數(shù)字信號(hào)處理總復(fù)習(xí)題答案-資料下載頁(yè)
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【正文】 3()13()3()()()(0)23()()13()()3()()()()(2031313313)23()13(3zXzzXzzXzrxzzrxzryzryzryznyzYzYnynxnynxnynxnyzXnxrrrrrrrrrrnn???????????????????????????????????????????????????????????解：。，求，系是：的關(guān)與，另一個(gè)序列、已知序列:)1()2()()1(101821432121平面零極點(diǎn)位臵圖解：。這是什么類(lèi)型的濾波器轉(zhuǎn)折頻率大致是多少？形狀。問(wèn)估畫(huà)出幅頻特性的大致；傳遞函數(shù)出平面零極點(diǎn)位臵圖，寫(xiě)畫(huà)出，，極點(diǎn)：；，的系統(tǒng)零點(diǎn)：、某工作頻率為zzHzppppzzk H z???????????????????1o600]Re[z]Im[zj這是一個(gè)帶通濾波器。，圖，轉(zhuǎn)折頻率大致是幅頻特性的大致形狀如323)2())(()1())()()(()1)(1()(212122323233?????????????????????????????zzzzzzezezezezzzzHjjjj3?32??w3???? ?32?|)(| jweH0)()()()()()]([)()]([)()()()()(1jwjwmj m wmnnj n wnj n wjwjwjweXnxeXemxenxnxD T F TenxnxD T F TeXeXnxeXnx????????????????????????? ?????????????證：，則、證明：若三、證明題 ???????????? ????????????????????????虛部奇對(duì)稱(chēng)實(shí)部奇對(duì)稱(chēng)為奇對(duì)稱(chēng)證：為純虛數(shù)且奇對(duì)稱(chēng)。其對(duì)應(yīng)的，則為實(shí)奇對(duì)稱(chēng)，即、證明：若)()()()]([)()]([)()()()()(210)(10))((10kXkNXWmxWnNxWnxnxD F TkXkXnNxnxnxNmmkNNmnNNnkNnNNNnnkN純虛奇對(duì)稱(chēng)。虛部奇對(duì)稱(chēng)實(shí)部偶對(duì)稱(chēng)虛部奇對(duì)稱(chēng)實(shí)部奇對(duì)稱(chēng)為虛部奇對(duì)稱(chēng)實(shí)部偶對(duì)稱(chēng)為共軛偶對(duì)稱(chēng)為實(shí)數(shù)??????????????????????????????????)()()(*)(**])([)(*)()()(*)()(101010kXkXkNXkXWnxWnxWnxkXnxnxnxNnnkNNnnkNNnnkN???????????? ?????????????????????????虛部偶對(duì)稱(chēng)實(shí)部偶對(duì)稱(chēng)為偶對(duì)稱(chēng)證：為純虛數(shù)且偶對(duì)稱(chēng)。其對(duì)應(yīng)的，則為純虛偶對(duì)稱(chēng)，即、證明：若)()()()()]([)()]([)()()()()(310)(1)(10))((10kXkNXWmxWmxWnNxWnxnxD F TkXkXnNxnxnxNmmkNNNmmkNNmnNNnkNnNNNnnkN純虛偶對(duì)稱(chēng)。虛部偶對(duì)稱(chēng)實(shí)部奇對(duì)稱(chēng)虛部偶對(duì)稱(chēng)實(shí)部偶對(duì)稱(chēng)為虛部偶對(duì)稱(chēng)實(shí)部奇對(duì)稱(chēng)為共軛奇對(duì)稱(chēng)為純虛數(shù)??????????????????????????????????????)()()(*)(**])([)(*)()()(*)()(101010kXkXkNXkXWnxWnxWnxkXnxnxnxNnnkNNnnkNNnnkN?)0(... ... ..00)0()(lim0)(lim|)(|... ... .])2()1()0([lim)(lim... ... .)2()1()0()()()0()(lim)()(|)(|)(421210xxzXznxMnxzxzxxzXzxzxxznxzXxzXzXnxMnxnxznzzznnz??????????????????????????????????????????證：。，則設(shè)。是因果序列且、證明：若是零點(diǎn)。，，是零點(diǎn)，零極點(diǎn)成共軛對(duì)出現(xiàn)是零點(diǎn)濾波器是一個(gè)零點(diǎn)設(shè)證：線性相位共軛對(duì)。倒數(shù)的濾波器的零點(diǎn)必是互為、證明：線性相位*)(*)(*)(*)(0)(00)()()()()1()(51010001001010010)1(0001)1(??????????????????????????????iiiiiiiiiiNiiiNzzzzzzzzHzF I RzHzzHzzHzzHnNhnhF I R?系統(tǒng)變成因果系統(tǒng)。時(shí)，級(jí)聯(lián)后的當(dāng)聯(lián)相級(jí)與一個(gè)全通時(shí)延系統(tǒng)令其它且，非因果系統(tǒng)為有限長(zhǎng)序列。系統(tǒng)證：級(jí)聯(lián)而變成因果系統(tǒng)。系統(tǒng)系統(tǒng)都可以通過(guò)與某種、證明：任何非因果F I RnNNnhnhnhnhNnnhnhnnnnnhnhnhF I RF I R112121121111)()()()()()()(00)()()(6??????????????? ????????????????????????????????||,1||0)(||,0||1)()()(1)()()()(7wwwweHwwwweHnnhzHzHzHnwccjwdHccjwdLdHdLc，理想高通，理想低通方法二：證：方法一：。應(yīng)序列之和等于濾波器，它們的脈沖響的理想低通和理想高通頻率、證明：具有同樣截止)()s i n ()()()()s i n ()s i n ()(21)()s i n (21)(nnnnhnhnhnnwnndwedwenhnnwdwenhdHdLcwj w nwj w ndHcwwj w ndLccccc??????????????????????????
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