The one dimensional fractional Fourier transform has an applications in several areas including image processing, optical propagation problems, signal processing, error analysis, some applications in quantum mechanics etc. The n-dimensional fractional Fourier transform is an extension of the one dimensional fractional Fourier transform. This paper is concerned with the n-dimensional fractional Fourier transform of product and convolution of two functions.
The Hartley transform generalizes to the fractional Hartley transform (FRHT) which gives various uses in different fields of image encryption. Unfortunately, the available literature of fractional Hartley transform is unable to provide its inversion theorem. So accordingly original function cannot retrieve directly, which restrict its applications. The intension of this paper is to propose inversion theorem of fractional Hartley transform to overcome this drawback. Moreover, some properties of fractional Hartley transform are discussed in this paper.
Protease enzyme has lot of commercial applications, so the cost-effective production of protease using sunflower oil seed waste was carried out from Oerskovia xanthineolyitca NCIM 2839. The maximum protease production was after 24 h of incubation with 2.5 % oil seed waste concentration. O. xanthineolytica was found to produce two proteases—P1 and P2. The proteases were purified using 60 % cold acetone precipitation and DEAE-cellulose ion exchange chromatography. SDS-PAGE revealed molecular weight of P1 and P2 was 36 and 24 kDa, respectively. P1 and P2 were optimally active at pH 7.0 and pH 7.5 at temperature 35 and 40 °C, respectively. Analysis of hydrolyzed product of P1 and P2 by HPLC reveals that the P1 has endoprotease and P2 has exoprotease activity. The treated soy milk with immobilized proteases showed increased shelf life and removal of off flavor.
This paper is motivated by the ideas of fractional Fourier transform and Hartley transform. Looking towards the practicality and demanding attention of fractional Hartley transform we take keen interest into it. In this paper, we deal with inverse theorem of FRHT and some important properties of fractional Hartley transform like exponential rule, multiplication rule, transform of derivative and derivative of transform, which play a very crucial role in the development of fractional Hartley transform.
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