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Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters
Abstract
A new method of designing linear-phase FIR filters is proposed by minimizing a quadratic measure of the error in the passband and stopband. The method is based on the computation of an eigenvector of an appropriate real, symmetric, and positive-definite matrix. The proposed design procedure is general enough to incorporate both time- and frequency-domain constraints. For example, Nyquist filters can be easily designed using this approach. The design time for the new method is comparable to that of Remez exchange techniques. The passband and stopband errors in the frequency domain can be made equiripple by an iterative process, which involves feeding back the approximation error at each iteration. Several numerical design examples and comparisons to existing methods are presented, which demonstrate the usefulness of the present approach.
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Cited by
Splitting the unit delay [FIR/all pass filters design]
Laakso, T. I., Valimaki, V., Karjalainen, M., & Laine, U. K. (1996) · IEEE Signal Processing Magazine · doi:10.1109/79.482137 · Cited by 1,168
Methodology of Resonant Equiangular Composite Quantum Gates
Low, G. H., Yoder, T. J., & Chuang, I. L. (2016) · Physical Review X · doi:10.1103/physrevx.6.041067 · Cited by 159
“Efficient algorithms for other optimality criteria such as least squares are also available [46,47].”
Background
Metadata
- Authors
- Vaidyanathan, P., & Nguyen, T.
- Venue
- IEEE Transactions on Circuits and Systems
- Published
- 1987-01
- Volume
- 34
- Issue
- 1
- Pages
- 11-23
- ISSN
- 0098-4094 (ISSN-L)
- OpenAlex
- W2161386327
- Cited by
- 341
- References
- 0
- FWCI
- 8.87
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters. https://app.cochat.ai/papers/10.1109/tcs.1987.1086033
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- Vaidyanathan, P., & Nguyen, T. (1987). Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters. IEEE Transactions on Circuits and Systems. https://doi.org/10.1109/tcs.1987.1086033
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