Novel Fractional Wavelet Transform with Closed-Form Expression

yesA new wavelet transform (WT) is introduced based on the fractional properties of the traditional Fourier transform. The new wavelet follows from the fractional Fourier order which uniquely identifies the representation of an input function in a fractional domain. It exploits the combined advantages of WT and fractional Fourier transform (FrFT). The transform permits the identification of a transformed function based on the fractional rotation in time-frequency plane. The fractional rotation is then used to identify individual fractional daughter wavelets. This study is, for convenience, limited to one-dimension. Approach for discussing two or more dimensions is shown

Performance Evaluation of Raised-Cosine Wavelet for Multicarrier Applications

YesWavelets are alternative building kernels of the multicarrier systems, such as the orthogonal frequency division multiplexing (OFDM). The wavelets can be designed by changing the parent basis functions or constructing new filters. Some two new wavelets are considered for multicarrier design; one is designed using raised-cosine functions while the other was constructed using ideal filters. The spectrums of raised cosine wavelet filters are controlled by a roll-off factor which leads to many distorting sidelobes. The second family of wavelet, which the raised-cosine wavelet is compared to, have no distorting sidelobes. It will be shown that raised-cosine wavelets are less suitable for multicarrier design in multicarrier environment, in terms of BER when compared to the wavelet constructed from the ideal filter

A New Approach for Designing Orthogonal Wavelets for Multicarrier Applications

yesThe Daubechies, coiflet and symlet wavelets, with properties of orthogonal wavelets are suitable for multicarrier transmission over band-limited channels. It has been shown that similar wavelets can be constructed by Lagrange approximation interpolation. In this work and using established wavelet design algorithms, it is shown that ideal filters can be approximated to construct new orthogonal wavelets. These new wavelets, in terms of BER behave slightly better than the wavelets mentioned above, and much better than biorthogonal wavelets, in multipath channels with additive white Gaussian noise (AWGN). It is shown that the construction, which uses a simple simultaneous solution to obtain the wavelet filters from the ideal filters based on established wavelet design algorithms, is simple and can easily be reproduced

On the application of raised-cosine wavelets for multicarrier systems design

YesNew orthogonal wavelet transforms can be designed by changing the wavelet basis functions or by constructing new low-pass filters (LPF). One family of wavelet may appeal, in use, to a particular application than another. In this study, the wavelet transform based on raisedcosine spectrum is used as an independent orthogonal wavelet to study multicarrier modulation behaviour over multipath channel environment. Then, the raised-cosine wavelet is compared with other well-known orthogonal wavelets that are used, also, to build multicarrier modulation systems. Traditional orthogonal wavelets do not have side-lobes, while the raised-cosine wavelets have lots of side-lobes; these characteristics influence the wavelet behaviour. It will be shown that the raised-cosine wavelet transform, as an orthogonal wavelet, does not support the design of multicarrier application well like the existing well-known orthogonal wavelets