This Figure shows the general frequency response for a half-band filter.
The magnitude frequency response is symmetrical about quarter sample frequency p /2 radians. The sample rate is normalized to 2 p radians/sec. The passband and stopband frequencies are positioned such that
The passband and stopband ripple,
and
respectively, are equal
. These properties are reflected in the filter impulse response
.
It can be shown (in
Digital Signal Processing in Communication Systems
[Ref 5]
) that approximately half of the filter coefficients are zero for an odd number of taps, as shown in
This Figure
for an 11-tap half-band filter.
The interleaved zero values in the coefficient data can be exploited to realize an efficient realization, as shown in This Figure . Note that the FIR Compiler also exploits coefficient symmetry for half-band filter structures, although this is not shown in This Figure .
The half-band filter selection in the compiler is intended for this purpose. This filter is available in the Coefficient Structure field of the user interface.
IMPORTANT: You must supply the complete list of filter coefficients, including the 0 value samples, when using the half-band filter.
The filter coefficient file format is discussed in greater detail in Filter Coefficient Data .