Signals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fifth Edition iCopyright © Orchard Publications

Table of Contents

1 Elementary Signals 1−1

1.1 Signals Described in Math Form ............................................................................... 1−11.2 The Unit Step Function ............................................................................................ 1−21.3 The Unit Ramp Function.......................................................................................... 1−91.4 The Delta Function.................................................................................................. 1−11

1.4.1 The Sampling Property of the Delta Function..............................................1−111.4.2 The Sifting Property of the Delta Function ..................................................1−12

1.5 Higher Order Delta Functions ................................................................................1−131.6 Summary ..................................................................................................................1−231.7 Exercises ...................................................................................................................1−241.8 Solutions to End−of−Chapter Exercises..................................................................1−25

MATLAB ComputingPages 1−19 through 1−22

Simulink ModelingPage 1−17

2 The Laplace Transformation 2−1

2.1 Definition of the Laplace Transformation ................................................................2−12.2 Properties and Theorems of the Laplace Transform.................................................2−2

2.2.1 Linearity Property ..........................................................................................2−32.2.2 Time Shifting Property ...................................................................................2−32.2.3 Frequency Shifting Property ..........................................................................2−42.2.4 Scaling Property .............................................................................................2−42.2.5 Differentiation in Time Domain Property ....................................................2−42.2.6 Differentiation in Complex Frequency Domain Property............................2−62.2.7 Integration in Time Domain Property ..........................................................2−62.2.8 Integration in Complex Frequency Domain Property ..................................2−72.2.9 Time Periodicity Property ..............................................................................2−82.2.10 Initial Value Theorem ...................................................................................2−92.2.11 Final Value Theorem ...................................................................................2−102.2.12 Convolution in Time Domain Property......................................................2−112.2.13 Convolution in Complex Frequency Domain Property .............................2−11

2.3 The Laplace Transform of Common Functions of Time........................................2−122.3.1 The Laplace Transform of the Unit Step Function ...........................2−122.3.2 The Laplace Transform of the Ramp Function .................................2−122.3.3 The Laplace Transform of ...............................................................2−142.3.4 The Laplace Transform of the Delta Function ....................................2−172.3.5 The Laplace Transform of the Delayed Delta Function .................2−17

u0 t( )u1 t( )

t nu0 t( )δ t( )

δ t a–( )