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.

Interpretation of gravity anomalies due to finite inclined dikes using Fourier transformation

Abstract: The Fourier transform of the gravity field due to a finite dipping dike is derived and its real and imaginary components are separated. Analysis of these two functions in a certain high-frequency range yields simple relations that can be used to estimate the unknown parameters of the dike. The theoretical considerations are tested on synthetic data after performing the discrete Fourier transform (DFT), and the validity of the method of interpretation is established from a comparison of the actual and estimated parameters.

Efficient recursive structures for forward and inverse discrete cosine transform

Abstract: In this paper, efficient architectures for realizing the recursive discrete cosine transform (DCT) and the recursive inverse DCT (IDCT) are proposed. By respectively folding the inputs of the DCT and the outputs of the IDCT, efficient formulations of the DCT and IDCT are derived to construct the transform kernels. The data throughput per transformation is twice that of the existing methods by spending only half of the computational cycles used by the single folding algorithms. To further improve efficiency, the double folding recursive architectures of the DCT and IDCT are developed. The computational cycles of the DCT are half of the single folding method, and the data throughput of the IDCT is twice that of the single folding method. The regular and modular properties of the proposed recursive architectures are suitable for very large scale integration (VLSI) implementation. With high throughput advantage, the proposed structures could be implemented with less power consumption, which could be applied to low rate video in mobile and portable information appliances.

Comments on Hilbert Transform Based Signal Analysis

Abstract: The use of the Hilbert transform for time/frequency analysis of signals is briefly considered. While the Hilbert transform is based on arbitrary continuous signals, most practical signals are digitially sampled and time-limited. To avoid aliasing in the sampling process the signals must also be bandlimited. It is argued that it is reasonable to consider such sampled signals as periodic (this is the basis of the Discrete Fourier Transform [DFT]) since any other interpretation is inconsistent. A simple derivation of the Hilbert transform for a sampled, periodic is then given. It is shown that the instantaneous frequency can be easily computed from the Discrete Fourier Series (or, equivalently, the DFT) representation of the signal. Since this representation is exact, the Hilbert transform representation is also exact.

The Discrete Fourier Transform and the Fast Fourier Transform

Abstract: The preceding chapters have made extensive mention of the Fourier transform (FT), the discrete Fourier transform (DFT), and the fast Fourier transform (FFT). This chapter examines the relationship between the FT and the DFT, discusses the FFT algorithm as a means of computing the DFT much more rapidly than can be achieved with the DFT algorithm directly, and presents some practical guidelines for using the FFT.

A polynomial-transform based computation of the 2-D DCT with minimum multiplicative complexity

Abstract: This paper provides a full description of a 2-D discrete cosine transform (DCT) which has the property of requiring only N 1-D DCT of size N for performing the 2-D algorithm. No multiplication is involved elsewhere in the algorithm, thus the multiplicative complexity is halved when compared to classical row/column algorithms. Compared to some other proposed algorithms, our approach has the characteristic of being formally very concise. Once the main result has been obtained, a remaining difficulty is the search for an in-place algorithm. This problem is also solved.