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.

An optimized algorithm for computing the modified discrete cosine transform and its inverse transform

Abstract: This paper presents an optimized algorithm for the modified discrete cosine transform (MDCT) and its inverse transform (IMDCT) computation in MPEG audio. The proposed algorithm is based on the DCT of type II (DCT-II). By extracting a common kernel form from the MDCT and IMDCT, we can obtain an optimized computation of the MDCT and the IMDCT using a unified structure. Also, our proposed structure is more symmetrical and simple than those of the existing researches. Proposed algorithm is, moreover, very useful in implementing the parallel VLSI system structure of the MDCT and IMDCT.

Uniform Discrete Curvelet Transform for Seismic Processing

Abstract: A novel implementation of the discrete curvelet transform is proposed in this work. The transform is based on the Fast Fourier Transform (FFT) and has the same order of complexity as the FFT. The discrete curvelet functions are defined by a parameterized family of smooth windowed functions that are 2-pi periodic and form a partition of unity. The transform is named the Uniform Discrete Curvelet Transform (UDCT) because the centers of the curvelet functions at each resolution are located on a uniform grid. The forward and inverse transforms form a tight frame, in the sense that they are the exact transpose of each other. The novel discrete transform has several advantages over existing transforms, such as lower redundancy, hierarchical data structure, ease of implementation and possible extension to N dimension. Finally, we present a simple initial application of the UDCT in sparseness constraint seismic data interpolation to recover missing traces.

A new single-phase PLL based on discrete fourier transform

Abstract: A new single-phase synchronous reference frame phase-locked loop (SRF-PLL) is proposed in this paper. The key point to implement single-phase SRF-PLL is how to generate the orthogonal signal accurately, even under polluted grids with harmonics and DC components. In this paper, the generation of the orthogonal signal is achieved by the discrete Fourier transform (DFT) filter. Compared with conventional SRF-PLLs, the DFT-based PLL (DFT-PLL) proposed offers better harmonics immunity and DC component rejection capacity. Besides, the proposed method incorporates grid frequency variations by adjusting the sampling period of DFT according to the estimated frequency. Also, digital implementation of DFT-PLL is simple and straightforward with low computational burden. These advantages make the proposed DFT-PLL especially suitable for harmonically distorted and frequency-varying applications. Experimental results and comparisons with two another widely used SRF-PLLs are given to validate the effectiveness and advantages of the proposed method.

A DCT approximation with low complexity for image compression

Abstract: This paper introduces an orthogonal approximation for the 8 point Discrete Cosine Transform (DCT). The proposed transformation matrix contains only ones and zeros. Bit shift operations and multiplication operations are absent. The approximate transform of DCT is obtained to meet the low complexity requirements. The implied transformation and approximation are orthogonal and are based on polar decomposition methods. The low complexity introduced in DCT reduces power consumption. The proposed image compression algorithm is comprehended using Matlab code. The proposed algorithm is less complex than Signed Discrete Cosine Transform (SDCT) and it requires two additional operations when compared to Bouguezel-Ahmed-Swamy (BAS) series of algorithms.

Autoregressive Modeling of Temporal/Spectral Envelopes With Finite-Length Discrete Trigonometric Transforms

Abstract: The theory of autoregressive (AR) modeling, also known as linear prediction, has been established by the Fourier analysis of infinite discrete-time sequences or continuous-time signals. Nevertheless, for various finite-length discrete trigonometric transforms (DTTs), including the discrete cosine and sine transforms of different types, the theory is not well established. Several DTTs have been used in current audio coding, and the AR modeling method can be applied to reduce coding artifacts or exploit data redundancies. This paper systematically develops the AR modeling fundamentals of temporal and spectral envelopes for the sixteen members of the DTTs. This paper first considers the AR modeling in the generalized discrete Fourier transforms (GDFTs). Then, we derive the modeling to all the DTTs by introducing the analytic transforms which convert the real-valued vectors into complex-valued ones. Through the process, we build the compact matrix representations for the AR modeling of the DTTs in both time domain and DTT domain. These compact forms also illustrate that the AR modeling for the envelopes can be performed through the Hilbert envelope and the power envelope. These compact forms can be used to develop new coding technologies or examine the possible defects in the existing AR modeling methods for DTTs, We apply the forms to analyze the current temporal noise shaping (TNS) tool in MPEG-2/4 advanced audio coding (AAC).