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Table of Contents

1.1 Types of signals
1.2 Signal transformations
1.3 Waveform properties
1.4 Nonperiodic waveforms
1.5 Signal power and energy
1.6 LAB: Getting started with MATLAB grader
1.7 LAB: Signals

.1 Linear time-invariant systems
2.2 Impulse response
2.3 Convolution
2.4 Graphical convolution
2.5 Convolution properties
2.6 Causality and BIBO stability
2.7 LTI sinusoidal response
2.8 Impulse response of second-order LCCDEs
2.9 Car suspension system
2.10 LAB: A second order circuit’s impulse and step response

3.1 Definition of the (unilateral) Laplace transform
3.2 Poles and zeros
3.3 Properties of the Laplace transform
3.4 Circuit analysis examples
3.5 Inverse Laplace transforms and partial fraction expansion
3.6 Transfer function H(s)
3.7 Poles and system stability
3.8 Invertible systems
3.9 Bilateral transform for continuous-time sinusoidal signals
3.10 Interrelating different descriptions of LTI systems
3.11 LTI system response partitions
3.12 LAB: Laplace transform and transfer function

4.1 s-domain circuit element models
4.2 s-domain circuit analysis
4.3 Electromechanical analogues
4.4 Biomechanical model of a person sitting in a moving chair
4.5 Op-amp circuits
4.6 Configurations of multiple systems
4.7 System synthesis
4.8 Basic control theory
4.9 Temperature control system
4.10 Amplifier gain-bandwidth product
4.11 Step response of a motor system
4.12 Control of a simple inverted pendulum on a cart
4.13 LAB: Laplace transform applications

5.1 Phasor-domain technique
5.2 Fourier series analysis technique
5.3 Fourier series representations
5.4 Computation of Fourier series coefficients
5.5 Circuit analysis with Fourier series
5.6 Parseval’s theorem for periodic waveforms
5.7 Fourier transform
5.8 Fourier transform properties
5.9 Parseval’s theorem for Fourier transforms
5.10 Additional attributes of the Fourier transform
5.11 Phasor vs. Laplace vs. Fourier
5.12 Circuit analysis with the Fourier transform
5.13 The importance of phase information
5.14 LAB: Circuit analysis using Fourier transform

6.1 Filtering a 2-D image
6.2 Types of filters
6.3 Passive filters
6.4 Active filters
6.5 Ideal brick-wall filters
6.6 Filter design by poles and zeros
6.7 Frequency rejection filters
6.8 Spectra of musical notes
6.9 Butterworth filters
6.10 Denoising a trumpet signal
6.11 Resonator filter
6.12 Modulation
6.13 Sampling theorem
6.14 LAB: Bode plots

7.1 Discrete signal notation and properties
7.2 Discrete-time signal functions
7.3 Discrete-time LTI systems
7.4 Properties of discrete-time LTI systems
7.5 Discrete-time convolution
7.6 The z-transform
7.7 Properties of the z-transform
7.8 Inverse z-transform
7.9 Solving difference equations with initial conditions
7.10 System transfer function H(z)
7.11 BIBO stability of H(z)
7.12 System frequency response
7.13 Discrete-time Fourier series (DTFS)
7.14 Discrete-time Fourier transform (DTFT)
7.15 Discrete Fourier transform (DFT)
7.16 Fast Fourier transform (FFT)
7.17 Cooley-Tukey FFT
7.18 LAB: Discrete-time signals and systems

8.1 Discrete-time filters
8.2 Notch filters
8.3 Comb filters
8.4 Deconvolution and dereverberation
8.5 Bilateral z-transforms
8.6 Inverse bilateral z-transforms
8.7 ROC, stability, and causality
8.8 Deconvolution and filtering using the DFT
8.9 Computing spectra of periodic signals
8.10 Computing spectra of nonperiodic signals
8.11 LAB: Applications of discrete-time signals and systems

9.1 Data windows
9.2 Spectrograms
9.3 Finite impulse response (FIR) filter design
9.4 Infinite impulse response (IIR) filter design
9.5 Multirate signal processing
9.6 Downsampling
9.7 Upsampling
9.8 Interpolation
9.9 Multirate signal processing examples
9.10 Oversampling by upsampling
9.11 Audio signal processing
9.12 Correlation
9.13 Biomedical applications
9.14 LAB: Discrete-time filter design
9.15 LAB: Discrete-time filter design with zpk and designfilt

10.1 Image processing basics
10.2 Discrete-space Fourier transform
10.3 2-D DFT
10.4 Downsampling and upsampling of images
10.5 Image denoising
10.6 Edge detection
10.7 Image deconvolution
10.8 Overview of the discrete-time wavelet transform
10.9 Haar wavelet transform
10.10 The family of wavelet transforms
10.11 Non-Haar single-stage perfect reconstruction
10.12 Daubechies scaling and wavelet functions
10.13 2-D wavelet transform
10.14 Denoising by thresholding and shrinking
10.15 Compressed sensing
10.16 Computing solutions to underdetermined equations
10.17 Landweber algorithm
10.18 Compressed sensing examples

11.1 Appendix A: Symbols, quantities, and units
11.2 Appendix B: Review of complex numbers
11.3 Appendix C: Mathematical formulas
11.4 Appendix D: MATLAB, MathScript, and Octave
11.5 Appendix E: A guide to using LabVIEW modules

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