Topic
Hartley transform
About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.
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TL;DR: A decimation-in-frequency vector split-radix algorithm that possesses the in-place property and needs no matrix transpose to decompose an N*N 2D discrete Hartley transform into one and twelve DHTs.
Abstract: A decimation-in-frequency vector split-radix algorithm is proposed to decompose an N*N 2D discrete Hartley transform (DHT) into one (N/2)*(N/2) DHT and twelve (N/4) DHTs. The proposed algorithm possesses the in-place property and needs no matrix transpose. Its computational structure is very regular and is simpler than those of all existing nonseparable 2D DHTs. >
14 citations
TL;DR: In this paper, a fast algorithm for computing the discrete Hartley transform (DHT) via the Walsh-Hadamard transform (WHT) is proposed, which is carried out on an interframe basis in (N × N) data blocks, where N is an integer power of two.
Abstract: A new fast algorithm is proposed to compute the discrete Hartley transform (DHT) via the Walsh-Hadamard transform (WHT). The processing is carried out on an interframe basis in (N × N) data blocks, where N is an integer power of two. The WHT coefficients are obtained directly, and then used to obtain the DHT coefficients. This is achieved by a transform matrix, the H-transform matrix, which is ortho-normal and has a block-diagonal structure. A complete derivation of the block-diagonal structure for the H-transform matrix is given.
14 citations
TL;DR: In this paper, the authors presented new convolution and correlation theorems in the OFRFT domain and discussed the design method of multiplicative filter for band-limited signals for OF-RFT by convolution in time domain based on fast Fourier transform (FFT) as well as in OF-FT domain.
Abstract: This paper presents new convolution and correlation theorems in the OFRFT domain. The authors also discuss the design method of multiplicative filter for bandlimited signals for OFRFT by convolution in time domain based on fast Fourier transform (FFT) as well as in OFRFT domain. Moreover, with the help of simulation, the effect of time-shifting and frequency-modulation parameters is shown in mapping one shape of an area to the same shape of another area.
14 citations
TL;DR: A novel critically sampled orientation-selective orthogonal lapped transform called the lapped Hartley transform (LHT) is derived and a statistical analysis shows that the LHT and LHT-PO have better redundancy removal properties than other block or lapped transforms.
Abstract: A novel critically sampled orientation-selective orthogonal lapped transform called the lapped Hartley transform (LHT) is derived. In a first step, overlapping basis functions are generated by modulating basis functions of a 2-D block Hartley transform by a cosine wave. To achieve invertibility and orthogonality, an iterative filter is applied as prefilter in the analysis and as postfilter in the synthesis operation, respectively. Alternatively, filtering can be restricted to analysis or synthesis, ending up with a biorthogonal transform (LHT-PR, LHT-PO). A statistical analysis based on a 4000-image data base shows that the LHT and LHT-PO have better redundancy removal properties than other block or lapped transforms. Finally, image compression and noise removal examples are given, showing the advantages of the LHT especially in images containing oriented textures.
14 citations
TL;DR: In this article, the authors investigated the behavior of Fourier transformation on the W-spaces of W-type spaces and applied it to the theory of partial differential equations, where the Fourier transform was applied to the problem of W -spaces.
Abstract: The spaces of W-type were studied by I.M. Gel’fand and G.E. Shilov [22]. They investigated the behaviour of Fourier transformation on theW-spaces. AlsoW-spaces are applied to the theory of partial differential equations.
14 citations