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 Laplace transform properties
3.4 Laplace transform pairs”
3.5 Laplace circuit analysis examples
3.6 Inverse Laplace transforms and partial fraction expansion
3.7 Partial fraction expansion, repeated poles
3.8 Partial fraction expansion using MATLAB
3.9 Transfer function
3.10 Poles and system stability
3.11 Invertible systems
3.12 Bilateral transform for continuous-time sinusoidal signals
3.13 Interrelating different descriptions of LTI systems
3.14 LTI system response partitions

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 Control system stability
4.10 Temperature control system
4.11 Amplifier gain-bandwidth product
4.12 Step response of a motor system
4.13 Control of a simple inverted pendulum on a cart

5.1 Phasor-domain technique
5.2 Fourier series analysis technique
5.3 Fourier series representations
5.4 Sinusoidal Fourier series coefficients
5.5 Amplitude/phase Fourier series
5.6 Complex exponential Fourier series
5.7 Fourier series symmetry considerations
5.8 Circuit analysis with Fourier series
5.9 Parseval’s theorem for periodic waveforms
5.10 Fourier transform
5.11 Fourier transform properties
5.12 Fourier transform pairs
5.13 Parseval’s theorem for Fourier transforms
5.14 Additional attributes of the Fourier transform
5.15 Phasor vs. Laplace vs. Fourier
5.16 Circuit analysis with the Fourier transform
5.17 The importance of Fourier phase information

6.1 Filtering a 2-D image
6.2 Filter types
6.3 Decibels
6.4 Introduction to Bode plots
6.5 Bode plots, continued
6.6 Bandpass filters
6.7 RLC highpass, lowpass, and band-reject filters
6.8 Filter order and 2nd order filters
6.9 Active filters
6.10 Cascaded active filters
6.11 Ideal brick-wall filters
6.12 Filter design by poles and zeros
6.13 Frequency rejection filters: sinusoidal interference
6.14 Comb filters
6.15 Spectra of musical notes
6.16 Butterworth filter pole placement and lowpass filter
6.17 Butterworth highpass and bandpass filters
6.18 Denoising a trumpet signal
6.19 Resonator filter

7.1 Signal Bandwidth
7.2 Multiplication of signals and switching modulation
7.3 Double-sideband amplitude modulation (DSB-AM)
7.4 Mixing, frequency division multiplexing (FDM), and Single-sideband amplitude modulation (SSB-AM)
7.5 Sampling analog signals
7.6 Shannon’s sampling theorem
7.7 Aliasing
7.8 Sampling bandpass signals

8.1 Discrete signal notation and properties
8.2 Discrete-time signal functions
8.3 Discrete-time LTI systems
8.4 Properties of discrete-time LTI systems
8.5 Discrete-time convolution
8.6 The z-transform
8.7 Properties of the z-transform
8.8 Inverse z-transform
8.9 Partial fractions method for inverse z-transforms
8.10 Solving difference equations with initial conditions
8.11 System transfer function H(z)
8.12 BIBO stability of H(z)
8.13 System frequency response

9.1 Discrete-time Fourier series (DTFS)
9.2 Discrete-time Fourier transform (DTFT)
9.3 Discrete Fourier transform (DFT)
9.4 Windowing in DFT
9.5 DFT and convolution
9.6 Fast Fourier transform (FFT)
9.7 Cooley-Tukey FFT

10.1 Discrete-time filters
10.2 Discrete-time filter types
10.3 Notch filters
10.4 Comb filters
10.5 Deconvolution
10.6 Dereverberation
10.7 Bilateral z-transforms
10.8 Inverse bilateral z-transforms
10.9 ROC, stability, and causality
10.10 Deconvolution and filtering using the DFT
10.11 Spectra of periodic signals
10.12 Spectral leakage
10.13 Computing spectra of nonperiodic signals

11.1 Data windows
11.2 Spectrograms
11.3 Finite impulse response (FIR) filters
11.4 FIR filter design methods
11.5 Infinite impulse response (IIR) filters
11.6 IIR Bilinear transformation design method
11.7 Multirate signal processing
11.8 Downsampling
11.9 Upsampling
11.10 Interpolation
11.11 Multirate signal processing examples
11.12 Oversampling by upsampling
11.13 Audio signal processing
11.14 Correlation and autocorrelation
11.15 Cross correlation
11.16 Biomedical applications

12.1 Image processing basics
12.2 Discrete-space Fourier transform
12.3 2-D DFT
12.4 Downsampling and upsampling of images
12.5 Image denoising
12.6 Edge detection
12.7 Canny edge detection
12.8 Image deconvolution
12.9 Overview of the discrete-time wavelet transform
12.10 Haar wavelet transform
12.11 Haar wavelet transform filter banks
12.12 The family of wavelet transforms
12.13 Non-Haar single-stage perfect reconstruction
12.14 Daubechies scaling and wavelet functions
12.15 Image analysis
12.16 Image synthesis and image compression”
12.17 Denoising by thresholding and shrinking
12.18 Compressed sensing
12.19 Computing solutions to underdetermined equations
12.20 Landweber algorithm
“12.21 Image inpainting and image reconstruction
12.22 Computed axial tomography (CAT) ”

13.1 Appendix A: Symbols, quantities, and units
13.2 Appendix B: Review of complex numbers
13.3 Appendix C: Mathematical formulas
13.4 Appendix D: MATLAB
13.5 Appendix E: Using LabVIEW modules

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