Abstract
The wavelet transform (WT) and the fractional Fourier transform (FRFT) are powerful tools for many applications in the field of signal processing. However, the signal analysis capability of the former is limited in the time-frequency plane. Although the latter has overcome such limitation and can provide signal representations in the fractional domain, it fails in obtaining local structures of the signal. In this paper, a novel fractional wavelet transform (FRWT) is proposed in order to rectify the limitations of the WT and the FRFT. The proposed transform not only inherits the advantages of multiresolution analysis of the WT, but also has the capability of signal representations in the fractional domain which is similar to the FRFT. Compared with the existing FRWT, the novel FRWT can offer signal representations in the time-fractional-frequency plane. Besides, it has explicit physical interpretation, low computational complexity and usefulness for practical applications. The validity of the theoretical derivations is demonstrated via simulations.
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References
Gargour C, Gabrea M, Ramachandran V, et al. A short introduction to wavelets and their applications. IEEE Circ Syst Mag, 2009, 2: 57–68
Flandrin P. Time-frequency and chirps. P SPIE, 2001, 4391: 161–175
Xia X G. On bandlimited signals with fractional Fourier transform. IEEE Signal Proc Let, 1996, 3: 72–74
Mendlovic D, Zalevsky Z, Mas D, et al. Fractional wavelet transform. Appl Optics, 1997, 36: 4801–4806
Bhatnagar G, Raman B. Encryption based robust watermarking in fractional wavelet domain. Rec Adv Mult Sig Proc Commun, 2009, 231: 375–416
Chen L, Zhao D. Optical image encryption based on fractional wavelet transform. Opt Commun, 2005, 254: 361–367
Huang Y, Suter B. The fractional wave packet transform. Multidim Syst Signal Process, 1998, 9: 399–402
Tao R, Deng B, Wang Y. Research progress of the fractional Fourier transform in signal processing. Sci China Ser F-Inf Sci, 2006, 49: 1–25
Tao R, Li Y L, Wang Y. Short-time fractional Fourier transform and its applications. IEEE Trans Signal Proces, 2010, 58: 2568–2580
Wood J C, Barry D T. Linear signal synthesis using the Radon-Wigner transform. IEEE Trans Signal Proces, 1994, 42: 2105–2111
Dinç E, Baleanu D. New approaches for simultaneous spectral analysis of a complex mixture using the fractional wavelet transform. Commun Nonlinear Sci Numer Simul, 2010, 15: 812–818
Shi J, Chi Y G, Zhang N T. Multichannel sampling and reconstruction of bandlimited signals in fractional domain. IEEE Signal Proc Let, 2010, 17: 909–912
Candan C, Kutay M A, Ozaktas H M. The discrete fractional Fourier transform. IEEE Trans Signal Proces, 2000, 48: 1329–1337
Tao R, Li X, Li Y, et al. Time-delay estimation of chirp signals in the fractional Fourier transform. IEEE Trans Signal Proces, 2009, 57: 2852–2855
Akay O, Erözden E. Employing fractional autocorrelation for fast detection and sweep rate estimation of pulse compression radar waveforms. Signal Process, 2009, 89: 2479–2489
Cowell D M J, Freear S. Separation of overlapping linear frequency modulated (LFM) signals using the fractional Fourier transform. IEEE Trans Ultrason Ferr, 2010, 57: 2324–2333
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Shi, J., Zhang, N. & Liu, X. A novel fractional wavelet transform and its applications. Sci. China Inf. Sci. 55, 1270–1279 (2012). https://doi.org/10.1007/s11432-011-4320-x
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DOI: https://doi.org/10.1007/s11432-011-4320-x