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.

Rapid computation of the discrete Fourier transform

Abstract: Algorithms for the rapid computation of the forward and inverse discrete Fourier transform for points which are nonequispaced or whose number is unrestricted are presented. The computational procedure is based on approximation using a local Taylor series expansion and the fast Fourier transform (FFT). The forward transform for nonequispaced points is computed as the solution of a linear system involving the inverse Fourier transform. This latter system is solved using the iterative method GMRES with preconditioning. Numerical results are given to confirm the efficiency of the algorithms.

Comparative performance of various trigonometric unitary transforms for transform image coding

Abstract: The feasibility of discrete sine transform (DST) and discrete sine cosine transform (DSCT) for digital image processing problems are investigated. Discrete sine transform and discrete cosine transform can be computed by using two FFT’s of original data sequence of length N. Discrete sine cosine coefficients are computed by FFT of data sequence of length N while the inverse is obtained by computing two FFT's. The performance of each of the unitary transforms in the trigonometric family is studied in terms of quantitative performance measures such as variance distribution, rate distortion, Wiener filtering and how well a transform decorrelates the data efficiently for possible bandwidth compression of a signal represented by a firstorder Markov process model. Computer simulation results on a monochrome image are presented.

Discrete cosine transform filtering

Abstract: Circular convolution-multiplication relationships for the discrete cosine transform (DCT) that are similar to those for the discrete Fourier transform (DFT) are developed. The relations are valid if the filter frequency response is real and even. Two fairly simple relations are developed. The multiplication of the DCT of signal sequence and the DFT of filter sequence results in circular convolution of the folded signal sequence and the filter sequence. Thus, it can be used to filter an image in the frequency domain as an approximation of circular convolution in the spatial domain. >

Fast computation of a discretized thin-plate smoothing spline for image data

Abstract: SUMMARY This paper describes a fast method of computation for a discretized version of the thinplate spline for image data. This method uses the Discrete Cosine Transform and is contrasted with a similar approach based on the Discrete Fourier Transform. The two methods are similar from the point of view of speed, but the errors introduced near the edge of the image by use of the Discrete Fourier Transform are significantly reduced when the Discrete Cosine Transform is used. This is because, while the Discrete Fourier Transform implicitly assumes periodic boundary conditions, the Discrete Cosine Transform uses reflective boundary conditions. It is claimed that the Discrete Cosine Transform may profitably be used in place of the Discrete Fourier Transform in a variety of image processing applications besides spline smoothing.

Fractional cosine, sine, and Hartley transforms

Abstract: In previous papers, the Fourier transform (FT) has been generalized into the fractional Fourier transform (FRFT), the linear canonical transform (LCT), and the simplified fractional Fourier transform (SFRFT). Because the cosine, sine, and Hartley transforms are very similar to the FT, it is reasonable to think they can also be generalized by the similar way. We introduce several new transforms. They are all the generalization of the cosine, sine, or Hartley transform. We first derive the fractional cosine, sine, and Hartley transforms (FRCT/FRST/FRHT). They are analogous to the FRFT. Then, we derive the canonical cosine and sine transforms (CCT/CST). They are analogous to the LCT. We also derive the simplified fractional cosine, sine, and Hartley transforms (SFRCT/SFRST/SFRHT). They are analogous to the SFRFT and have the advantage of real-input-real-output. We also discuss the properties, digital implementation, and applications (e.g., the applications for filter design and space-variant pattern recognition) of these transforms. The transforms introduced in this paper are very efficient for digital implementation. We can just use one half or one fourth of the real multiplications required for the FRFT and LCT to implement them. When we want to process even, odd, or pure real/imaginary functions, we can use these transforms instead of the FRFT and LCT. Besides, we also show that the FRCT/FRST, CCT/CST, and SFRCT/SFRST are also useful for the one-sided (t /spl isin/ [0, /spl infin/]) signal processing.