Digital computation of the fractional Fourier transform
Open accessAbstract
An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time. A definition for the discrete fractional Fourier transform that emerges from our analysis is also discussed.
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The Wigner distribution of a chirp multiplication and of a chirp convolution for an f under consideration will be compact and contained in a circle with radius Δ, twice the original support, as explained in appendix A of Ozaktas et al. (1996).
“As explained in the appendix A of [16]. The Wigner distribution of a chirp multiplication and of a chirp convolution for an f under consideration, will be compact and contained in a circle with radius ∆. That is twice the original support.”
From Computation of the fractional Fourier transform (2004) · cites this paper as [16]
Appendix A says chirp multiplication preserves the compactness of the Wigner distribution and gives a bandwidth bound of up to twice the original; it says a similar argument holds for chirp convolution. But it describes the original circle by its diameter, not its radius, and does not establish that both resulting distributions lie in a circle of radius Δ. Its practical definition of compactness also allows a sufficiently large percentage of energy within the circle rather than requiring strict containment. (LLM, conf=0.88)
Experimental — accuracy not yet measuredThe bandwidth after chirp multiplication can be doubled, so that the number of samples must be doubled to avoid aliasing, as explained in appendix A of Ozaktas et al. (1996).
“As explained in the appendix A of [16], the bandwidth after chirp multiplication can be doubled, so that we need to double the number of samples to avoid aliassing.”
From Computation of the fractional Fourier transform (2004) · cites this paper as [16]
The matlab routine fracF implements the algorithm described in Ozaktas et al. (1996) and can be found on the book's web page.
“First there is the matlab routine fracF , implementing the algorithm described in [16] (see also [17, Section 6.7]). It can we found on the web page [12].”
From Computation of the fractional Fourier transform (2004) · cites this paper as [16]
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“The most representative one is the decomposition fast algorithm proposed in [29], where the definition of FrFT is rewritten as:”
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- Authors
- Ozaktas, H. M., Arikan, O., Kutay, M. A., & Bozdagt, G.
- Affiliations
- Bilkent University (TR)
- ORCID
- Kutay, M.A.
- Venue
- IEEE Transactions on Signal Processing
- Published
- 1996-09
- Volume
- 44
- Issue
- 9
- Pages
- 2141-2150
- ISSN
- 1053-587X (ISSN-L)
- 1941-0476
- OpenAlex
- W2108710836
- Semantic Scholar
- d774b8b767eb53873e0dd0ea4bfaa7744fabcb31
- Cited by
- 1,187
- References
- 41
- Citations by year
- 2026: 40 · 2025: 37 · 2024: 71 · 2023: 51 · 2022: 50 · 2021: 45 · 2020: 55 · 2019: 55 · 2018: 58 · 2017: 57 · 2016: 42 · 2015: 47 · 2014: 53 · 2013: 45 · 2012: 61
- FWCI
- 26.76
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Licence
- Locations
- IEEE Transactions on Signal Processing (publishedVersion)
- Bilkent University Institutional Repository (Bilkent University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Electrical Measurement Techniques
- Keywords
- fractional Fourier transform, discrete fractional Fourier transform, time-bandwidth product, computational complexity
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