Advances in Signal Transforms Theory and Applications

Contents Preface ix 1. Wavelet and frame transforms originated from continuous and discrete splines, Amir Z. Averbuch and Valery A. Zheludev 1 1.1. Introduction 1 1.2. Preliminaries 4 1.3. Prediction filters originated from splines 9 1.4. Biorthogonal wavelet transforms generated by filter banks with downsampling factor N = 2 (diadic transforms) 17 1.5. Application of spline-based wavelet transforms to image compression 24 1.6. Wavelet frames (framelets) generated by 3-channel filter banks with downsampling factor N = 2 28 1.7. Erasure recovery properties of the designed wavelet frames 37 1.8. Biorthogonal wavelet transforms generated by filter banks with downsampling factor N = 3 (triadic transforms) 42 Appendix 52 Bibliography 54 2. Recent developments in Haar wavelet transform for application to switching and multivalued logic functions representations, Radomir S. Stankovi´c, Karen Egiazarian, and Jaakko Astola 57 2.1. Introduction: logic design and spectral transforms 57 2.2. Discrete Haar functions 58 2.3. Decision diagrams and their optimization 60 2.4. Haar expressions for discrete functions 61 2.5. Haar spectral diagrams 63 2.6. Haar spectral transform decision diagrams 69 2.7. HSTDDs with the minimal number of paths 71 2.8. Experimental results 77 2.9. Multivalued Haar functions 81 2.10. Closing remarks 88 Bibliography 89 3. Discrete transforms, fast algorithms, and point spread functions of numerical reconstruction of digitally recorded holograms,