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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.25931 |
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| _version_ | 1866911185745477632 |
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| author | Moryakova, Oksana Johansson, Håkan |
| author_facet | Moryakova, Oksana Johansson, Håkan |
| contents | This paper introduces a closed-form least-squares (LS) design approach for fast-convolution (FC) based variable-bandwidth (VBW) finite-impulse-response (FIR) filters. The proposed LS design utilizes frequency sampling and the VBW filter frequency-domain implementation using the overlap-save (OLS) method, that together offer significant savings in implementation and online bandwidth reconfiguration complexities. Since combining frequency-domain design and OLS implementation leads to a linear periodic time-varying (LPTV) behavior of the VBW filter, a set of the corresponding time-invariant impulse responses is considered in the proposed design. Through numerical examples, it is demonstrated that the proposed approach enables not only closed-form design of FC-based VBW filters with substantial complexity reductions compared to existing solutions for a given performance, but also allows the variable bandwidth range to be extended without any increase in complexity. Moreover, a way of reducing the maximum approximation error energy over the whole set of the time-invariant filters of the LPTV system is shown by introducing appropriate weighting functions in the design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Closed-Form Least-Squares Design of Fast-Convolution Based Variable-Bandwidth FIR Filters Moryakova, Oksana Johansson, Håkan Signal Processing This paper introduces a closed-form least-squares (LS) design approach for fast-convolution (FC) based variable-bandwidth (VBW) finite-impulse-response (FIR) filters. The proposed LS design utilizes frequency sampling and the VBW filter frequency-domain implementation using the overlap-save (OLS) method, that together offer significant savings in implementation and online bandwidth reconfiguration complexities. Since combining frequency-domain design and OLS implementation leads to a linear periodic time-varying (LPTV) behavior of the VBW filter, a set of the corresponding time-invariant impulse responses is considered in the proposed design. Through numerical examples, it is demonstrated that the proposed approach enables not only closed-form design of FC-based VBW filters with substantial complexity reductions compared to existing solutions for a given performance, but also allows the variable bandwidth range to be extended without any increase in complexity. Moreover, a way of reducing the maximum approximation error energy over the whole set of the time-invariant filters of the LPTV system is shown by introducing appropriate weighting functions in the design. |
| title | Closed-Form Least-Squares Design of Fast-Convolution Based Variable-Bandwidth FIR Filters |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2509.25931 |