# Synthesis and Realization of High-Speed Recursive Digital Filters

Sammanfattning: Recursive digital filters restrict the sample frequency at which an implementation of the filters can operate. This bound is determined by the ratio between the number of delay elements and the operation latency in the recursive loops of the filters. The bound can be increased by using recursive filters for which the maximal sample frequency is higher than for conventional filters, so called high-speed filters. Such filters are also candidates for low power consumption since excess speed may be converted into low power consumption through power supply voltage scaling techniques. High-speed recursive digital filters can be obtained by increasing the number of delay elements and/or decreasing the latency in the recursive loops of the filters. In this thesis we introduce new recursive digital filters to this end. These are based on two different approaches. In the first one, the filters are derived by using frequency masking techniques. Here, the filter structures make use of periodic model filters and, possibly periodic, masking filters. Using these techniques, the recursive parts automatically contain a number of delay elements in the loops which increases the maximal sample frequency substantially. Earlier, only some special cases of these techniques have been considered for narrow-band and wideband filtering. We generalize one of these techniques and extend them to arbitrary bandwidths and to interpolation and decimation filters, and Hilbert transformers. For these techniques both IIR and FIR filters are used. We also extend the techniques to the use of only IIR filters, the motivation being that this can reduce the arithmetic complexity. One advantage of frequency masking techniques is that they are not based upon pole-zero cancellations, which is inherent in and a potential drawback of algorithm transformation techniques.In the second approach the structures are composed of identical allpass subfilters that are interconnected via multipliers. The maximal sample frequency is increased since the coefficient sensitivity of the allpass subfilters is reduced, implying a reduced operational latency in the recursive loops. This technique has earlier been used for single-rate filters. We extend it to interpolation and decimation filters, filter banks with perfect magnitude reconstruction, and Hilbert transformers.All filter structures introduced in this thesis make use of allpass filters, possibly in combination with FIR filters. An advantage of this is that robust filters can be obtained by using wave digital filters (WDFs) for the allpass filters. There is also a large freedom to choose structures for both the allpass and FIR filters that are suitable for the problem at hand.

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