{"ID":2862607,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.25931","arxiv_id":"2509.25931","title":"Closed-Form Least-Squares Design of Fast-Convolution Based Variable-Bandwidth FIR Filters","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2509.25931","url_pdf":"https://arxiv.org/pdf/2509.25931v1","authors":"[\"Oksana Moryakova\",\"Håkan Johansson\"]","published":"2025-09-30T08:24:28Z","proceeding":"eess.SP","tasks":"[\"eess.SP\"]","methods":"[]","has_code":false}