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.

Signal-processing apparatus and method

Abstract: First and second coefficients are fed into a Fast Fourier Transform unit through real number input and imaginary number input portions thereof, respectively, to perform the Fast Fourier Transform of the entered first and second coefficients, thereby producing a frequency-domain coefficient vector. The Fast Fourier Transform of an input signal is performed to transform the input signal into a frequency-domain signal vector. Thereafter, the transformed signal vector is multiplied by the coefficient vector for each element, thereby providing a multiplication result. The Inverse Fast Fourier Transform of the multiplication result renders real number output and imaginary number output portions of the inverse transformation result as first and second series of output signals, respectively.

Image and video processing using discrete fractional transforms

Abstract: The mathematical transforms such as Fourier transform, wavelet transform and fractional Fourier transform have long been influential mathematical tools in information processing. These transforms process signal from time to frequency domain or in joint time–frequency domain. In this paper, with the aim to review a concise and self-reliant course, the discrete fractional transforms have been comprehensively and systematically treated from the signal processing point of view. Beginning from the definitions of fractional transforms, discrete fractional Fourier transforms, discrete fractional Cosine transforms and discrete fractional Hartley transforms, the paper discusses their applications in image and video compression and encryption. The significant features of discrete fractional transforms benefit from their extra degree of freedom that is provided by fractional orders. Comparison of performance states that discrete fractional Fourier transform is superior in compression, while discrete fractional cosine transform is better in encryption of image and video. Mean square error and peak signal-to-noise ratio with optimum fractional order are considered quality check parameters in image and video.

Adaptive discrete cosine transform image coding using gain/Shape vector quantizers

Abstract: An efficient discrete cosine transform image coding system using the gain/shape vector quantizers (DCT-G/S VQ) is presented. In the coding system, AC transform coefficients in a subblock are partitoned into several bands according to the Schaming's method, and the normalized AC transform coefficients of each band are quantized with the gain/shape vector quantizer designed on a spherically symmetric probability model. In addition, an adaptive DCT-G/S VQ (A-DCT-G/S VQ) is presented by incorporating a modification of the recursive quantization technique in the DCT-G/S VQ. The coding systems are simulated on color images, and their performance is compared to that of previously reported discrete cosine transform coding systems using the Max-type scalor quantizers.

A cyclic correlated structure for the realization of discrete cosine transform

Abstract: The authors propose using the correlated cosine structure (CCS) for the computation of the discrete cosine transform (DCT) This structure has circulant property and is most suitable for the hardware realization They show that there exists a close relationship between the CCS and the DCT In such a case, a 2/sup m/ length DCT can be decomposed recursively into shorter length CCS and DCT This new approach results in very simple and straightforward structure and gives the minimum number of multiplications for its realization >

On the generalized convolution with a weight function for the Fourier sine and cosine transforms

Abstract: The generalized convolution with a weight function for the Fourier sine and cosine transforms is introduced. Its properties and applications to solving system of integral equations are considered.