Fractional Fourier Sound Synthesis

Carlos Sing Long; Esteban Guti\'errez; Frederic Font; Rodrigo C\'adiz; Xavier Serra

REVIEW 3 major objections 4 minor 21 references

Fractional Fourier Sound Synthesis

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper argues that applying the fractional Fourier transform directly to audio signals—rotating the time-frequency plane by a continuously adjustable angle—yields new, controllable timbres through two methods, alpha-synthesis and…

desk verdict A mathematically sound but empirically thin proof-of-concept for FrFT-based synthesis; the new techniques are worth a look, but the claims outrun the evidence. read the letter →

arxiv 2506.09189 v1 pith:L77VMGJG submitted 2025-06-10 cs.SD eess.AS

Esteban Gutiérrez , Rodrigo Cádiz , Carlos Sing Long , Frederic Font , Xavier Serra This is my paper

classification cs.SDeess.AS

keywords fractionalFouriertransformsoundsynthesisalpha-synthesisalpha-filteringtime-frequencyrotationchirptexturestimbralcontrolaudiosignalprocessing

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that the Fractional Fourier Transform, which rotates a signal's time-frequency representation by a continuously adjustable angle, can be used directly as a sound synthesis tool. The authors introduce two methods: $\alpha$-synthesis, applying the FrFT to pure sinusoids to generate complex chirp-like textures, and $\alpha$-filtering, multiplying signals in the fractional domain to create a generalization of spectral filtering. If these methods hold up, composers gain a new continuous parameter, the fractional order $\alpha$, for shaping timbre, in addition to the usual frequency-domain controls. The paper's central reason to care is that a single rotation parameter can turn simple tones into dynamic, evolving sonic material.

What carries the argument

The machinery is the fractional Fourier transform of order $\alpha$, defined by the integral kernel $K_\alpha(s,t)$ that interpolates between the identity ($\alpha=0$) and the ordinary Fourier transform ($\alpha=\pi/2$). Its defining property here is that it rotates the Wigner time-frequency distribution by angle $\alpha\pi/2$; equivalently, it is a symmetric linear canonical transform. The synthesis pipeline combines this transform with three practical choices: projecting the complex output to its real part, using small angles ($\alpha<0.5$), and applying the transform over finite windows with overlap-add. These choices make the rotated time-frequency plane audible and controllable.

What would settle it

Compute the FrFT of a pure 10025 Hz sinusoid, the paper's own test tone, using a discrete implementation that exactly satisfies the rotation-additivity property, for the same window sizes and $\alpha$ values as in Section 4, and compare the resulting spectrogram and audio to the output produced by the implementation of [10]/[13]. If the prominent chirps and boundary reflections vanish or change qualitatively, those sonic features are artifacts of the approximate transform rather than intrinsic FrFT rotation.

Watch

Extended reading notes

Core claim

The central discovery is that the time-frequency rotation property of the FrFT is not just an analysis curiosity; it can be the engine of a synthesis technique. Because the FrFT of order $\alpha$ rotates a signal's Wigner distribution by $\alpha\pi/2$, applying it to a pure sinusoid and taking the real part produces families of chirps moving in parallel lines, together with mirror-image reflections about the fundamental frequency and reflections against the window boundaries. This gives a direct mechanism for generating intelligible but complex spectra from a single sine wave, with $\alpha$ acting as the control. In the $\alpha$-domain, filtering by multiplication is likewise possible, and the authors report that $\alpha$-domain bands are sonically similar to each other rather than behaving like frequency bands, showing that this is a genuinely new filtering dimension.

Load-bearing premise

The argument assumes that the fast numerical FrFT used for the sound examples is faithful to the true time-frequency rotation, even though the implementation is acknowledged not to guarantee the rotation-composition property.

Editorial extensions

If this is right

If the central claim is right, the fractional order $\alpha$ becomes a continuously variable timbral control, roughly like the modulation index in FM synthesis but operating by rotating the time-frequency plane rather than by frequency modulation.
Because low values of $\alpha$ keep the signal closer to the time domain, the method works as a gradual morphing tool, from nearly unprocessed audio at $\alpha\approx 0.01$ to chirp-heavy textures near $\alpha\approx 0.5$.
Alpha-domain filtering offers a filtering axis whose bands are not frequency bands: 'low' and 'high' alpha filters do not correspond to bass and treble, so this is a new sonic dimension rather than a re-labeled equalizer.
The observed boundary reflections mean that finite-window processing shapes the resulting texture, so window size and hop size become compositional parameters, not just implementation details.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial: the mirror-reflection of the spectrum at the fundamental and the subsequent boundary reflections suggest a possible closed-form description of the real-part projection as a kind of time-frequency folding; if worked out, that description would let a composer predict exactly which chirps appear for a given $\alpha$ and window.
Editorial: the reported resemblance to FM synthesis could be turned into a quantitative comparison, measuring spectral spread or harmonic-ratio evolution of $\alpha$-swept FrFT output versus FM output with rising modulation index, to reveal a formal mapping between the two parameter spaces.
Editorial: since the implementation used does not guarantee rotation additivity, a direct test with an exact discrete FrFT on short windows would separate genuine FrFT behavior from numerical diffraction, a natural step before relying on the technique in real-time systems.
Editorial: if alpha-domain bands are indeed sonically similar, alpha-filtering might be more useful for controlled brightness or roughness variation than for selective filtering, making it a candidate for cross-synthesis between two sounds' alpha-domain envelopes.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a legitimate proof-of-concept paper. The FrFT math is presented correctly; α-synthesis and α-filtering are genuinely new in the cited literature; and they shipped code and audio examples, which is more than many papers do. The problems are in the gap between the claims and the evidence.

The two methods are simple: rotate a sinusoid in the time-frequency plane and take the real part; or multiply in the alpha-domain by a Gabor-like kernel and invert. Because the FrFT is a rotation, the spectrograms show chirps and reflections, and the authors use that to argue for new timbral possibilities. The connection to the rotation property is clear, and the examples are consistent with it. The paper also honestly notes that previous work dismissed FrFT for synthesis and that the fast implementation they use does not guarantee the homomorphism property.

Three soft spots, in increasing order. First, the evaluation is entirely qualitative: spectrogram eyeballing and informal listening. There are no baseline comparisons (e.g., FM synthesis, vocoding, standard filtering) and no perceptual tests, which matters because the authors themselves draw an analogy to FM. Second, the implementation issue is real. They use the Ozaktas fast FrFT via [13], knowing it does not satisfy Fα∘Fβ = Fα+β. For α-filtering, the forward/inverse pair may not be exact, so some of what you hear could be artifact. A simple check against a reference discrete FrFT or the continuous kernel evaluated numerically would settle this, and the paper doesn't include it. Third, the abstract and conclusion oversell the work: 'redefine', 'transformative', 'unattainable through conventional methods' is not supported by the evidence presented. The reader's conditional verdict is right, not because the idea fails, but because the claims are a step ahead.

Who is this for? People working in computer music and sound synthesis who want a new parameter to play with. It deserves a serious referee; a good revise-and-resubmit would ask for validated implementation, baseline comparisons, and more modest claims. I would send it out rather than desk reject, but I would expect heavy revision.

Referee Report

3 major / 4 minor

Summary. The manuscript proposes two sound synthesis/processing methods based on the fractional Fourier transform (FrFT): alpha-synthesis, which applies the FrFT to pure sinusoids and keeps the real part of the transformed signal, and alpha-filtering, which multiplies the short-time FrFT of an audio signal by a kernel and applies the inverse transform. The paper reviews the FrFT's mathematical properties (including time-frequency rotation), describes the implementation choice, and presents audio/visual examples in three groups. The authors claim these methods afford new timbral possibilities and dynamic sonic textures by exploiting the FrFT's rotation property, and they argue that low fractional orders and windowed processing are important practical considerations.

Significance. If the central claims are validated, the paper would introduce a simple, new parametric control (the fractional order alpha) for sound design, and the proposal to synthesize directly in the alpha-domain is a genuinely unusual idea. The authors provide the code and examples, which supports reproducibility. However, the significance currently rests on qualitative spectrogram observations and informal listening; there is no perceptual evaluation, no comparison with conventional synthesis methods, and no quantitative validation that the chosen discrete FrFT implementation preserves the continuous rotation property that the interpretations depend on. The novelty also depends on the completeness of the prior-art search, which the paper only briefly addresses.

major comments (3)

[Section 2.3 and Section 5] The manuscript explicitly states in Section 2.3 that the fast FrFT implementations of [10] as provided in [13] do not ensure the homomorphism property (3). Since property (3) is exactly what makes the FrFT a time-frequency rotation, the chirps, reflections, and boundary effects reported in Section 5 are only evidence about the specific discrete transform used, not about the continuous FrFT, unless the approximation error is shown to be negligible for the chosen parameters. I request a concrete numerical validation: for the actual window sizes (approx. 0.046 s to 1 s) and alpha values (0.01 to 0.5), compare the output of the [13] implementation with a reference discrete FrFT (e.g., Pei-Yeh or Candan definitions) or with the continuous FrFT kernel evaluated numerically, and report the error. Without this, the central sonic claims could be artifacts of the approximate algorithm.
[Section 5, first paragraph] The observation that taking the real part of the FrFT produces a reflection against a horizontal line, and that new reflections appear at the boundaries, is not derived from the FrFT's mathematical properties. The paper treats these phenomena as confirmations of the rotation property, but the mirror chirp and boundary reflections are additional features that are not explained. The authors should either provide a derivation (for example, relating Re(F_alpha f) to the FrFT symmetries of a real sinusoid) or explicitly label these as empirical observations awaiting a theoretical explanation. The current text conflates the well-established rotation property with these unexplained visual features.
[Section 4 and Section 5] The paper's central claim is that the proposed methods create 'novel timbral possibilities and dynamic sonic textures' (abstract and conclusion), but the evidence consists of subjective spectrogram readings and the authors' own listening impressions. There is no perceptual evaluation, no comparison to existing synthesis methods, and no quantitative measure of the generated audio. In particular, the claim of a 'weak inverse relationship' between alpha-domain bands and frequency-domain content (Section 5, paragraph 3) is presented as anecdotal; it could be substantiated or refuted by a simple spectral centroid or MFCC analysis across the varying center frequencies c. Without such evidence, the usefulness of these methods for sound design remains unsupported.

minor comments (4)

[Author affiliations] There is a typo in the second affiliation: 'Electrical Enginering' should be 'Electrical Engineering'.
[Section 2.1] The sentence 'where F correspond to the Fourier Transform' should be 'where F corresponds to the Fourier Transform'.
[Section 4.1] The text states that the sinusoid frequency 10025 Hz is 'exactly in the middle of the sampleable frequency domain,' but the sample rate is never given. Please specify the sample rate used in the examples.
[Section 3.2] The phrase 'there is no known analog to the Convolution Theorem for the FrFT' could be softened, since a qualified statement (e.g., 'no direct analog that preserves the simple multiplication form') would be more precise and more accurate to the literature.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the FrFT synthesis methods are direct applications of a standard transform, with no fitted parameters, predictions, or load-bearing self-citations.

full rationale

The paper's derivation chain is self-contained and non-circular. α-synthesis (§3.1) is defined as applying the FrFT to sinusoids and keeping the real part; α-filtering (§3.2) is defined as FrFT → multiplication by a kernel → inverse FrFT. Neither method fits a parameter to data nor derives a prediction from its own output; the 'results' in §5 are qualitative observations of examples, not quantities claimed to be predicted by the model. The rotation property used for interpretation is established in §2.2 from the known LCT/Wigner-distribution theorem, which is an external mathematical fact, not derived from the sound examples. The only flagged limitation is in §2.3, where the authors explicitly state that the fast implementations of [10] provided in [13] 'did not ensure the homomorphism property (3)'. This is a disclosed implementation-fidelity concern and a correctness risk (the discrete transform may not exactly rotate), but it is not circularity: the paper neither defines the FrFT in terms of that implementation nor uses the observed sounds to justify the rotation property. No equations are equivalent by construction, no fitted input is renamed as a prediction, and no load-bearing argument rests on the authors' own prior work. The paper therefore has no significant circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard FrFT mathematics plus several domain assumptions about the perceptual value of the projected signals. No new physical entities are introduced. The free parameters are experimental choices, not fits to data, but they shape the qualitative results.

free parameters (3)

Fractional order alpha = 0 to 0.5 (increments of 0.01, 0.05, 0.1, 0.25, 0.5)
Chosen by hand; the paper restricts to alpha < 0.5 because values closer to the frequency domain are considered not sonically interesting. This choice constrains all demonstrations.
Window size and hop size = Windows of 0.046 to 11.88 seconds, hop equal to half window
Hand-selected for the examples; results vary strongly with window size (Figure 1), but no systematic study is provided.
Alpha-filter kernel parameters b and c = b = 1, c from 100 to 10000 (exponential base 2)
Hand-selected impulse response parameters; results are described as anecdotal in Section 5.

assumptions (5)

standard math FrFT definition and its fundamental properties (linearity, index additivity, reduction to FT at multiples of pi/2)
Used in Sections 2.1 and 3; these are accepted mathematical facts from standard references [6,7,8].
standard math FrFT rotates the Wigner distribution by angle alpha*pi/2
Invoked in Section 2.2 to interpret sonic results; proven in LCT literature [9].
domain assumption The discrete fast FrFT implementation [10] approximates the continuous FrFT closely enough for audio synthesis
Section 2.3 acknowledges [10] implementations do not ensure homomorphism property (3), yet they are adopted via [13]. The paper never validates how this affects the rotation-based expectations.
domain assumption Taking only the real part of the FrFT produces audible signals that retain the intended sonic character
Section 3: methods use only the real or imaginary part of transformed signals; no justification is given for why this projection is perceptually acceptable.
domain assumption Alpha-domain bands are perceptually distinct or meaningful to human hearing
Section 3.2 states no studies have explored human perception of alpha-domain signals; the method and discussion rely on an unverified assumption.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Fractional Fourier Sound Synthesis." pith.science (2026). https://pith.science/paper/L77VMGJG

@misc{pith2026250609189,
  author       = {Pith},
  title        = {Pith review of: Fractional Fourier Sound Synthesis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L77VMGJG}},
  note         = {Machine review of arXiv:2506.09189}
}

read the original abstract

This paper explores the innovative application of the Fractional Fourier Transform (FrFT) in sound synthesis, highlighting its potential to redefine time-frequency analysis in audio processing. As an extension of the classical Fourier Transform, the FrFT introduces fractional order parameters, enabling a continuous interpolation between time and frequency domains and unlocking unprecedented flexibility in signal manipulation. Crucially, the FrFT also opens the possibility of directly synthesizing sounds in the alpha-domain, providing a unique framework for creating timbral and dynamic characteristics unattainable through conventional methods. This work delves into the mathematical principles of the FrFT, its historical evolution, and its capabilities for synthesizing complex audio textures. Through experimental analyses, we showcase novel sound design techniques, such as alpha-synthesis and alpha-filtering, which leverage the FrFT's time-frequency rotation properties to produce innovative sonic results. The findings affirm the FrFT's value as a transformative tool for composers, sound designers, and researchers seeking to push the boundaries of auditory creativity.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages

[13]

Hermitian polynomials and fourier analysis,

N. Wiener, “Hermitian polynomials and fourier analysis,” Journal of Mathematics and Physics , vol. 8, no. 1-4, pp. 70–73, 1929. [Online]. Avail- able: https://onlinelibrary.wiley.com/doi/abs/10.1002/ sapm19298170

work page 1929
[10]

Time–frequency localization for the fractional fourier transform in signal processing and uncertainty principles,

Z. Aloui and K. Brahim, “Time–frequency localization for the fractional fourier transform in signal processing and uncertainty principles,” Circuits Systems and Signal Processing, vol. 40, no. 10, p. 4924–4945, May

work page
[1]

Fractional Fourier Sound Synthesis

INTRODUCTION Sound synthesis has traditionally relied on mathematical tools such as the Fourier Transform (FT) to analyze and generate audio signals. While the FT has served as a cor- nerstone in audio signal processing, its limitations become apparent when dealing with non-stationary signals or when flexible time-frequency representations are required. T...

work page Pith review arXiv 2025
[2]

FRACTIONAL FOURIER TRANSFORM OVERVIEW In this section, we formally introduce the Fractional Fourier Transform (FrFT) along with some of its properties, and briefly discuss various implementations. Different imple- mentations can produce significantly different results, so it is important to discuss their differences and explain why we chose one implementa...

work page
[3]

While we be- lieve much more can be done, we have chosen to keep this simple, as our aim is to consolidate the foundations of the creative use of the FrFT in audio

FRACTIONAL FOURIER TRANSFORM SYNTHESIS AND PROCESSING METHODS In this section, we explore sound synthesis and manipu- lation methods strongly based on the FrFT. While we be- lieve much more can be done, we have chosen to keep this simple, as our aim is to consolidate the foundations of the creative use of the FrFT in audio. Before discussing any methods, ...

work page
[4]

A brief explanation of some of the visual and sonic examples is provided in this section, but more examples can be found on this article’s webpage

AUDIO AND VISUAL EXAMPLES Accompanying this article, we have created several videos and sound examples 1 showcasing a series of sound exam- ples built using the techniques discussed herein. A brief explanation of some of the visual and sonic examples is provided in this section, but more examples can be found on this article’s webpage. 4.1 Time-Frequency ...

work page
[5]

RESULTS AND DISCUSSION Our examples concerning the rotation property of the FrFT confirm that this property is clearly satisfied when consid- ering the full (complex) FrFT of the signal. More signif- icantly for this research, they also demonstrate that when only the real part is considered, the spectrogram appears to exhibit a reflection against a horizo...

work page
[6]

The proposed approaches, α-synthesis and α-filtering, demonstrate how the FrFT can be used to generate complex and timbrally di- verse audio signals

CONCLUSION This study examines the application of the Fractional Fourier Transform (FrFT) in sound synthesis, introducing methods that exploit its time-frequency rotation property to synthe- size and process sounds in the α-domain. The proposed approaches, α-synthesis and α-filtering, demonstrate how the FrFT can be used to generate complex and timbrally ...

work page 2023

Show all 21 references

[7]

Sound synthesis by fractional wave- shaping,

G. De Poli, “Sound synthesis by fractional wave- shaping,” Journal of The Audio Engineering Society , vol. 32, no. 11, p. 849–861, Nov. 1984. [Online]. Avail- able: https://www.aes.org/e-lib/browse.cfm?elib=4475

1984
[8]

R. Ram, H. K. Palo, and M. N. Mohanty, Frac- tional Segmental Transform for Speech Enhancement . Springer, Singapore, Jan. 2019, p. 135–142. [Online]. Available: https://link.springer.com/chapter/10.1007% 2F978-981-13-2182-5 14

2019
[9]

On the application of fractional fourier transform for enhancing noisy speech,

Z. Wang and X. Zhang, “On the application of fractional fourier transform for enhancing noisy speech,” IEEE International Symposium on Mi- crowave, Antenna, Propagation and EMC Tech- nologies for Wireless Communications , vol. 1, p. 289–292, Aug. 2005. [Online]. Available: htt...

2005
[11]

The dis- crete fractional fourier transform,

C. Candan, M. Kutay, and H. Ozaktas, “The dis- crete fractional fourier transform,” in 1999 IEEE In- ternational Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258), vol. 3, 1999, pp. 1713–1716 vol.3

1999
[12]

Development and exploration of a timbre space representation of audio,

C. A. Nicol, “Development and exploration of a timbre space representation of audio,” PhD thesis, University of Glasgow, 2005. [Online]. Available: https://theses.gla.ac.uk/id/eprint/74229

2005
[14]

On a hilbert space of analytic functions and an associated integral transform part i,

V . Bargmann, “On a hilbert space of analytic functions and an associated integral transform part i,” Communications on Pure and Applied Mathematics , vol. 14, no. 3, pp. 187–214, 1961. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10. 1002/cpa.3160140303

1961
[15]

Discrete fractional fourier transform,

S.-C. Pei and M.-H. Yeh, “Discrete fractional fourier transform,” 06 1996, pp. 536 – 539 vol.2

1996
[16]

J. J. Healy, M. Alper Kutay, H. M. Ozaktas, and J. T. Sheridan, Eds., Linear Canonical Transforms: Theory and Applications , ser. Springer Series in Optical Sciences. New York, NY: Springer New York, 2016, vol. 198. [Online]. Available: https: //link.springer.com/10.1007/978-1...

2016 doi
[17]

Introduction to the fractional fourier transform and its applications,

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, “Introduction to the fractional fourier transform and its applications,” ser. Advances in Imaging and Electron Physics, P. Hawkes, Ed. Elsevier, 1999, vol. 106, pp. 239–291. [Online]. Avail- able: https://www.sciencedirect.com/scie...

1999
[19]

Discrete fractional fourier transform based on orthogonal pro- jections,

S.-C. Pei, M.-H. Yeh, and C.-C. Tseng, “Discrete fractional fourier transform based on orthogonal pro- jections,” IEEE Transactions on Signal Processing , vol. 47, no. 5, pp. 1335–1348, 1999

1999
[20]

Trainable fractional fourier transform,

E. Koc ¸, T. Alikas ¸ifo˘glu, A. C. Aras, and A. Koc ¸, “Trainable fractional fourier transform,” IEEE Signal Processing Letters, vol. 31, pp. 751–755, 2024

2024
[21]

Research of frft rotation factor sensitivity and diffusion based on audio,

J. G. Jin, C. Chen, M. J. Wei, and L. C. Xia, “Research of frft rotation factor sensitivity and diffusion based on audio,” Applied Mechanics and Materials, p. 337–341, Feb. 2012. [Online]. Available: https://www.scientific.net/AMM.155-156.337

2012
[2021]

Available: https://link.springer.com/ article/10.1007/s00034-021-01698-6

[Online]. Available: https://link.springer.com/ article/10.1007/s00034-021-01698-6

doi

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [13]

Hermitian polynomials and fourier analysis,

N. Wiener, “Hermitian polynomials and fourier analysis,” Journal of Mathematics and Physics , vol. 8, no. 1-4, pp. 70–73, 1929. [Online]. Avail- able: https://onlinelibrary.wiley.com/doi/abs/10.1002/ sapm19298170

work page 1929

[2] [10]

Time–frequency localization for the fractional fourier transform in signal processing and uncertainty principles,

Z. Aloui and K. Brahim, “Time–frequency localization for the fractional fourier transform in signal processing and uncertainty principles,” Circuits Systems and Signal Processing, vol. 40, no. 10, p. 4924–4945, May

work page

[3] [1]

Fractional Fourier Sound Synthesis

INTRODUCTION Sound synthesis has traditionally relied on mathematical tools such as the Fourier Transform (FT) to analyze and generate audio signals. While the FT has served as a cor- nerstone in audio signal processing, its limitations become apparent when dealing with non-stationary signals or when flexible time-frequency representations are required. T...

work page Pith review arXiv 2025

[4] [2]

FRACTIONAL FOURIER TRANSFORM OVERVIEW In this section, we formally introduce the Fractional Fourier Transform (FrFT) along with some of its properties, and briefly discuss various implementations. Different imple- mentations can produce significantly different results, so it is important to discuss their differences and explain why we chose one implementa...

work page

[5] [3]

While we be- lieve much more can be done, we have chosen to keep this simple, as our aim is to consolidate the foundations of the creative use of the FrFT in audio

FRACTIONAL FOURIER TRANSFORM SYNTHESIS AND PROCESSING METHODS In this section, we explore sound synthesis and manipu- lation methods strongly based on the FrFT. While we be- lieve much more can be done, we have chosen to keep this simple, as our aim is to consolidate the foundations of the creative use of the FrFT in audio. Before discussing any methods, ...

work page

[6] [4]

A brief explanation of some of the visual and sonic examples is provided in this section, but more examples can be found on this article’s webpage

AUDIO AND VISUAL EXAMPLES Accompanying this article, we have created several videos and sound examples 1 showcasing a series of sound exam- ples built using the techniques discussed herein. A brief explanation of some of the visual and sonic examples is provided in this section, but more examples can be found on this article’s webpage. 4.1 Time-Frequency ...

work page

[7] [5]

RESULTS AND DISCUSSION Our examples concerning the rotation property of the FrFT confirm that this property is clearly satisfied when consid- ering the full (complex) FrFT of the signal. More signif- icantly for this research, they also demonstrate that when only the real part is considered, the spectrogram appears to exhibit a reflection against a horizo...

work page

[8] [6]

The proposed approaches, α-synthesis and α-filtering, demonstrate how the FrFT can be used to generate complex and timbrally di- verse audio signals

CONCLUSION This study examines the application of the Fractional Fourier Transform (FrFT) in sound synthesis, introducing methods that exploit its time-frequency rotation property to synthe- size and process sounds in the α-domain. The proposed approaches, α-synthesis and α-filtering, demonstrate how the FrFT can be used to generate complex and timbrally ...

work page 2023