arXiv:2607.14054v2 Announce Type: replace Abstract: Recursive (IIR) filters realized as cascaded second-order sections (biquads) offer both design generality and robustness against coefficient quantization. However, their inherent sample-to-sample feedback dependency poses a fundamental obstacle to parallel computation. This paper reformulates the biquad difference equation as a banded block-Toeplitz linear system. It relies on a stride-$N$ permutation that maps a group of $NL$ samples into a block-tridiagonal structure whose entries are scalar multiples of identity and shift matrices. Within this framework, two data-parallel algorithms are developed which, to the best of our knowledge, are the fastest, single-core IIR filter implementations reported to date. A partial LU (PH) factorization preserves the sparse block structure and a cyclic reduction reduces the sequential dependency depth from $\mathcal{O}(N)$ to $\mathcal{O}(\log_2 N)$. For a cascade of $K$ biquads, the intermediate permutations between successive sections cancel exactly, so that only a single pair of permutations is required for the entire cascade. Exact block-level operation counts are derived for every algorithmic stage and validated against cycle-accurate measurements on three micro-architectures supporting AVX2 SIMD instructions. Experimental results for a 16th-order system show that the proposed multi-block algorithms reduce clock cycles per sample by up to $10\times$ compared to scalar filtering, with both algorithms scaling favorably on newer architectures. On a single Meteor Lake core, cyclic reduction achieves approximately 616 MS/s---four times the throughput of Intel's vendor-tuned IPP library.