Discrete Mathematics for ComputingDSP System Design presents the investigation of special type of IIR polyphase filter structures combined with frequency transformation techniques used for fast, multi-rate filtering, and their application for custom fixed-point implementation. Detailed theoretical analysis of the polyphase IIR structure has been presented for two and three coefficients in the two-path arrangement. This was then generalized for arbitrary filter order and any number of paths. The use of polyphase IIR structures in decimation and interpolation is being presented and performance assessed in terms of the number of calculations required for the given filter specification and the simplicity of implementation. Specimen decimation filter designs to be used in Sigma-Delta lowpass and bandpass A/D converters are presented which prove to outperform other traditional approaches. New frequency transformation types have been suggested for both real and complex situations. A new exact multi-point frequency transformation approach for arbitrary frequency choice has been suggested and evaluated. Applying such transformations to the existing filter allows to change their frequency response in an intuitive manner without the need of re-designing them, thus simplifying the designer's job when the specification changes during the prototyping and testing. A new bit-flipping' algorithm has been developed to aid in filter design where the coefficient word length is constraint. Also, the standard Downhill Simplex Method (floating-point) was modified to operate with the constrained coefficient word length. Performance of both these advances is being evaluated on a number of filter cases. Novel decimation and interpolation structures have been proposed, which can be implemented very efficiently. These allow an arbitrary order IIR anti-aliasing filter to operate at the lower rate of the decimator/interpolator. Similar structures for polyphase IIR decimator/interpolator structures are being discussed too. A new approach to digital filter design and implementation has been suggested which speeds-up silicon implementation of designs developed in Matlab. The Simulink block description is converted automatically into a bit-to-bit equivalent VHDL description. This in turn can be compiled, simulated, synthesized and fabricated without the need to go through the design process twice, first algorithmic/structural design and then the implementation. The book is full of design and analysis techniques. It contains sufficient introductory material enabling non-expert readers to understand the material given in it. DSP System Design may be of interest to graduate students, researchers, and professionals circuit designers, who would require fast and low-complexity digital filters for both single and multi-rate applications, especially those with low-power specification. |
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... theorem . = Suppose the theorem is true for all trees with fewer than p vertices . Let T be any tree with p vertices . Choose any edge e = ( x , y ) of T. The graph T { e } is not connected . For if it were , there would be a path P ( x ...
... theorems . Theorem 9.2 Let the set A be partitioned into cells A1 , A2 , A. Then : n ( A ) = n ( A1 ) + n ( A2 ) + ... + n ( As ) The theorem is sometimes called the ' rule of addition ' . It may be proved by mathematical induction on s .
... Theorem 10.6 Let p be an element of a finite group ( G , □ ) and let n , the number of elements in G , satisfy n ... theorem 10.4 part 2 = pb □ ( pa ) -1 definition 10.14 = pb ( pb ) -1 argument above = definition 10.7 also 0 < a < b ...
Contents
Graphs and Trees | 8 |
Numbers in Different Bases Real Numbers | 17 |
Sets Functions and Relations | 41 |
Copyright | |
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