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contentsxiii10.5 Unit II. Filtering Noisy Signals 24610.6 Noise Reduction via Autocorrelation (Theory) 24610.6.1 Autocorrelation Function Exercises 24910.7 Filtering with Transforms (Theory) 25010.7.1 Digital Filters: Windowed Sinc Filters ⊙ 25310.8 Unit III. Fast Fourier Transform Algorithm ⊙ 25610.8.1 Bit Reversal 25810.9 FFT Implementation 25910.10 FFT Assessment 26311 Wavelet Analysis & Data Compression 26411.1 Unit I. Wavelet Basics 26411.2 Wave Packets and Uncertainty Principle (Theory) 26611.2.1 Wave Packet Assessment 26811.3 Short-Time Fourier Transforms (Math) 26811.4 The Wavelet Transform 26911.4.1 Generating Wavelet Basis Functions 27011.4.2 Continuous Wavelet Transform Implementation 27311.5 Unit II. Discrete Wavelet Transform andMultiresolution Analysis ⊙ 27411.5.1 Pyramid Scheme Implementation ⊙ 27911.5.2 Daubechies Wavelets via Filtering 28311.5.3 DWT Implementation and Exercise 28612 Discrete & Continuous Nonlinear Dynamics 28912.1 Unit I. Bug Population Dynamics (Discrete) 28912.2 The Logistic Map (Model) 28912.3 Properties of Nonlinear Maps (Theory) 29112.3.1 Fixed Points 29112.3.2 Period Doubling, Attractors 29212.4 Mapping Implementation 29312.5 Bifurcation Diagram (Assessment) 29412.5.1 Bifurcation Diagram Implementation 29512.5.2 Visualization Algorithm: Binning 29512.5.3 Feigenbaum Constants (Exploration) 29712.6 Random Numbers via Logistic Map(Exploration) ⊙ 29712.7 Other Maps (Exploration) 298−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.34811_fm — 2008/2/13 — Page xiii