Half-band FIR Filter - 7.2 English - PG149

The following figure shows the general frequency response for a half-band filter.

Figure 1. Half-band Filter Magnitude Frequency Response

The magnitude frequency response is symmetrical about quarter sample frequency π/2 radians. The sample rate is normalized to 2π radians/sec. The passband and stopband frequencies are positioned such that

The passband and stopband ripple, δ_p and δ_s respectively, are equal δ_p= δ_s . These properties are reflected in the filter impulse response. It can be shown (in Digital Signal Processing in Communication Systems that approximately half of the filter coefficients are zero for an odd number of taps, as shown in for an 11-tap half-band filter.

Figure 2. Half-band Filter Impulse Response

The interleaved zero values in the coefficient data can be exploited to realize an efficient realization, as shown in the following figure. The FIR Compiler also exploits coefficient symmetry for half-band filter structures, although this is not shown in the following figure.

Figure 3. Half-band Filter Impulse Response

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.

The filter coefficient file format is discussed in greater detail in Filter Coefficient Data.