Topic
Discrete sine transform
About: Discrete sine transform is a research topic. Over the lifetime, 3269 publications have been published within this topic receiving 73181 citations.
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TL;DR: A version of the resolution of the identity and some properties of FRWPT connected with those of FRFT and WPT are shown.
Abstract: We introduce the concept of the Fractional Wave Packet Transform(FRWPT), based on the idea of the Fractional Fourier Transform(FRFT) and Wave Packet Transform(WPT). We show a version of the resolution of the identity and some properties of FRWPT connected with those of FRFT and WPT.
43 citations
TL;DR: The theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions is proposed and evaluated and can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximation the continuous Fouriertransform.
Abstract: Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform.
43 citations
TL;DR: This paper proposes reality-preserving fractional versions of the discrete Fourier, Hartley, generalized Fouriers, and generalized Hartley transforms, which have random outputs and many parameters and thus are very flexible.
Abstract: Real transforms require less complexity for computations and less memory for storages than complex transforms. However, discrete fractional Fourier and Hartley transforms are complex transforms. In this paper, we propose reality-preserving fractional versions of the discrete Fourier, Hartley, generalized Fourier, and generalized Hartley transforms. All of the proposed real discrete fractional transforms have as many as $O(N^{2})$ parameters and thus are very flexible. The proposed real discrete fractional transforms have random eigenvectors and they have only two distinct eigenvalues 1 and $-$ 1. Properties and relationships of the proposed real discrete fractional transforms are investigated. Besides, for the real conventional discrete Hartley and generalized discrete Hartley transforms, we propose their alternative reality-preserving fractionalizations based on diagonal-like matrices to further increase their flexibility. The proposed real transforms have all of the required good properties to be discrete fractional transforms. Finally, since the proposed new transforms have random outputs and many parameters, they are all suitable for data security applications such as image encryption and watermarking.
43 citations
TL;DR: It is shown that it is possible to replace the real-numbered elements of a discrete cosine transform (DCT) matrix with integers and still maintain the structure, i.e., relative magnitudes and orthogonality, among the matrix elements.
Abstract: It is shown that it is possible to replace the real-numbered elements of a discrete cosine transform (DCT) matrix with integers and still maintain the structure, i.e., relative magnitudes and orthogonality, among the matrix elements. The result is an integer cosine transform (ICT). Thirteen ICTs have been found, and some of them have performance comparable to the DCT. The main advantage of the ICT lies in having only integer values, which in two cases can be represented perfectly by 6-bit numbers, thus providing a potential reduction in the computational complexity. >
42 citations
TL;DR: A technique whereby both lowpass filtering and subsampling can be combined in the transform domain results in greater computational efficiency as the constraint of filter length to meet certain specifications is removed permitting the use of smaller transform block sizes.
42 citations