+I2(C3)+0(C4)+I3(C5)+0(C6))
Y(3) = -1(R1(C0)+0(C1)+R2(C2)+0(C3)+R3(C4)+0(C5)+R4(C6))+
0(I1(C0)+0(C1)+I2(C2)+0(C3)+I3(C4)+0(C5)+I4(C6))
-f^’S/2
0
f^’S/2 f^’S
f_S = INPUT SAMPLE RATE
f^’S = INTERPOLATED SAMPLE RATE, 2f_S
FIGURE 18. QUADRATURE TO REAL CONVERSION
The Quadrature to Real Conversion mode is most easily
understood by first considering an implementation using a
7 tap transversal filter as shown in Figure 19. By examining
the combination of interpolation, filtering, and up
conversion it is seen that a particular output is only
dependent on the sum-of-products for the even indexed
samples and coefficients or the sum-of-products for the
odd indexed samples and coefficients. This computational
partitioning allows the dual interpolation filters required in
this mode to be realized using the same polyphase filter
structure used in the other modes. A functional block
diagram of the polyphase implementation for Quadrature to
Real Conversion mode is shown in Figure 20. In this
implementation, the real and imaginary components of a
complex input stream drive the even and odd tap filters.
The output of each filter is then modulated by the non-zero
mix factors and multiplexed into a single real output stream.
FIGURE 19. QUADRATURE TO REAL CONVERTER USING
TRANSVERSAL FILTERS
EVEN TAP FILTER
..R1,R0
..I1,I0
C0 C2 C4 C6
ODD TAP FILTER
1,-1,1,-1,..
COS LO
M _..,Y2,Y1,Y0
U
X
R
E
G
C1 C3 C5
-1,1,-1,1..
SIN LO
Y(0) = -1(I0(C1)+I1(C3))+I2(C5))
Y(1) = 1(R0(C0)+R1(C2)+R2(C4))+R3(C6))
Y(2) = 1(I1(C1)+I2(C3)+I3(C5))
Y(3) = -1(R1(C0)+R2(C2)+R3(C4)+R4(C6))
FIGURE 20. POLYPHASE IMPLEMENTATION OF
QUADRATURE TO REAL CONVERTER
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