## Table of Contents

1. Signals

1.1 Types of signals

1.2 Signal transformations

1.3 Waveform properties

1.4 Nonperiodic waveforms

1.5 Signal power and energy

2. Linear Time-Invariant Systems

2.1 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

3. Laplace Transform

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 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

4. Applications of the Laplace Transform

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

5. Fourier Analysis Techniques

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

6. Applications of the Fourier Transform

6.1 Chapter overview and 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

7. Discrete-Time Signals and Systems

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

8. Applications of Discrete-Time Signals and Systems

8.1 Chapter overview, and 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

9. Discrete-Time Filter Design, Multirate, and Correlation

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

10. Image Processing, Wavelets, and Compressed Sensing

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. Appendix

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

**zyVersions** are leading print titles converted and adapted to zyBooks’ interactive learning platform, allowing for a quick and easy transition to an engaging digital experience for instructors and students.

## What You’ll Find In This zyVersion:

### More action with less text.

- The NI Engineering Signals and Systems texts gets a new, interactive version as a zyBooks title for 2020.
- Applications of signals and systems for engineering are presented alongside concepts and mathematical models.
- Practice problems with fixed parameters allow students to practice more advanced problems and see different examples.
- Auto-graded challenge activities also help students practice solving problems with variables and increasing difficulty levels. Includes labs that encourage students to vary parameter values to clarify many of the examples and associated problem-solving assignments.

## Contributors

**Yasaman Adibi**

*Content Developer, zyBooks/ Ph.D. Electrical Engineering, University of Minnesota*

**Mark Atkins**

*Associate Professor of Electrical Engineering, Ivy Tech Community College*

**Nikitha Sambamurthy**

*Content Lead, zyBooks, Ph.D. Engineering Education, Purdue University*

**Mohsen Sarraf**

*Visiting Associate Professor of Electrical Engineering, University of New Haven*