Name
Abstract | ||
|---|---|---|
This paper considers finite-length impulse response (FIR) filter approximation of differentiators and integrators, collectively called differintegrators. The paper introduces and compares three different FIR filter structures for this purpose, all of which are optimized in the minimax sense using iterative reweighted l1-norm minimization. One of the structures is the direct-form structure, but featuring equal-valued taps and zero-valued taps, the latter corresponding to sparse filters. The other two structures comprise two subfilters in parallel and cascade, respectively. In their basic forms, nothing is gained by realizing the filters in parallel or in cascade, instead of directly. However, as the paper will show, these forms enable substantial further complexity reductions, because they comprise symmetric and antisymmetric subfilters of different orders, and also features additional equal-valued and zero-valued taps. The cascade structure employs a structurally sparse filter. The additional sparsity, as well as tap equalities, are for all three structures found automatically in the design via the l1-norm minimization. Design examples included reveal feasible multiplication complexity savings of more than 50% in comparison with regular (unconstrained) direct-form structures. In addition, an example shows that the proposed designs can even have lower complexity than existing infinite-length impulse response filter designs. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/JETCAS.2013.2273853 | Emerging and Selected Topics in Circuits and Systems, IEEE Journal |
Keywords | Field | DocType |
FIR filters,approximation theory,integrated circuits,iterative methods,minimisation,FIR filter approximation,FIR filter structures,antisymmetric subfilters,complexity reductions,differintegrators,direct-form structure,equal-valued taps,finite-length impulse response filter approximation,fractional-order differentiators,fractional-order integrators,infinite-length impulse response filter designs,iterative reweighted l1-norm minimization,structurally sparse filter,symmetric subfilters,zero-valued taps,$ell_{1}$ -norm minimization,Differentiators,finite-length impulse response (FIR) filters,fractional-order systems,integrators,low complexity | Impulse response,Iterative method,Computer science,Differentiator,Approximation theory,Antisymmetric relation,Electronic engineering,Multiplication,Cascade,Finite impulse response | Journal |
Volume | Issue | ISSN |
3 | 3 | 2156-3357 |
Citations | PageRank | References |
7 | 0.55 | 15 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Håkan Johansson | 1 | 505 | 65.36 |