There are three basic second-order-section (SOS) structures for infinite impulse response (IIR) filters in DSP applications, form I, form II, and transposed form I. To determine which structure creates the best performance in terms of quantization noise level, instruction cycles, and memory locations, noise models for these three structures are presented. The structures can be combined in cascade or in parallel to implement more complicated filters. Noise models for cascade and parallel form connection are discussed. In order to obtain high signal-to-noise ratios on the filter output, a general filter structure with double precision internal states is designed to achieve more than 96-dB signal-to-noise ratio. Real tests were performed, and test results show that the form I structure is the best second-order section, and the parallel form connection for high-order IIR filters is superior to the cascade form.
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