數(shù)字通信第3章-通信信號(hào)與系統(tǒng)-.課件

1、第3章 通信信號(hào)與系統(tǒng)的表征帶通信號(hào)與系統(tǒng)的表示信號(hào)空間表示數(shù)字調(diào)制信號(hào)的表示（第4章介紹）數(shù)字調(diào)制信號(hào)的頻譜特性（第4章介紹）1窄帶信號(hào)（帶通信號(hào)）定義：信號(hào)s(t)稱(chēng)為是帶通的，或窄帶的，指它的Fourier變換S( f )在 某個(gè)高頻 f0 附近一個(gè)小領(lǐng)域上不為零，在其它地方為零。 f0AS( f )-f03.1 帶通信號(hào)與系統(tǒng)的表示幾個(gè)術(shù)語(yǔ)解析信號(hào)時(shí)域表示頻域表示等效低通Hilbert transform: To shift the phase angle of the given signal by 90Assume a filter with response function o

2、f This filter produce a phase shift of -90 degrees for all the positive frequencies of the input signal and +90 degrees for all the negative frequencies fPhase of H(f)+90-90Assume the passband signal s(t) is real valued. fc-fcS(f)Therefore we have We define the pre-envelope of the signal s(t) as s+(

3、t)The s+(t) has the positive spectrumfc-fcS+(f) f0AS( f )-f02AS+( f )f02ASl( f )2）把 S+(f)向左移 f0 ，得到s(t) 的低通等效的時(shí)域表示 sl(t)如何得到帶通信號(hào)s(t) 的復(fù)包絡(luò)表示（即等效低通表示）？1)首先在頻域上刪除S(f)的負(fù)頻分量，再乘以2，得到 s+(t)的頻譜S+(f)Therefore s+(t) can be written as sl(t) is the complex valued lowpass signal which can be expressed asTherefor

4、e s(t) can be expressed asorIn general, the Fourier transform S(f) is a complex function of frequency f, so that we may express it in the form is amplitude spectrum, and (f) is phase spectrumFor the real valued signal g(t), we have*: the complex conjugateThat isFor the real valued signal1. The ampli

5、tude spectrum is an even function of frequencies. That is the amplitude is symmetric about the vertical axis.2. The phase of the signal is an odd function of the frequency. That is the phase spectrum is anti-symmetric about the vertical axis.實(shí)信號(hào)的頻率特性同樣，帶通系統(tǒng)（窄帶系統(tǒng)）是指它的傳遞函數(shù)H( f )是窄帶的，以“理想帶通系統(tǒng)”為例2帶通系統(tǒng)3窄

6、帶信號(hào)通過(guò)窄帶系統(tǒng) 4、平穩(wěn)帶通過(guò)程 設(shè)一組標(biāo)準(zhǔn)正交函數(shù)為fn(t),n=1,2,.,N，即信號(hào)s(t)可以由fn(t)的線(xiàn)性組合來(lái)近似 這一近似的誤差為如何求得系數(shù)sk , 使得誤差的能量最小？3.2 信號(hào)的矢量空間表示 結(jié)論：When e(t)=0, the orthogonal function is said to be complete.In such a case,thus信號(hào)的正交展開(kāi)方法 (Gran Schmidt)設(shè)一組信號(hào)為si(t),i=1,2,M,現(xiàn)求一組正交函數(shù)來(lái)表示這組信號(hào)。第一步:設(shè)歸一化的s1(t)為第一個(gè)正交函數(shù),即第一個(gè)單位長(zhǎng)度的正交矢量為第二步:計(jì)算f1(t)在s2(t)上的投影從s2(t)中減去c12f1(t),即得到s2(t)信號(hào)中所包含的與f1(t)正交的部分將f2(t)歸一化,即得到第二個(gè)單位長(zhǎng)度的正交矢量這里第三步:求第k個(gè)正交函數(shù)正交化過(guò)程繼續(xù)下去，直到所有M個(gè)信號(hào)波形處理完畢，則NM個(gè)標(biāo)準(zhǔn)正交波形構(gòu)造完成。其中信號(hào)的空間表示例4-2-2解:同理信號(hào)