Fluorometry, ion-exchange chromatography, electrophoretic separations and Fourier transform±infrared (FT±IR) spectra were used to determine and characterize amino acids and proteins in 15 di€erent beer samples. Proteins precipitated by ammonium sulfate yielded complex electrophoretic patterns. The major bands corresponded to 45±40 kDa as determined by a two-dimensional gel electrophoresis (2-DE...

Harmonic analysis is at the heart of much of signal and image processing. This is mainly the harmonic analysis of abelian groups, and ultimately, after sampling, and quantizing, finite abelian groups. Nevertheless, this general group theoretic viewpoint has proved fruitful, yielding a natural group-based multiresolution framework as well as some new and potentially useful nonabelian examples. T...

The Fast Fourier Transform was applied to spatial spectrum modeling of a one-dimensional fractal (Cantor set), a two-dimensional fractal (Sierpinski carpet), and a three-dimensional fractal (Menger sponge). A spectrum is developed for different levels. The spatial spectrum was also obtained and modeled for various filling parameters. The ParaView software package was used for 3D modeling.

The split-radix FFT computes a size-n complex DFT, when n is a large power of 2, using just 4n lgn−6n+8 arithmetic operations on real numbers. This operation count was first announced in 1968, stood unchallenged for more than thirty years, and was widely believed to be best possible. Recently James Van Buskirk posted software demonstrating that the split-radix FFT is not optimal. Van Buskirk’s ...

It is widely believed, in the areas of optics, image analysis, and visual perception, that the Hilbert transform does not extend naturally and isotropically beyond one dimension. In some areas of image analysis, this belief has restricted the application of the analytic signal concept to multiple dimensions. We show that, contrary to this view, there is a natural, isotropic, and elegant extensi...

With the knowledge of the syndromes Sa,b, 0 ≤ a, b ≤ q − 2, the exact error values cannot be determined by using the conventional (q − 1)2-point discrete Fourier transform in the decoding of a plane algebraic-geometric code over GF (q). In this letter, the inverse q-point 1-dimensional and q2-point 2dimensional affine Fourier transform over GF (q) are presented to be used to retrieve the actual...

We construct two-dimensional codes for correcting burst errors using the finite field Fourier transform. The encoding procedure is performed in the transformed domain using the conjugacy property of the finite field Fourier transform. The decoding procedure is also done in the transformed domain. Our code is capable of correcting multiple non-overlapping occurrence of different error patterns f...

Digital Image Watermarking is used recently to secure the image by embedding another digital image. It is typically used to identify ownership of the copyright of the signal. Frequency domain transformation methods used widely in Digital Image Compression and Digital Image Watermarking. They reduce the weakness of classics digital image watermarking such as Least Significant Bit (LSB) methods w...

Two-dimensional Fourier transform electronic spectra were recorded for the LH3 light harvesting complex. The spectra reveal the weak coupling between B800 molecules, the ultrafast dynamics within B820 and energy flow from B800 to B850.