caco3 nanoparticles have been synthesized via heat-treatment of a new precursor and solid state reaction. effect of calcinations temperature and quantity of surfactant on particle size has been investigated. the products were characterized by x-ray diffraction (xrd), scanning electron microscopy (sem), transmission electron microscopy (tem) and fourier transform infrared (ft–ir) spectroscopy.

ruthenium dioxide nanoparticles (ruo2 ) with an average particle size of 50 nm are readily synthesized from rucl3.xh2o via the precipitation process in the presence of in-situ sodium octanoate as anionic surfactant. the phase composition, morphology, lattice parameters and size of nanoparticles in these products are characterized by fourier transform infrared spectroscopy (ft-ir), x-ray diffrac...

FRACTIONAL FOURIER INTEGRAL THEOREM AND FRACTIONAL FOURIER SINE AND COSINE TRANSFORM Saleem Iqbal, S.M. Raza, * LalaRukh Kamal and Farhana Sarwar Department of Mathematics/Physics, University of Balochistan, Quetta, Pakistan e-mail: fs1005,saleemiqbal81,[email protected]. ABSTRACT: The fractional Fourier transform (FRFT) is a generalization of the ordinary Fourier transform (FT). Recently...

This paper looks at an approach that uses symmetric properties of the basis function to remove redundancies in the calculation of the discrete Fourier transform (DFT). We develop an algorithm, called the quick Fourier transform (QFT), that reduces the number of oating point operations necessary to compute the DFT by a factor of two or four over direct methods or Goertzel's method for prime leng...

The nonuniform discrete Fourier transform (NDFT), used in many processing schemes, can be computed using a fast algorithm known as the non uniform fast Fourier transform (NFFT). The NFFT is not a new algorithm, but it is an approximation scheme that can be use to calculate an approximate spectrum. In one dimension, computational complexity of the NFFT is O(NlogN) which is a dramatic improvement...

The discrete cosine transform (DCT) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. It is equivalent to a DFT of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), where in some variants the input and/or output data are shifted by half a sampl...

The symmetry and periodicity properties of the discrete Fourier transform (DFT) allow a variety of useful and interesting decompositions. In particular, by clever grouping and reordering of the complex exponential multiplications it is possible to achieve substantial computational savings while still obtaining the exact DFT solution (no approximation required). Many “fast” algorithms have been ...

The discrete cosine transform (DCT) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. It is equivalent to a DFT of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), where in some variants the input and/or output data are shifted by half a sampl...

Discrete Fourier transform (DFT) is one of the most important tools used in almost all fields of science and engineering. DFT can be implemented with efficient algorithms generally classified as fast Fourier transforms (FFT). The most widely used approaches are so-called the algorithms for, such as radix-2, radix 4 and split radix FFT (SRFFT). Considerable researches have carried out and result...

Disclaimer: These notes are intended to be an accessible introduction to the subject, with no pretense at completeness. In general, you can find more thorough discussions in Oppenheim's book. Please let me know if you find any typos. In this lecture, we discuss the Discrete Fourier Transform (DFT), which is a fourier representation for finite length signals. The main practical importance of thi...