and the inverse Fourier transform is f (x) = 1 2π ∫ ∞ −∞ F(ω)e dω Recall that i = √−1 and eiθ = cos θ+ i sin θ. Think of it as a transformation into a different set of basis functions. The Fourier transform uses complex exponentials (sinusoids) of various frequencies as its basis functions. (Other transforms, such as Z, Laplace, Cosine, Wavelet, and Hartley, use different basis functions). A Fo...

This paper presents a new method of detecting Analog to Digital Converter harmonic distortion. The new method is based on Wavelet multi-resolution process to identify instantaneous harmonic components. In classical testing, Fourier transform algorithm was long adopted to estimate Total Harmonic Distortion by obtaining signal power spectrum. While the conventional method of Fourier transform ten...

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...

Traditional linear signal processing is based on viewing signals as sequences or functions in time that flow in one direction, from past through present into future. Somewhat surprisingly, the assumption that the most basic operation that can be performed on a signal is a time shift, or “delay,” is sufficient to derive many relevant signal processing concepts, including spectrum, Fourier transf...

Warp and weft spacing and its coefficient of variation affect the physical properties of fabrics such as fabric hand, frictional and mechanical properties. In this paper the weft and warp spacing and its coefficient of variation for plain weave is calculated using Fourier transforms. Different methods have been used in this work including autocorrelation function. First, two dimensional power s...

Warp and weft spacing and its coefficient of variation affect the physical properties of fabrics such as fabric hand, frictional and mechanical properties. In this paper the weft and warp spacing and its coefficient of variation for plain weave is calculated using Fourier transforms. Different methods have been used in this work including autocorrelation function. First, two dimensional power s...

Fourier Wavefront Reconstruction Over a Rectangular Pupil The iterative and boundary methods developed here for circular and elliptical pupils are based on a method to reconstruct the wavefront over the rectangular pupil. To fully understand this development, it is necessary to first summarize the approach used by Freischlad and Koliopoulos to derive an inverse spatial filter to reconstruct a w...

To develop a noise-insensitive texture classification algorithm for both optical and underwater sidescan sonar images, we study the multichannel texture classification algorithm that uses the wavelet packet transform and Fourier transform. The approach uses a multilevel dominant eigenvector estimation algorithm and statistical distance measures to combine and select frequency channel features o...

copper vanadate nanostructures were prepared via ex-situ precipitation approach in presence of schiff-base ligand (n,n׳ -buthylenebis(acetylacetone iminato)dianion = acacbn) as a new capping agent. the effect of different cu sources and ph on the size, morphology and size distribution of copper vanadate nanostructures was investigated. the as-prepared products were characterized using x-ray dif...