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9.2 Linear-Phase FIR Filters

    Type 1 - symmetric, odd length
    Type 2 - symmetric, even length
    Type 3 - antisymmetric, odd length
    Type 4 - antisymmetric, even length

Figure 9.2.1. Illustration of four types of impulse response symmetry.

Note additionally that a Type 3 filter must have h [(N-1)/2 ] = 0. Each filter type has unique frequency domain characteristics. Here we summarize these characteristics to guide the users in matching the filter type with the application [Mit98, Opp89]. A Type 1 filter may be used to implement any desired bandpass frequency response. The symmetry condition of a Type 2 filter requires that H()=0, and therefore it may not be used to define a highpass filter. Otherwise it may be used instead of Type 1 in cases where an even-length filter is preferable. In contrast, antisymmetric filters (Type 3 and 4) cannot be used to implement any sort of bandpass filter. They are the only choice, however, for designing FIR differentiators, which are an important class of filters (recall the discussion of edge detectors).