【正文】 of time at a point in space. It’s a onedimensional signal: x(t) ? Waveform of the speech signal ―light up‖and ―豆豆你好” are shown below 0 500 1000 1500 2022 2500 3000 3500 4000 450032101234s p e e c h s i g n a l x(t) Onedimensional and multidimensional signals ? Blackand white picture – Represent light intensity as a function of two spatial coordinates. ? Twodimensional signal: I(x,y) I(x,y) Lena Onedimensional and multidimensional signals ? Color picture – represent red, green and blue light intensity as a function of two spatial coordinates ???????????),(),(),(),(yxIyxIyxIyxIBGRmandrill(山魈 ) Onedimensional and multidimensional signals ? Video signals – consists of a sequence of images, called frames , and is a function of 3 variables: 2 spatial coordinates and time ? blackwhite video signal:I(x,y,t) ? Color video signal: ???????????),(),(),(),(tyxbtyxgtyxrtyxuOnedimensional and multidimensional signals ? Throughout this book, we only discuss such signals which are the functions of one independent variable. ? For convenience, we will generally refer to the independent variable as time, although it may not in fact represent time in specific applications. Continuous Time（ CT） and discrete time（ DT） Signals ? Continuous Time Signal: A signal f(t) is said to be a continuoustime signal or an analog signal if the independent variable is continuous. For a continuoustime signal the function values of the signal and its independent variable are both continuous monly. ? Discrete Time Signals: A signal f[k] is said to be a discretetime signal if its time independent variable takes on only a discrete set of values. The stock market index, as illustrated in the following Figure, is an example of a discretetime signal. f(t) f[k] k 0 1 2 3 4 5 6 7 8 9 思考以下的區(qū)別： 模擬信號和數(shù)字信號 連續(xù)時間信號和離散時間信號 連續(xù)信號 時間、幅度上都連續(xù)的信號（模擬信號） 時間上連續(xù)、幅度上不連續(xù)的信號（脈沖信號） 離散信號 時間上不連續(xù)、幅度連續(xù)的信號（采樣信號） 時間、幅度上都不連續(xù)的信號（數(shù)字信號） Periodic and Aperiodic Signals Periodic and Aperiodic Signals Periodic signals are such that f(t+T) = f(t) for all t. The smallest value of T that satisfies the definition is called the period. In general, for CT signals )()( tfrTtf ??)()( nfrNnf ??for DT signals Where r, N are integers 設 )2,2(c o ss i n)( 21 nTmTntmttf ?? ????? ?? 為有理數(shù)時，則為周期函數(shù)，且其最小公共周期為其周期的最小公倍數(shù)。 ? 確定信號：在任何時刻的取值都能唯一地確定。 odd, etc. 3. Building block signals eternal plex exponentials and singularity functions are a rich class of signals and we will show that they can be summed to represent virtually any signal of physical interest. ?Addition ： f(t) = f1(t)+f2(t) f1( t )t? tt1f ( t )Operations on signals ?Multiplication : f(t) = f1(t) f2(t) f1( t )t1? 1 1f 2 ( t )t12? 2t1? 1 1?Time scaling f(t) ? f(at) a0 1t2 4f ( t )??? ????其它 042 2/)2()(tttf??? ???其它 0422 2/)22( tt??? ????其它 021 1 tt1t1 2f (2 t )?)2( tf??? ????其它 042/2 2/)22/()2/(tttf??? ????其它 084 4/)4( tt1t4 8f ( t /2 )尺度變換小結(jié)： 若 0a1，則 f(at)是 f(t)的擴展。 例 : 已知 f(t)的波形如圖所示，試畫出 f(6?2t)的波形。 系統(tǒng)響應： 零狀態(tài)響應：當輸入信號 f(t) 加入時，系統(tǒng)的狀態(tài)為零，即 系統(tǒng)沒有任何儲能，則系統(tǒng)的響應由激勵 f(t) 唯一確定。 設球體與平面間的摩擦力及空氣阻力忽略不計 。 其中 ， 電壓源 us1(t)和 us2(t)是電路的激勵 。 當系統(tǒng)的數(shù)學模型為 n階線性常系數(shù)微分方程時 ， 寫成一般形式有 ? ?? ??nimjjjii tfbtya0 0)()( )()( 式中 ， f(t)是系統(tǒng)的激勵 ， y(t)為系統(tǒng)的響應 ，