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FIR filters offer several advantages over IIR filters
* They can easily be designed to be "linear phase" (and usually are). Put simply, linear-phase filters delay the input signal, but don’t distort its phase.
* They are simple to implement. On most DSP microprocessors, the FIR calculation can be done by looping a single instruction.
* They are suited to multi-rate applications. By multi-rate, we mean either "decimation" (reducing the sampling rate), "interpolation" (increasing the sampling rate), or both. Whether decimating or interpolating, the use of FIR filters allows some of the calculations to be omitted, thus providing an important computational efficiency. In contrast, if IIR filters are used, each output must be individually calculated, even if it that output will discarded (so the feedback will be incorporated into the filter).
* They have desireable numeric properties. In practice, all DSP filters must be implemented using "finite-precision" arithmetic, that is, a limited number of bits. The use of finite-precision arithmetic in IIR filters can cause significant problems due to the use of feedback, but FIR filters have no feedback, so they can usually be implemented using fewer bits, and the designer has fewer practical problems to solve related to non-ideal arithmetic.
* They can be implemented using fractional arithmetic. Unlike IIR filters, it is always possible to implement a FIR filter using coefficients with magnitude of less than 1.0. (The overall gain of the FIR filter can be adjusted at its output, if desired.) This is an important considertaion when using fixed-point DSP's, because it makes the implementation much simpler.
* Completely constant group delay throughout the frequency spectrum. * Complete stability at all frequencies regardless of the size of the filter.
* Can be implemented with fast convolution
* Relatively insensitive to quantization
FIR filters also come with some disadvantages as well:
* The frequency response is not as easily defined as it is with IIR filters
* The number of states required to meet a frequency specification may be far larger than that required for IIR filters.
* FIR filters sometimes have the disadvantage that they require more memory and/or calculation to achieve a given filter response characteristic
* Also, certain responses are not practical to implement with FIR filters.
Sin(x)/x Compensation
To compensate for Sin(X)/X due to sampling, the option exists to insert an approximate X/Sin(X) into the FIR Z transform to offset the effect of sampling. Filter Solutions offers 1st, 2nd, and 3rd order compensations that maintain the FIR characteristic of the filter and approximate X/Sin(X) that are valid for frequencies up to half the sample rate. You may view the effect of this compensation by viewing the magnitude response of a high pass or band stop filter at half the sample rate. The graph below shows Filter Solutions' 3rd order compensation against the ideal compensation
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