A general f ramework is presented for constructing transforms in the field of the input which have a convolutionlike property. The construction is carried out over finite fields, but is shown to be valid over the real and complex fields as well. It is shown that these basefield transforms can be v iewed as “projections” of the discrete Fourier transform @IT) and that they exist for all lengths ...

Spectral observations in the 2.5–12 μm range of comet 103P/Hartley 2 were performed on 1 Jan. 1998 by the ISOPHOT instrument, on board the Infrared Space Observatory. The obtained spectrum evidences intense bands at 2.66 and 4.26 μm, attributable to H2O and CO2, respectively. The derived molecular production rates are Q(H2O) = (3.1 ± 0.2) × 1028 molec. s−1 and Q(CO2) = (2.5 ± 0.3) × 1027 molec....

Fragile digital watermarking has been applied for authentication and alteration detection in images. Utilizing the cosine and Hartley transforms over finite fields, a new transform domain fragile watermarking scheme is introduced. A watermark is embedded into a host image via a blockwise application of two-dimensional finite field cosine or Hartley transforms. Additionally, the considered finit...

We present a color image encryption algorithm by using chaotic mapping and Hartley transform. The three components of color image are scrambled by Baker mapping. The coordinates composed of the scrambled monochrome components are converted from Cartesian coordinates to spherical coordinates. The data of azimuth angle is normalized and regarded as the key. The data of radii and zenith angle are ...

In this paper, it is shown that the use of real trigonometric transforms can advantageously replace the Fourier transform in optical communication systems, for both all-optical and electronic signal processing. All-optical discrete Hartley transform (DHT) and discrete Cosine transform (DCT) architectures for high-speed optical signal processing, filtering and data compression are given and comp...

This paper is concerned with the definitions of the discrete fractional Hartley transform (DFRHT) and the discrete fractional Fourier transform (DFRFT). First, the eigenvalues and eigenvectors of the discrete Fourier and Hartley transform matrices are investigated. Then, the results of the eigendecompositions of the transform matrices are used to define DFRHT and DFRFT. Also, an important relat...

The fast Hartley transform and algorithm for DHT was introduced by Bracewell. The split radix decimation-infrequency algorithm that requires less number of operation counts as compared to the radix-2 and radix-4 algorithms was developed by Sorenson et al. In this paper, an analog architecture for a split radix decimation-in-time algorithm is proposed. It utilizes three different structures in t...