精品課程《大學(xué)物理》-信號與系統(tǒng)-文庫吧
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【正文】 ordinates 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(shè) )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)。 21 /TT 為無理數(shù)時，則是非周期函數(shù)。 21 /TT例： Page 6 Deterministic and Stochastic (nondeterministic) Signals Definitions 信號的未來值可以用時間變量的數(shù)學(xué)關(guān)系式準(zhǔn)確描述的信號稱為 確定性信號 。 如果給定任一時間，信號的值是隨機(jī)的，換句話說，信號的未來值不能用準(zhǔn)確的時間函數(shù)式來描述，無法準(zhǔn)確地預(yù)測，在相同的條件下也不能準(zhǔn)確地重現(xiàn)，則稱該信號為 不確定信號或隨機(jī)信號 。 ? 確定信號：在任何時刻的取值都能唯一地確定。 ? 隨機(jī)信號：在任何時刻的取值都是隨機(jī)的、不確定，信號發(fā)生前不能準(zhǔn)確預(yù)測信號的取值。 ? 例如 : ? x(t)=sint 是確定信號，把帶入可以求出任何一時刻的x(t)值 ? 生活中大多是隨機(jī)信號（新信息）： 耗電、打電話等 Deterministic and Stochastic (nondeterministic) Signals 確定性信號隨機(jī)信號 (非確定性信號 ) ? Even signal A signal x(t) or x[n] is referred to as an even signal if it is identical to its timereversed counterpart, ., with its reflection about the origin. In continuous time a signal is even if ? ?tftf ee ??)(Odd and Even Signals while a discretetime signal is even if ][][ kfkf ??? Odd signal A signal is said to be odd if ][][ kfkf ???)()( tftf ???In continuous time In discrete time )()()( tftftf eo ??)]()()()([21)( tftftftftf ???????)]()([21)]()([21 tftftftf ??????)()( tftf oe ??Odd and Even Signals In fact, any signal f(t) can be expressed as a sum of its even part and its odd part, that is )]()([21)( txtxtx e ???)]()([21)( txtxtx o ???Even part: Odd part: So: 11 0t21f ( t )t11 021f ( ? t ) t11 0fe( t )t11f0( t )Example:Determine the even and odd parts of the signal f(t) given by Buildingblock signals (典型信號 ) 正弦信號 sine signals 指數(shù)信號 exponential signals 沖激信號 impulse signals 階躍信號 step signals sine signals )s i n ()( 0 ?? ?? tAtft A ? A 0???exponential signals指數(shù)信號 tAetfa?)(At0a0aReal Exponential Signals ????? ?0 00,0 )(ttAetf t aata/1A則？若 ,0,)( ? ? aa tAetf Eternal, plex exponentials 指數(shù)信號 For is plotted for different values of s superimposed on the plex splane. tAetfIAetf tst ?? s i n)]([,)( ??Complex Exponential tjetf 0)( ??復(fù)指數(shù)信號的基波周期： 0/2 ???TEuler’s relation： )(21)c o s ( tjtj eet ??? ???)(2 1)s
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