Conventional Fourier analysis has many schemes for different types of signals. They are Fourier transform (FT), Fourier series (FS), discrete-time Fourier transform (DTFT), and discrete Fourier transform (DFT). The goal of this correspondence is to develop two absent schemes of fractional Fourier analysis methods. The proposed methods are fractional Fourier series (FRFS) and discrete-time fract...

Turmeric powder (Curcuma longa L.) is valued both for its medicinal properties and for its popular culinary use, such as being a component in curry powder. Due to its high demand in international trade, turmeric powder has been subject to economically driven, hazardous chemical adulteration. This study utilized Fourier Transform-Raman (FT-Raman) and Fourier Transform-Infra Red (FT-IR) spectrosc...

The 2-D Fourier transform has been generalized into the 2-D separable fractional Fourier transform (replaces 1-D Fourier transform by 1-D fractional Fourier transform for each variable) and the 2-D separable canonical transform (further replaces the fractional Fourier transform by canonical transform) in [3]. It also has been generalized into the 2-D unseparable fractional Fourier transform wit...

Biochemical analyses of substances rely upon the ability of techniques to identify qualitatively and quantitatively the components present and are based on physicochemical characteristics as well as chemical nature of substances being detected. While chemical analyses usually depend on reactions of a given substance and can be destructive, spectral studies are usually non-destructive and deal w...

Suppose we have a function s(t) that measures the sound level at time t of an analog audio signal. We assume that s(t) is piecewise-continuous and of finite duration: s(t) = 0 when t is outside some interval a ≤ t ≤ b. Make a change of variable x = (t− a)/(b− a) and set f(x) = s(t). Then 0 ≤ x ≤ 1 when a ≤ t ≤ b, and f(x) is a piecewise continuous function of x. We convert f(x) into a digital s...

A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT's in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from -1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT...

Telah dilakukan penelitian tentang adsorpsi logam timbal (Pb) menggunakan adsorben kulit rambutan. Penelitian ini bertujuan untuk mengkaji karakter rambutan dalam aktivitas Pb(II) dan interaksi adsorbat dengan adsorben. Dalam ini, yang digunakan terbagi menjadi 2 (dua) yaitu non-aktivasi teraktivasi asam nitrat (HNO3) natrium hidroksida (NaOH). Dilakukan uji variasi waktu 5, 10, 20, 30 menit. B...

This chapter covers the fundamental principles and current applications of Fourier transform (FT) infrared and Fourier transform Raman spectroscopies as utilized in the analysis of polymeric materials. The primary emphasis of the first part is on the principles and advantages of these interferometric methods, whereas the remaining sections illustrate numerous applications focusing on the struct...

This paper proposes new image compression technique that uses Real Fourier Transform. Discrete Fourier Transform (DFT) contains complex exponentials. It contains both cosine and sine functions. It gives complex values in the output of Fourier Transform. To avoid these complex values in the output, complex terms in Fourier Transform are eliminated. This can be done by using coefficients of Discr...