Implementation Structures for Recursive Digital Filters

This chapter introduces the four direct-form filter implementations, and discusses implementation of filters as parallel or series combinations of smaller filter sections. A careful study of filter forms can be important when numerical issues arise, such as when implementing a digital filter in a fixed-point processor. (The least expensive ``DSP chips'' use fixed-point numerical processing, sometimes with only a 16-bit word length in low-cost audio applications.) For implementations in floating-point arithmetic, especially at 32-bit word-lengths or greater, the choice of filter implementation structure is usually not critical. In matlab software, for example, one rarely uses anything but the filter function, which is implemented in double-precision floating point (typically 64 bits at the time of this writing, and more bits internally in the floating-point unit).