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

Chapter 1 Continuous-time Signals and Systems

Chapter 1 Continuous-time Signals and Systems

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

§1.1 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

§1 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 most simplest signals which will pass though the system and produce a response. Combine the responses of l simplest signals which is the system response of the original signal This is the basic method to study the signal nalyses and processing

§1.1 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 most simplest signals which will pass though the system and produce a response. Combine the responses of all simplest signals, which is the system response of the original signal.
This is the basic method to study the signal analyses and processing

81.2 Continue-time Signal ☆ All sig nals 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)=0t0 Call the signal causal

§1.2 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 the signal causal

Typical signals and their representation o Unit Step u(t(in our textbook u(t) t>0 t<0 u(t-to) ●☆u( 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 asin(ot+o) f(t=asin(ot+)= Asin(nit+o) A- amplitude f- frequency (hz o=2f angular frequency(radians/sec) a-start phase(radians)

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

Typical signals and their representation oo sin/cos signals may be represented by complex exponential A sin( at+o)=c(e/tonto j(at+o) A cos( at+o)=(e/tp)+ e (at+o) ☆ Euler' s relation s ej(ax+p)=cOS(@t+o)+ jsin(at+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 ☆Si inusoidal is basic periodic signal which is important both in theory and engineering &sinusoidal is non-causal signal. All of eriodic signals are non-causal because they have no start and no end f(t)=f(tmT)m=0,±1,±2,…,如

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 .a is rea a 0 growing

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

Typical signals and their representation 冷 Exponential f(t)=e a is complex a=0+io f(t=Ae at= Allot jo)t Aeot cos ot +i aeot sin ot sInusoidal 0>0, growing sinusoidal 0<0, decaying sinusoidal(damped)

Typical signals and their representation
Exponential f(t) = eαt •α is complex α = σ + jω f(t) = Ae αt = Ae(σ + jω)t = Aeσ t cos ωt + j Aeσ t sin ωt σ = 0, sinusoidal σ > 0 , growing sinusoidal σ < 0 , decaying sinusoidal (damped)