1.3 Exponential and Sinusoidal Signals 1.3.1 Continuous-Time Complex Exponential and Sinusoidal Signals Real Exponential Signals (C and a are real) If a>0, x(t) is a growing exponential If a<0, x(t) is a decaying exponential Impulse responses for first-order systems

Pure Imaginary Exponential Signals (C=1 and a=j0 )

Sinusoidal Signals Impulse responses for second-order systems

Fundamental Frequency and Fundamental Period

Infinite-Energy but Finite-Power signals

Euler’s Relation

1.3 Exponential and Sinusoidal Signals 1.3.1 Continuous-Time Complex Exponential and Sinusoidal Signals General Complex Exponential Signals (C and a are complex numbers)

General Complex Exponential Signals (C and a are complex numbers)

1.3 Exponential and Sinusoidal Signals 1.3.2 Discrete-Time Complex Exponential and Sinusoidal Signals

Discrete-Time Real Exponential Signals (C and a are real)

Discrete-Time Sinusoidal Signals

Discrete-Time Sinusoidal Signals (C=1 and a =j0)

General Complex Exponential Signals (C and a are complex numbers)

1.21 1.22 (a), (b), (e), (f) 1.23 (a)

SAS实验一 画出CTS实指数信号、正弦信号、虚指数信号（实部、虚部）的波形图，并进行讨论 画出DTS实指数信号、正弦信号、虚指数信号（实部、虚部）的波形图，并进行讨论 要求：Word或PPT文档 文件名：学号_姓名_实验1

1.3.3 Periodicity Properties of Discrete-Time Pure Imaginary Exponential and Sinusoidal Signals The large the magnitude 0 of e j 0 t, the higher is the rate of oscillation in the signal. What about e j 0 n ?

What is the low frequency of e j 0 n ? 1.3.3 Periodicity Properties of Discrete-Time Pure Imaginary Exponential and Sinusoidal Signals What is the low frequency of e j 0 n ? What is the high frequency of e j 0 n ?

e j 0 t is periodic for any value of 0. What about e j 0 n ?

What is the fundamental frequency of e j 0 n (if it is periodic)?

1.3.3 Periodicity Properties of Discrete-Time Pure Imaginary Exponential and Sinusoidal Signals

1.25 1.26