By Artur Krukowski
This e-book offers the research of particular form of IIR polyphase clear out constructions mixed with frequency transformation ideas, and their program for customized fixed-point implementation. that includes a wealth of layout and research concepts, it comprises enough introductory fabric to let non-experts to appreciate the themes.
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Extra info for DSP system design : complexity reduced IIR filter implementation for practical applications
4 Example 2 converting a real prototype to real sections This example demonstrated the decomposition of the real prototype filter from previous example into equal-order sections, but this time forced to be real ones. This was achieved by cancelling all imaginary parts of calculated branch filter numerator coefficients. Peak error values resulting from the performed calculations are summarised in Table 1-5 and the full-band error profiles shown in Figure 1-29. 1. Polyphase IIR Filters 41 For the real decomposition case it is essential to pair (recombine) conjugate roots of the prototype filter into each section of the decomposed structure in order to achieve small errors of the overall decomposition.
Then the new IIR filter numerator B’(z) coefficients can be calculated as the remainder of the division of B(z) by A(z) of original filter transfer function (49). Another way of incorporating of the FIR part of the filter numerator is to place it into an extra parallel path, as shown in Figure 1-24(b). 1 IIR-to-IIR decomposition For IIR-to-IIR decomposition coefficients of the structure can be calculated directly by comparing transfer functions of the general form of an IIR filter with the one of the decomposed structure, (49), as in Figure 1-23.
4 Converting general IIR filter into parallel structure Parallel realization of filtering tasks is gaining importance as the parallel processing capability of DSP engines is enhanced and advanced. However, there is relatively little methodology developed in the field for tackling the problem of converting from direct-form IIR transfer functions to parallel equivalents. g. -, ) approaches the task from another direction, composing the overall IIR filter as a combination of elementary IIR filters.