Efficient Computation of Time-Index Powered Weighted Sums Using Cascaded Accumulators
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912949923217408 |
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| author | Linares, Deijany Rodriguez Moryakova, Oksana Johansson, Håkan |
| author_facet | Linares, Deijany Rodriguez Moryakova, Oksana Johansson, Håkan |
| contents | This letter presents a novel approach for \mbox{efficiently} computing time-index powered weighted sums of the form $\sum_{n=0}^{N-1} n^{K} v[n]$ using cascaded accumulators. Traditional direct computation requires $K{\times}N$ general multiplications, which become prohibitive for large $N$, while alternative strategies based on lookup tables or signal reversal require storing entire data blocks. By exploiting accumulator properties, the proposed method eliminates the need for such storage and reduces the multiplicative cost to only $K{+}1$ constant multiplications, enabling efficient real-time implementation. The approach is particularly useful when such sums need to be efficiently computed in sample-by-sample processing systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Computation of Time-Index Powered Weighted Sums Using Cascaded Accumulators Linares, Deijany Rodriguez Moryakova, Oksana Johansson, Håkan Signal Processing Data Structures and Algorithms Numerical Analysis This letter presents a novel approach for \mbox{efficiently} computing time-index powered weighted sums of the form $\sum_{n=0}^{N-1} n^{K} v[n]$ using cascaded accumulators. Traditional direct computation requires $K{\times}N$ general multiplications, which become prohibitive for large $N$, while alternative strategies based on lookup tables or signal reversal require storing entire data blocks. By exploiting accumulator properties, the proposed method eliminates the need for such storage and reduces the multiplicative cost to only $K{+}1$ constant multiplications, enabling efficient real-time implementation. The approach is particularly useful when such sums need to be efficiently computed in sample-by-sample processing systems. |
| title | Efficient Computation of Time-Index Powered Weighted Sums Using Cascaded Accumulators |
| topic | Signal Processing Data Structures and Algorithms Numerical Analysis |
| url | https://arxiv.org/abs/2509.15069 |