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### LEARNING OBJECTIVES

- Learn to describe signals mathematically and understand how to perfrom transformations
- Understand the classification of signals and the importance of analyzing signals in the frequency domain
- Understand the meaning of system property characteristics and identify systems by their type

### COURSE ALIGNMENT

Level |
University |

Topic |
Signals and Systems |

Style |
Textbook |

Prerequisite Skills |
Familiarity with mathematical concepts used in engineering including calculus, complex variables, and algebra. |

Signals come in many forms: continuous, discrete, analog, digital, periodic, nonperiodic, with even or odd symmetry or no symmetry at all, and so on. This chapter introduces vocabulary, the properties, and the transformations commonly associated with signals in preparation for exploring in future chapters how signals interact with systems.

By modeling a car suspension system in terms of a differential equation, we can determine the response of the car's body to any pavement profile it is made to drive over. The same approach can be used to compute the response to any linear system to any input excitation. This chapter provides the languages, the mathematical models, and the tools for characterizing linear, time-invariant systems.

The beauty of the Laplace-transform technique is that it transforms a complicated differential equation into a straightforward algebraic equation. This chapter covers the A-to-Z of how to transform a differential equation from the time domain to the complex frequency s domain, solve it, and the inverse transform the solution to the time domain.

The Laplace-Transform tools learned in the previous chapter are now applied to model and solve a wide variety of mechanical and thermal systems, including how to compute the movement of a passenger's head as the car moves over curbs and other types of pavements, and how to design feedback to control motors and heating systems.

Time-domain signals have frequency domain spectra. Because many analysis and design projects are easier to work with in the frequency domain, the ability to easily transform signals and systems back and forth between the two domain will prove invaluable in succeeding chapters.

Noise filtering, modulation, frequency division multiplexing, signal sampling, and many related topics are among those treated in this chapter. These are examples of applications that rely on the properties of the Fourier transform introduced in Chapter 5.

This chapter introduces discrete-time signals and systems. This z-transform of a discrete-time signal, which is the analog of the Laplace transform of a continuous-time signal, is examined in great detail in preparation for Chapter 8 where applications of discrete-time signals and systems are highlighted.

In real-time signal processing the output of signal is generated from the input signal as it arrives, using an ARMA difference equation. In batch signal processing, a previously digitized and stored signal can be processed in its entirety, all at once. This chapter presents examples of how noise filtering and other applications are performed in discrete time.

This chapter explores multiple approaches to discrete-time filter design, multirate signal processing, and correlation, and illustrates these techniques through examples of biomedical application.

The one-dimensional (1-D) discrete-time signals and systems tools are extended in in this chapter to 2-D spatial images, which are used to perform image-processing enhancements, including denoising, edge detection and deconvolution. This is followed by a treatment of the discrete-space wavelet transform and examples of its many applications, including inpainting and compressed sensing.

### myDAQ

Combines a comprehensive set of plug-and-play computer-based lab instruments with portability for hands-on student learning in or outside the lab.

### LabVIEW

An integrated development environment designed specifically for engineers and scientists.