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HSP43216

Halfband Filter

Intersil 

HSP43216

For added flexibility, a spectrally reversed version of the

above process may be realized by configuring the Down

Convert processor to impart a positive fS/4 spectral shift on

the input signal. This has the effect of centering the lower

sideband of the input signal at DC and is achieved by

reversing the sign of the sine term in the quadrature mix as

shown below:

x(n)ej(πn ⁄ 2) = x(n) cos(πn ⁄ 2) + jx(n) sin(πn ⁄ 2)

(EQ. 2)

The direction of the spectral shift imparted by the Down

Convert Processor is set by the Upper Sideband/ Lower

Sideband control input, USB/LSB. When this input is high, a

-fS/4 spectral shift is used to center the input signal’s upper

sideband at DC. When asserted low, a spectral shift of fS/4

is used to center the lower sideband at DC. The SYNC

control input may be used to synchronize the incoming data

stream with the zero degree phase of the complex

exponential as described in the Operational Modes section.

The real and imaginary sample streams generated by the

down convert operation are passed to the Halfband Filter

block on the upper and lower processing legs respectively.

The Down Convert Processor is only active in Down Convert

and Decimate Mode, MODE1-0 = 10. In the other modes,

the data on the upper and lower processing legs pass

unaltered.

67-Tap Halfband Filter Processor

The processing required to implement the 67-Tap Halfband

filter is distributed across two polyphase branches

comprised of even and odd tap filters as shown in Figure 1.

The Even Tap Filter performs a filtering operation using the

even indexed coefficients (even phase) of the halfband filter.

The Odd Tap Filter uses the odd indexed coefficients (odd

phase) of the halfband filter. NOTE: the odd tap filter’s

processing reduces to a delay and scale operation since

the center tap is the only non-zero odd tap for a

halfband filter. Together the polyphase filters perform the

sum of-products required to implement the 67-tap halfband

filter in an architecture capable of supporting a variety of

operational modes. The frequency response of the halfband

filter is given graphically in Figure 2 and in tabular form in

Table 3. Table 2 shows the different modes and the related

frequency with which the spectra in Figure 2 is normalized.

TABLE 2. NORMALIZED FREQUENCY vs MODE

MODE

fS

Decimate by Two

CLK

Interpolate by Two

CLK/2

Down Convert and Decimate

CLK

Quadrature to Real

CLK/2

The polyphase implementation of the halfband filter

provides the flexibility to realize a variety of filter

configurations. In Decimate by Two Mode, the outputs of

the each polyphase branch are summed to yield the filter

output. In Interpolate by Two mode, the polyphase filters

produce independent outputs which are multiplexed into a

single sample stream at the interpolated data rate. In the

Up Convert and Down Convert Modes, the polyphase

branches filter the real and imaginary components of a

complex sample stream with the equivalent of identical 67-

Tap Halfband Filters. For these modes, the real component

is processed by the Even Tap filter and the imaginary

component is processed by the Odd Tap filter. The

Operational Modes Section provides further details

regarding the data flow and operation of the Filter

Processor for the various modes.

0

-20

-40

-60

-80

-100

-120

0

fS/8

fS/4

3fS/8

NORMALIZED FREQUENCY

FS/2

FIGURE 2. FREQUENCY RESPONSE OF 67-TAP HALFBAND

FILTER

As a standard DSP term, group delay is defined as the time

it takes to obtain valid filtered data given a certain input

pattern. Both the Even Tap and Odd Tap filters have an

identical group delay of 19 clocks relative to the operating

mode of the halfband. The group delay has been specified in

the data flow diagrams following this section. The delay

clocks equal CLK when INT/EXT = 0 and CLK/2 when

INT/EXT = 1.

NOTE: Pipeline delay specifies the time it takes for bits to

toggle at the output given a certain input pattern. The Odd tap

filter has a pipeline delay of 19 CLKs with respect to the

operating mode because it consists of only the center tap of the

67-tap halfband. The Even tap filter has a pipeline delay of 2-35

CLKs with respect to the operating mode.

5

FN3365.10

October 6, 2008

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