Filter Structures and Filter Coefficients (Digital Filter Design Toolkit)
June 2008
NI Part Number:
371988B-01
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Different filter structures use different groups of filter coefficients. The LabVIEW Digital Filter Design Toolkit categorizes filter coefficients into three groups: zeroes, poles, and gain. For example, FIR filter coefficients, IIR forward coefficients, and lattice ladder coefficients correspond to zeroes. IIR reverse coefficients and lattice reflection coefficients, excluding lattice MA reflection coefficients, correspond to poles. Different groups of filter coefficients have different data ranges. Therefore, in addition to the gain, the Digital Filter Design Toolkit provides the following two quantizers for these groups: coefficients a/k and coefficients b/v.
When you quantize the filter coefficients, configure the appropriate quantizer according to the filter structure type. The following table lists the filter structures, the filter coefficients, and the corresponding quantizers.
| Filter Structure | Filter Coefficients and the Corresponding Quantizer |
|---|---|
| FIR structures | All FIR filter coefficients correspond to the coefficients b/v quantizer. |
| IIR Direct Form structures | The reverse coefficients correspond to the coefficients a/k quantizer. The forward coefficients correspond to the coefficients b/v quantizer. |
| IIR Cascaded Second-Order Sections Form structures | |
| Lattice Allpass structures | The reflection coefficients correspond to the coefficients a/k quantizer. |
| Lattice AR structures | |
| Lattice MA structures | |
| Lattice ARMA structures | The reflection coefficients correspond to the coefficients a/k quantizer. The ladder coefficients correspond to the coefficients b/v quantizer. |