The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Fast Convolution using fermat number transforms with applications to digital filtering
Abstract
The structure of transforms having the convolution property is developed. A particular transform is proposed that is defined on a finite ring of integers with arithmetic carried out modulo Fermat numbers. This Fermat number transform (FNT) is ideally suited to digital computation, requiring on the order ofN \log Nadditions, subtractions and bit shifts, but no multiplications. In addition to being efficient, the Fermat number transform implementation of convolution is exact, i.e., there is no roundoff error. There is a restriction on sequence length imposed by word length but multi-dimensional techniques are discussed which overcome this limitation. Results of an implementation on the IBM 370/155 are presented and compared with the fast Fourier transform (FFT) showing a substantial improvement in efficiency and accuracy.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Gold, B., & Rader, C. M. (1969) · CERN Document Server (European Organization for Nuclear Research) · Cited by 940
An algorithm for computing the mixed radix fast Fourier transform
Singleton, R. (1969) · IEEE Transactions on Audio and Electroacoustics · doi:10.1109/tau.1969.1162042 · Cited by 539
The fast Fourier transform in a finite field
Pollard, J. M. (1971) · Mathematics of Computation · doi:10.1090/s0025-5718-1971-0301966-0 · Cited by 467
Effects of finite register length in digital filtering and the fast Fourier transform
Oppenheim, A. V., & Weinstein, C. J. (1972) · Proceedings of the IEEE · doi:10.1109/proc.1972.8820 · Cited by 305
Number Theory and Its History.
Pall, G., & Ore, O. (1949) · The American Mathematical Monthly · doi:10.2307/2304748 · Cited by 252
The Relationship Between Two Fast Fourier Transforms
Good, I. J. (1971) · IEEE Transactions on Computers · doi:10.1109/t-c.1971.223236 · Cited by 138
Fast one-dimensional digital convolution by multidimensional techniques
Agarwal, R. K., & Burrus, C. S. (1974) · IEEE Transactions on Acoustics Speech and Signal Processing · doi:10.1109/tassp.1974.1162532 · Cited by 131
Self-citationBlock realization of digital filters
Burrus, C. S. (1972) · IEEE Transactions on Audio and Electroacoustics · doi:10.1109/tau.1972.1162387 · Cited by 103
Self-citationAlgebraic theory of finite fourier transforms
Nicholson, P. J. (1971) · Journal of Computer and System Sciences · doi:10.1016/s0022-0000(71)80014-4 · Cited by 74
Cited by
Fast Algorithms for Signal Processing
Blahut, R. E. (2010) · doi:10.1017/cbo9780511760921 · Cited by 274
Metadata
- Authors
- Agarwal, R., & Burrus, C.
- Venue
- IEEE Transactions on Acoustics, Speech, and Signal Processing
- Published
- 1974-04
- Volume
- 22
- Issue
- 2
- Pages
- 87-97
- ISSN
- 0096-3518 (ISSN-L)
- OpenAlex
- W2113994308
- Cited by
- 295
- References
- 9
- FWCI
- 15.76
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Fast Convolution using fermat number transforms with applications to digital filtering. https://app.cochat.ai/papers/10.1109/tassp.1974.1162555
- The paper
- Agarwal, R., & Burrus, C. (1974). Fast Convolution using fermat number transforms with applications to digital filtering. IEEE Transactions on Acoustics, Speech, and Signal Processing. https://doi.org/10.1109/tassp.1974.1162555
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
