Elements of Wavelets for Engineers and Scientists
An indispensable guide to understanding wavelets
Elements of Wavelets for Engineers and Scientists is a guide to wavelets for "the rest of us"-practicing engineers and scientists, nonmathematicians who want to understand and apply such tools as fast Fourier and wavelet transforms. It is carefully designed to help professionals in nonmathematical fields comprehend this very mathematically sophisticated topic and be prepared for further study on a more mathematically rigorous level.
Detailed discussions, worked-out examples, drawings, and drill problems provide step-by-step guidance on fundamental concepts such as vector spaces, metric, norm, inner product, basis, dimension, biorthogonality, and matrices.
Chapters explore . . .
* Functions and transforms
* The sampling theorem
* Multirate processing
* The fast Fourier transform
* The wavelet transform
* QMF filters
* Practical wavelets and filters
. . . as well as many new wavelet applications-image compression, turbulence, and pattern recognition, for instance-that have resulted from recent synergies in fields such as quantum physics and seismic geology.
Elements of Wavelets for Engineers and Scientists is a must for every practicing engineer, scientist, computer programmer, and student needing a practical, top-to-bottom grasp of wavelets.
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Basis and Dimension
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aliasing allpass Answer bandwidth basis functions basis vectors calculate Chapter Goals codomain coefficients at level component vector concept convolution convolve coordinate vectors correlation defined definition derived diagram discrete-time signals distance downsampling Drill DTFS energy signal equation Example exponential Figure filter bank Find the matrix finite form a basis formula Fourier transform frequency functions and wavelets geometric vectors given gives h0 and h Haar wavelet high-pass filter impulse response inner product inverse linear combination low-pass filter magnitude and phase MATLAB matrix of transformation multiply norm Nyquist rate obtain operations original signal orthonormal output perfect reconstruction filter pole-zero plot polynomials poo(t power signals quadrature mirror filters real number reciprocal basis reconstruction filter represents sampling rate satisfy scalar scaling and wavelet sequence shown in Fig shows sinusoids Solution Step subset subspace unit circle upsampling values vector space waveforms wavelet coefficients wl wl wl