Abstract
This manuscript aims to find out the error in the operations of Fourier Transform (FT) and Fast Fourier Transform (FFT) in digital image processing. We apply FT to transform the time-domain signal to the frequency domain signal. FT is a basic technique in the field of Mathematical and Engineering works. We use Fourier analysis in digital image processing. The Fourier analysis represents a lot of things such as filters, transformation, representation, encoding, data processing, and valid more fields. The FFT development in recent times is very important for the case of image processing. FFT is very exquisite and ubiquitous work in Enfield of digital image processing. In this paper, we study FT and FFT to demonstrate how it solves relative technology problems in the field of security of images. Also, we analyzed the error when changing the fraction order inside FFT, what changes in the mean square error, and on which fraction order our mean square error is obtained the least.
Highlights
Fourier Transform (FT) is very important for conducting Fourier spectroscopy; this alone will explain its importance
Fast Fourier Transform (FFT) is introduced in normal state FT which increases the area of FT, it is used in many places such as signal processing optics and quantum mechanics
Which is the optical implementation of the FFT that was given by Mendlovic and Ozaktas in 1993, Which is used a lot in the optical field
Summary
FT is very important for conducting Fourier spectroscopy; this alone will explain its importance. The Fourier Transform is subsequently an expansion of this plan to non-occasional capacities This causes the Fourier to change tremendously compelling in conduction of warmth, wave engendering, computerized signal handling, picture preparing, separating, and so forth [2,3]. A signal has a specific level of sparsity or compressibility It exists in numerous spaces, for example, picture processing, packed detecting, computational learning hypothesis, multi-scale analysis, and so on [4]. FFT-based Image handling has arrived at a bottleneck where further speed improvement from the algorithmic point of view is troublesome. Be that as it may, some continuous applications request quicker. The FFTs are among the main calculations in applied and designing math and in software engineering, for one and multidimensional frameworks hypothesis and sign preparing [10]
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