Half-band Filter - 7.2 English

FIR Compiler (PG149)

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

As previously described, every second filter coefficient for a half-band filter with an odd number of terms is zero. When specifying the filter coefficient data for this filter class, the zero value entries must be included in the coefficient file. For example, the filter coefficient file that specifies the filter impulse response in This Figure is shown in This Figure .

Figure 3-43: 11-Tap Half-band Filter Impulse Response

X-Ref Target - Figure 3-43

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Figure 3-44: Coefficient File for the Half-band Filter Impulse Response

X-Ref Target - Figure 3-44

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The filter coefficient set is parsed by the FIR Compiler . If either the alternating zero entries are absent or the coefficient set is not even-symmetric, this condition is flagged as an error and the filter is not generated. A dialog box is presented to indicate the issue under these circumstances.

Technically, the zero-valued entries for a half-band filter can occur at the filter impulse response extremities as shown in This Figure . However, observe that these values do not contribute to the result.

Figure 3-45: 9-Tap Half-band Filter Impulse Response

X-Ref Target - Figure 3-45

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This condition is detected when the filter is specified. If the number of taps is such that the zero-valued coefficients form the first and last entry of the impulse response, the filter length is reported as an invalid value. The number of taps N for a half-band filter must obey N=3 + 4n, where n=0,1,2,3,…. For example, a half-band filter can have 11, 15, 19, and 23 taps, but not 9, 13, 17, or 21 taps.