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.

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.

Two-dimensional discrete Hilbert transform and computational complexity aspects in its implementation

Abstract: It is first shown that the impulse response operator for a two-dimensional discrete Hilbert transform (DHT), although not by itself sum-separable, becomes so after appropriate classification. Subsequently, it is proved that the multiplicative complexity of computation of a two-dimensional DHT is not greater than twice the sum of multiplicative complexities of two one-dimensional DHT's. Finally, the consequences of Winograd's algebraical computational complexity theory on the problem considered here are discussed.

The generalized discrete Fourier transform in rings of algebraic integers

Abstract: Conditions are presented for a transform of the DFT structure, defined in a ring of residues of a ring of algebraic integers, to map cyclic convolution isomorphically into a pointwise product. The conditions are used to verify that a number of potentially useful transforms (which require no general multiplications) satisfy this property. In particular, transforms defined in residue rings of the Gaussian integers, the Eisenstein integers, and a biquadratic domain are studied.

Fast Fourier Transform for Hexagonal Aggregates

Abstract: Hexagonal aggregates are hierarchical arrangements of hexagonal cells These hexagonal cells may be efficiently addressed using a scheme known as generalized balanced ternary for dimension 2, or GBT_2 The objects of interest in this paper are digital images whose domains are hexagonal aggregates We define a discrete Fourier transform (DFT) for such images The main result of this paper is a radix-7, decimation-in-space fast Fourier transform (FFT) for images defined on hexagonal aggregates The algorithm has complexity N log_7 N It is expressed in terms of the p-product, a generalization of matrix multiplication Data reordering (also known as shuffle permutations) is generally associated with FFT algorithms However, use of the p-product makes data reordering unnecessary