电子科技大学：《数字信号处理 Digital Signal Processing》课程教学资源（课件讲稿）Chapter 01 Continuous-time Signals and Systems

Chapter 1 Continuous-time Signals and Systems

Chapter 1 Continuous-time Signals and Systems

Introduction Any problems about signal analyses and processing may be thought of letting signals trough systems. f(t) h( y(t) From f(t)and h(t),find y(t),Signal processing From f(t)and y(t),find h(t),System design From y(t)and h(t),find f(t),Signal reconstruction

Introduction Any problems about signal analyses and processing may be thought of letting signals trough systems. h(t) f(t) y(t) From f(t) and h(t)，find y(t)， Signal processing From f(t) and y(t) ，find h(t) ，System design From y(t) and h(t)，find f(t) ， Signal reconstruction

Introduction There are so many different signals and systems that it is impossible to describe them one by one The best approach is to represent the signal as a combination of some kind of the simplest signals which will pass through the system and produce a response.Combine the responses of all simplest signals,which is the system response for the original input signal. This is the basic approach to study the signal analyses and processing

Introduction There are so many different signals and systems that it is impossible to describe them one by one The best approach is to represent the signal as a combination of some kind of the simplest signals which will pass through the system and produce a response. Combine the responses of all simplest signals, which is the system response for the original input signal. This is the basic approach to study the signal analyses and processing

Continue-time Signal All signals are thought of as a pattern of variations in time and represented as a time function f(t). In the real-world,any signal has a start. Let the start as t=0 that means f()=0 t<0 Call such signals causal

Continue-time Signal All signals are thought of as a pattern of variations in time and represented as a time function f(t). In the real-world, any signal has a start. Let the start as t=0 that means f(t) = 0 t<0 Call such signals causal

Typical signals and their representation Unit Step u(t)(in our textbook u(t)) t>0 t<0 tu(t-to) 0 to u(t)is basic causal signal,multiply which with any non-causal signal to get causal signal

Typical signals and their representation Unit Step u(t) (in our textbook µ(t)) {1 0 0 0 ( ) > = < t t u t u(t) 1 0 t u(t- t0) 1 0 t t 0 u(t) is basic causal signal, multiply which with any non-causal signal to get causal signal

Typical signals and their representation Sinusoidal A sin(ot+o) f(t)=A sin(ot+p)=A sin(2nft+o) A-Amplitude f-frequency (Hz,cycle per second) o=2af angular frequency (radians/sec) -start phase(radians)

Typical signals and their representation Sinusoidal A sin(ωt+φ) f(t) = A sin(ωt+φ)= A sin(2πft+φ) A - Amplitude f – frequency (Hz, cycle per second) ω= 2πf angular frequency (radians/sec) φ – start phase(radians)

Typical signals and their representation sin/cos signals may be represented by complex exponential )) A Asin(at+p)= cos(t+p)=号 (eo+o）+ejo+p)） Euler's relation e)-cos(@t+p)+jsin(ot+p)

Typical signals and their representation sin/cos signals may be represented by complex exponential ( ) 2 cos( ) ( ) 2 sin( ) ( ) ( ) ( ) ( ) ω ϕ ω ϕ ω ϕ ω ϕ ω ϕ ω ϕ + − + + − + + = + + = − j t j t j t j t e e A A t e e j A A t Euler’s relation cos( ) sin( ) ( ) ω ϕ ω ϕ ω ϕ = + + + + e t j t j t

Typical signals and their representation Sinusoidal is basic periodic signal which is important both in theory and engineering. Sinusoidal is non-causal signal.All of periodic signals are non-causal because they have no start and no end. f (t)=f(t+mT) m=0,士1，士2，…，士o0

Typical signals and their representation Sinusoidal is basic periodic signal which is important both in theory and engineering. Sinusoidal is non-causal signal. All of periodic signals are non-causal because they have no start and no end. f (t) = f (t + mT) m=0, ±1, ±2, ···, ±∞

Typical signals and their representation Exponential f(t)=eat a is real a 0 growing

Typical signals and their representation Exponential f(t) = eαt •α is real α 0 growing

Typical signals and their representation Exponential f(t)=eat a is complex a=0+jo f(t)=Aeat =Ae(o+jo)t =Aeot cosωt+jAeot sinωt o 0,sinusoidal o >0,growing sinusoidal o<0,decaying sinusoidal (damped)

Typical signals and their representation Exponential f(t) = eαt •α is complex α = σ + jω f(t) = Aeαt = Ae(σ + jω)t = Aeσ t cosωt + j Aeσ t sinωt σ = 0, sinusoidal σ > 0 , growing sinusoidal σ < 0 , decaying sinusoidal (damped)