Filter Symmetry - 7.2 English

FIR Compiler (PG149)

Document ID

PG149

Release Date

2022-10-26

Version

7.2 English

The impulse response for many filters possesses significant symmetry. This symmetry can generally be exploited to minimize arithmetic requirements and produce area-efficient filter realizations. This Figure shows the impulse response for a 9-tap symmetric FIR filter.

Figure 3-13: Symmetric FIR – Odd Number of Terms
X-Ref Target - Figure 3-13

Instead of implementing this filter using the architecture shown in This Figure , the more efficient signal flow-graph in This Figure can be used. In general, the former approach requires N multiplications and ( N -1) additions. In contrast, the architecture in This Figure requires only [N/2] multiplications and approximately N additions. This significant reduction in the computation workload can be exploited to generate efficient filter hardware implementations.

Figure 3-14: Exploiting Coefficient Symmetry – Odd Number of Filter Taps
X-Ref Target - Figure 3-14

Coefficient symmetry for an even number of terms can be exploited as shown in This Figure .

Figure 3-15: Exploiting Coefficient Symmetry – Even Number of Filter Taps
X-Ref Target - Figure 3-15

This Figure shows the impulse response for a negative, or odd, symmetric filter.

Figure 3-16: Negative Symmetric Impulse Response
X-Ref Target - Figure 3-16

This symmetry is exploited in a manner similar to that shown in This Figure and This Figure . In this case, the middle layer of adders are replaced by subtracters, as shown in This Figure .

Figure 3-17: FIR Architecture Exploiting Negative Symmetry
X-Ref Target - Figure 3-17

Filter coefficient symmetry is inferred by the core GUI from the coefficient definition file. You can override this inferred value. When the structure is inferred, the inferred setting is displayed in the Summary page and in the ToolTip for the Coefficient Structure field.