Name
Abstract | ||
|---|---|---|
The elimination of zero-input limit cycles in direct form filter sections using either a rounding or a magnitude truncation fixed-point quantizer is considered. The well-known criterion of Chang is reformulated for second-order filter sections in a more practical form using the bilinear transformation. This enables graphical interpretation and quantitative analysis of the possible error feedback solutions for different pole locations.The synthesis of limit-cycle-free error feedback for second-order filter sections is addressed in detail and several solutions are proposed. The error feedback coefficients are constrained to power-of-two values or to symmetric values so that the implementation is efficient, e.g. with signal processors. Different limit-cycle-free solutions are discussed with design examples and their round-off noise properties are compared.The absence of limit cycles is related to the round-off noise properties of the filter section. The main conclusion of the paper is that when the EF coefficients are appropriately chosen, low round-off noise and the absence of limit cycles can always be accomplished at the same time. A particularly close correlation between limit cycles and round-off noise is demonstrated with a rounding quantizer: a limit-cycle-free implementation always guarantees low round-off noise. For most complex conjugate pole locations the converse relation also holds, i.e. low round-off noise implies the absence of limit cycles. |
Year | DOI | Venue |
|---|---|---|
1993 | 10.1002/cta.4490210204 | INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS |
Keywords | Field | DocType |
limit cycle,digital filter | Digital filter,Floating point,Control theory,Round-off error,Limit cycle,Electronic engineering,Rounding,Bilinear transform,Recursive filter,Quantization (signal processing),Mathematics | Journal |
Volume | Issue | ISSN |
21 | 2 | 0098-9886 |
Citations | PageRank | References |
1 | 0.52 | 3 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Timo I. Laakso | 1 | 129 | 34.24 |