Spiral is a program generation system (software that generates other software) for linear transforms and an increasing list of other mathematical functions. The goal of Spiral is to automate the development and porting of performance libraries. Linear transforms include the discrete Fourier transform (DFT), discrete cosine transforms, convolution, and the discrete wavelet transform. The input t...

The two-dimensional discrete cosine transform (DCT) can be found in the heart of many image compression algorithms. Specifically, the JPEG format uses a lossy form of compression based on that transform. Since the standardization of the JPEG, many other transforms become practical in lossy data compression. This article aims to analyze the use of these transforms as the DCT replacement in the J...

Digital Image Watermarking is used recently to secure the image by embedding another digital image. It is typically used to identify ownership of the copyright of the signal. Frequency domain transformation methods used widely in Digital Image Compression and Digital Image Watermarking. They reduce the weakness of classics digital image watermarking such as Least Significant Bit (LSB) methods w...

This paper extends the group testing for wavelets (IEEE Trans. Image Process. 11 (2002) 901) algorithm to code coefficients from the wavelet packet transform, the discrete cosine transform, and various lapped transforms. Group testing offers a noticeable improvement over zerotree coding techniques on these transforms; is inherently flexible; and can be adapted to different transforms with relat...

The discrete cosine and sine transforms are generalized to a triangular fragment of the honeycomb lattice. The two-variable orbit functions of the Weyl group A2, discretized simultaneously on the weight and root lattices, induce the family of the extended Weyl orbit functions. The periodicity and von Neumann and Dirichlet boundary properties of the extended Weyl orbit functions are detailed. Th...

This paper focuses on constructing efficient algorithms of the main DSP discrete procedures: convolution, correlation functions and filtering of signals based on discrete cosine transform (DCTII) and presenting them using unified structure. This structure is very useful in reducing the computational complexity by 3 N 2 − real multiplications and 2 N − real additions in comparison with indirect ...

This paper presents stability results for various fast trigonometric transforms. We consider the numerical stability of the classical fast Fourier transform (FFT) with respect to diierent precomputation methods for the involved twiddle factors and show the strong innuence of precomputation errors on the numerical stability of the FFT. The examinations are extended to fast algorithms for the com...