Half-band FIR Filter - 7.2 English

FIR Compiler (PG149)

Document ID
PG149
Release Date
2022-10-26
Version
7.2 English

This Figure shows the general frequency response for a half-band filter.

Figure 3-19: Half-band Filter Magnitude Frequency Response

X-Ref Target - Figure 3-19

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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

inset_6_pg149.jpg

The passband and stopband ripple, inset_7_pg149.jpg and inset_8_pg149.jpg respectively, are equal inset_9_pg149.jpg . 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.

Figure 3-20: Half-band Filter Impulse Response

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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 .

Figure 3-21: Half-band Filter Impulse Response

X-Ref Target - Figure 3-21

half_band_fir_pg32_pg149.jpg

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 .