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The fractional Fourier transform is a rotation operation on a time–frequency distribution. From the definition above, for α = 0, there will be no change after applying the fractional Fourier transform, while for α = π/2, the fractional Fourier transform becomes a plain Fourier transform, which rotates the time–frequency distribution with ...
The fractional Fourier transform (FRFT), [1] a generalization of the Fourier transform (FT), serves a useful and powerful analyzing tool [2] in optics, communications, signal and image processing, etc. This transform, however, has one major drawback due to using global kernel, i.e., the fractional Fourier representation only provides such FRFT ...
He broadened the field of Fractional Fourier transform which early defined by V. Namias and published a book on that field. He published more than 400 papers and 5 books. The Fractional Fourier transform with applications in optics and signal H. M. Ozaktas, Z. Zalevsky and M. A. Kutay, processing, John Wiley and Sons (2001).
The Fourier transform is suitable to filter out the noise that is a combination of sinusoid functions. If signal are not separable in both time and frequency domains, using the fractional Fourier transform (FRFTs) is suitable to filter out the noise that is a combination of higher order exponential functions.
The fractional Fourier transform corresponds to rotation by an arbitrary angle; they are the elliptic elements of SL 2 (R), represented by the matrices [] = [ ]. The Fourier transform is the fractional Fourier transform when θ = 90 ∘ . {\displaystyle \theta =90^{\circ }.}
While the Fourier transform can simply be interpreted as switching the time domain and the frequency domain, with the inverse Fourier transform switching them back, more geometrically it can be interpreted as a rotation by 90° in the time–frequency domain (considering time as the x-axis and frequency as the y-axis), and the Fourier transform ...
A signal, as a function of time, may be considered as a representation with perfect time resolution.In contrast, the magnitude of the Fourier transform (FT) of the signal may be considered as a representation with perfect spectral resolution but with no time information because the magnitude of the FT conveys frequency content but it fails to convey when, in time, different events occur in the ...
Fourier transform, with special cases: Fourier series. When the input function/waveform is periodic, the Fourier transform output is a Dirac comb function, modulated by a discrete sequence of finite-valued coefficients that are complex-valued in general. These are called Fourier series coefficients. The term Fourier series actually refers to ...