Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.

Computer-generated Fourier transforms of helical particles

Abstract: An alternative method has been found to display the information contained in the Fourier transform of a helical particle. This allows a strong selection rule to be defined for the transform on the layer lines and consequently the discrimination between signal and noise contributions to the data can be improved.

The Application of Filtered Transforms to the General Classification Problem

Abstract: An image classification model based on nearest prototypes in filtered Fourier and Walsh transform domains is presented. A computer simulation of the model applied to handwritten English letters, Russian letters, numerals, and electromagnetic signals is also presented. Experiments to date fail to refute the working hypothesis that generalized harmonic analysis can be used to reliably classify alphabet characters, time-varying signals, and other images.

High-order seislet transform and its application of random noise attenuation

Abstract: The seislet transform is a wavelet-like transform that analyzes seismic data by following variable slopes of seismic events across different scales.It generalizes the discrete wavelet transform(DWT)in the sense that DWT in the lateral direction is simply the seislet transform with zero slopes.An earlier work used low-order versions of DWT to construct the seislet transform.In this work,we extend this approach to a higher order,using the Cohen-Daubechies -Feauveau 9/7 biorthogonal wavelet transform(the basis for the JPEG2000 compression scheme)as a template.Using synthetic and field-data examples,we demonstrate that the new transform can provide a better compression rate for seismic events than the Fourier transform,DWT,or the low-order seislet transform.Therefore,the high-order seislet transform can be more suitable for data processing tasks such as data regularization and noise attenuation.

ImageCompression Using Real Fourier Transform, Its Wavelet Transform And Hybrid Wavelet With DCT

Abstract: 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 Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST). DCT as well as DST are orthogonal even after sampling and both are equivalent to FFT of data sequence of twice the length. DCT uses real and even functions and DST uses real and odd functions which are equivalent to imaginary part in Fourier Transform. Since coefficients of both DCT and DST contain only real values, Fourier Transform obtained using DCT and DST coefficients also contain only real values. This transform called Real Fourier Transform is applied on colour images. RMSE values are computed for column, Row and Full Real Fourier Transform. Wavelet transform of size N2xN2 is generated using NxN Real Fourier Transform. Also Hybrid Wavelet Transform is generated by combining Real Fourier transform with Discrete Cosine Transform. Performance of these three transforms is compared using RMSE as a performance measure. It has been observed that full hybrid wavelet transform obtained by combining Real Fourier Transform and DCT gives best performance of all. It is compared with DCT Full Wavelet Transform. It beats the performance of Full DCT Wavelet transform. Reconstructed image quality obtained in Real Fourier-DCT Full Hybrid Wavelet Transform is superior to one obtained in DCT, DCT Wavelet and DCT Hybrid Wavelet Transform.