Wavelets : a concise guide
- Najmi, Amir-Homayoon.
- Baltimore : Johns Hopkins University Press, 2012.
- Physical description
- xxix, 270 p. : ill ; 24 cm.
QA403.3 .N34 2012
- Unknown QA403.3 .N34 2012
- Includes bibliographical references (p. 261-266) and index.
- 1. Analysis in vector and function spaces
- 2. Linear time-invariant systems
- 3. Time, frequency, and scale lozalising transforms
- 4. The Haar and Shannon wavelets
- 5. General properties of scaling and wavelet functions
- 6. Discrete wavelet transforms of discrete time signals
- 7. Wavelet regularity and Daubechies solutions
- 8. Orthogonal wavelet packest
- 9. Wavelet transform in two dimensions.
- Publisher's Summary
- Introduced nearly three decades ago as a variable resolution alternative to the Fourier transform, a wavelet is a short oscillatory waveform for analysis of transients. The discrete wavelet transform has remarkable multi-resolution and energy-compaction properties. Amir-Homayoon Najmi's introduction to wavelet theory explains this mathematical concept clearly and succinctly. Wavelets are used in processing digital signals and imagery from myriad sources. They form the backbone of the JPEG2000 compression standard, and the Federal Bureau of Investigation uses biorthogonal wavelets to compress and store its vast database of fingerprints. Najmi provides the mathematics that demonstrate how wavelets work, describes how to construct them, and discusses their importance as a tool to investigate and process signals and imagery. He reviews key concepts such as frames, localizing transforms, orthogonal and biorthogonal bases, and multi-resolution. His examples include the Haar, the Shannon, and the Daubechies families of orthogonal and biorthogonal wavelets. Our capacity and need for collecting and transmitting digital data is increasing at an astonishing rate. So too is the importance of wavelets to anyone working with and analyzing digital data. Najmi's primer will be an indispensable resource for those in computer science, the physical sciences, applied mathematics, and engineering who wish to obtain an in-depth understanding and working knowledge of this fascinating and evolving field.
(source: Nielsen Book Data)
- Wavelets (Mathematics)
- Publication date
- Amir-Homayoon Najmi.