This work describes the development of the Basic Multiresolution Wavelet System and some of its components, as well as some of the techniques used to design and implement these systems.Expand

Introduction to Digital Filters Properties of Finite Impulse-Response Filters Design of Linear-Phase Finite Filters Minimum Phase and Complex Approximation and Comparison of Filtering Alternatives Appendix Index.Expand

The structure of transforms having the convolution property is developed and an implementation on the IBM 370/155 is presented and compared with the fast Fourier transform (FFT) showing a substantial improvement in efficiency and accuracy.Expand

A set of necessary and sufficient condition on the M-band scaling filter for it to generate an orthonormal wavelet basis is given, very similar to those obtained by Cohen and Lawton (1990) for 2-band wavelets.Expand

An efficient algorithm, called transform decomposition, is introduced, based on a mixture of a standard FFT algorithm and the Horner polynomial evaluation scheme equivalent to the one in Goertzel's algorithms, which requires fewer operations and is more flexible than pruning.Expand

A new implementation of the real-valued split-radix FFT is presented, an algorithm that uses fewer operations than any otherreal-valued power-of-2-length FFT.Expand

A complete set of fast algorithms for computing the discrete Hartley transform is developed, including decimation-in-frequency, radix-4, split radix, prime factor, and Winograd transform algorithms.Expand

The algorithm developed by Cooley and Tukey clearly had its roots in, though perhaps not a direct influence from, the early twentieth century, and remains the most Widely used method of computing Fourier transforms.Expand

A new nonlinear noise reduction method is presented that uses the discrete wavelet transform instead of the usual orthogonal one, resulting in a significantly improved noise reduction compared to the original wavelet based approach.Expand

The author explains the development of the Wiener Solution and some of the techniques used in its implementation, including Optimum Processing: Steady State Performance and theWiener Solution, which simplifies the implementation of the Covariance Matrix.Expand