信号与图像处理基础 Introduction 中国科学技术大学自动化系 曹洋
University of Science and Technology of China 信号与图像处理基础 中国科学技术大学 自动化系 曹 洋 Introduction
信号与系统：Signals and Systems Signal:a function carrying information Describe a system (physical,mathematical,or computational)by the way it transforms an input signal into an output signal signal signal system in out 7
信号与系统：Signals and Systems • Signal: a function carrying information • Describe a system (physical, mathematical, or computational) by the way it transforms an input signal into an output signal 7
信号与系统：Signals and Systems Signal:a function carrying information Describe a system (physical,mathematical,or computational)by the way it transforms an input signal into an output signal signal signal system in out 8
信号与系统：Signals and Systems • Signal: a function carrying information • Describe a system (physical, mathematical, or computational) by the way it transforms an input signal into an output signal 8
Example System:水箱 Formulate a mathematical description of this system. r ro(t) r1(t) What determines the leak rate? 9
Example System: 水箱 Formulate a mathematical description of this system. 9 What determines the leak rate?
Check yourself The holes in each of the following tanks have equal size. Which tank has the largest leak rate r1(t)? 2 3. 4. 10
Check yourself 10
Check yourself The holes in each of the following tanks have equal size. Which tank has the largest leak rate r1(t)?2 2. 3. 4. 11
Check yourself 11
Example System:水箱 ro(t) hi(t) r1(t) Assume linear leaking:1(t)(t) What determines the height h (t)? 12
Example System: 水箱 12 Assume linear leaking: What determines the height h1 (t)?
Example System:水箱 ro(t) hi(t r1(t) Assume linear leaking:1(t)(t) Assume water is conserved: dh1() dt x ro(t)-ri(t) Solve: dri( dt 2xro()-r1() 13
Example System: 水箱 13 Assume linear leaking: Assume water is conserved: Solve:
Example System:水箱 Call the constant of proportionality 1/. Then t is called the time constant of the system dr(=o()_r1() dt T T 14
Example System: 水箱 14 Call the constant of proportionality Then τ is called the time constant of the system
Check yourself Which of the following tanks has the largest time constant T? 2 3 4. 15
Check yourself 15