for some fixed τ , which is called the period of f . Though function approximation using orthogonal polynomials is very convenient, there is only one kind of periodic polynomial, that is, a constant. So, polynomials are not good for approximating periodic functions. In this case, trigonometric functions are quite useful. A large class of important computational problems falls under the category...

In order to supply a gap of current resonance vibration and STFT demodulation method applied to rolling bearing fault feature extraction of city rail vehicle, a fault diagnosis method for rolling bearing is presented, which is based on the integration of improved wavelet packet, frequency energy analysis and Hilbert marginal spectrum. When faults occur in rolling bearing, the energy of the roll...

‎There are different feature extraction methods in brain-computer interfaces (BCI) based on Steady-State Visually Evoked Potentials (SSVEP) systems‎. ‎This paper presents a comparison of five methods for stimulation frequency detection in SSVEP-based BCI systems‎. ‎The techniques are based on Power Spectrum Density Analysis (PSDA)‎, ‎Fast Fourier Transform (FFT)‎, ‎Hilbert‎- ‎Huang Transform (H...

for some fixed τ , which is called the period of f . Though function approximation using orthogonal polynomials is very convenient, there is only one kind of periodic polynomial, that is, a constant. So, polynomials are not good for approximating periodic functions. In this case, trigonometric functions are quite useful. A large class of important computational problems falls under the category...

Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor’s algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular exponentiation function. In a generalization of this idea, quantum Fourier sampling can be used to discover hidden subgroup structures of some functions much mo...

Continuous four hours EEG (electroencephalogram) recordings and its power spectrum analysis using fast fourier transform (FFT) in urethane anesthetized male Charles Foster rats were performed in two groups: open brain injury and p-CPA (para-Chlorophenylalanine) pretreated before brain injury, respectively, and compared with the EEG power spectrum of control rats. The EEG power spectrum analysis...

In this paper, we propose the Fourier frequency vector (FFV), inherently, associated with multidimensional Fourier transform. With the help of FFV, we are able to provide physical meaning of so called negative frequencies in multidimensional Fourier transform (MDFT), which in turn provide multidimensional spatial and space-time series analysis. The complex exponential representation of sinusoid...

Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the proposed algorithms for the arithmetic Fourier transform are surveyed. A new arithmetic transform for computing the discrete Hartley transform is introduced:...

Ramanujan sums are exponential sums with exponent defined over the irreducible fractions. Until now, they have been used to provide converging expansions to some arithmetical functions appearing in the context of number theory. In this paper, we provide an application of Ramanujan sum expansions to periodic, quasiperiodic and complex time series, as a vital alternative to the Fourier transform....

in this research zinc oxide (zno) nano-crystalline powders were prepared by sol-gel method using zinc acetate. the zno nanoparticles were characterized by x-ray diffraction (xrd), scanning electron microscopy (sem), ultraviolet-visible (uv-vis), fourier transform infra-red (ft-ir) and energy dispersive x-ray (edx) spectroscopy. the structure of nanoparticles was studied using xrd pattern. the c...