What are the useful techniques in the process of FIR filter?

　　FIR tricks center on two things 1) not calculating things that don't need to be calculated, and 2) "faking" circular buffers in software.

　　How to skip unnecessary calculations?

　　First, if your filter has zero-valued coefficients, you don't actually have to calculate those taps; you can leave them out. A common case of this is "half-band" filter, which have the property that every-other coefficient is zero.

　　Second, if your filter is "symmetric" (linear phase), you can "pre-add" the samples which will be multiplied by the same coefficient value, prior to doing the multiply. Since this technique essentially trades an add for a multiply, it isn't really useful in DSP microprocessors which can do a multiply in a single instruction cycle. However, it is useful in ASIC implementations (in which addition is usually much less expensive than multiplication); also, some newer DSP processors now offer special hardware and instructions to make use of this trick.

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