已知因果离散系统的系统函数[tex=2.143x1.357]SHXQ2hcrZBkMS6Tm0ZJ+dA==[/tex]的零、极点分布如题图所示, 并且[tex=4.214x1.357]PtaoCHwK0fW6A7zguIDOoQ==[/tex] 。求系统的频率响应[img=634x257]17b071f729a23e0.png[/img]

2022-07-26

已知因果离散系统的系统函数[tex=2.143x1.357]SHXQ2hcrZBkMS6Tm0ZJ+dA==[/tex]的零、极点分布如题图所示, 并且[tex=4.214x1.357]PtaoCHwK0fW6A7zguIDOoQ==[/tex] 。求系统的频率响应[img=634x257]17b071f729a23e0.png[/img]

答案：

因 [tex=5.286x1.357]SXh2FeMkUtHnWRL5wKbMbMNX0IBT78ST6MFz1OcBncY=[/tex]收敛域均含单位圆，故系统频率响应可分别表示为[tex=17.357x7.0]exiFrBoyU/xXN0ulG845vfQbXHDpxQ7949psnXx9CyEgSh5Lk/6+uOKm9cQnwcUHMbx6T26Nm9b03VbUVLnT5MAinK5LOMzin5N2qEhTsoy1E6KOYGGtO9tJJX2VGGGgIIN6Z/bkTuA834RFtSgeF3zEo+l62CMaAjK7XBSKkj9rhR4jWLLyQ5Ib0aqoBKxDNpo8JlHn6TVXeft5eY5/U1SIs/lmqXcfnOLxtjMAoG6AzUUNIL5PAQw+f1WC8+W5fO0egv141OZ+w5yLkSeXOgcA0ZP/rOFzX/x7v+3DeiRFT46dKMzgSyNMB+6Pex7jp3za7XWx2wPZps1wEUnyDC6PIE21OuSjY65TB2kQlYrS0m+cP5+dT91JGJTR422NTUUrh78cLNIMBcwkFxGAATsAXXis3rOBkQ9sLwFto599SqJVdddbgrIKO9VA2kcy[/tex][tex=20.286x6.214]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[/tex][tex=16.429x7.0]xICaigU98qjFZJbPls09n/GvJhrVAxiUoC3nB8f04FAvPoujI9FhgU+n8nNxd0TthZGMsROwr5yZ7pH7v6QG1/0bF3Qt8SOJ8ZYM3dZrDmt7MIB7Cs44NCX95LWSAHfX4ttHQhAR4uTxjmInlanpjyIG+E5on6JN8rFnNehpufuBXAsdFowPvzzx2DJwhqFYhiKcDaXuhzPn/wq/eKOsx0C/wLrQ7XZ/jOMUR+Z3tu04Q952M/OModCbtBFnnH25mJ5Yb++lmfPHl16rx6nCtvEUvXCS+SwjpHHN7RhuQOZ0hrQXaXqJNd9qLFDsJYxU1enKtBnjY2/X0FBdrepdQ2AeixbrMWcu/htKVWcyptvWcr2Cmm02vXPUoUtDVZocnaXQtkqymy5WDbjlmsXOoN3BFRlRdiSmF2LnSc7+sbB41KytVy+9ch4cO3/Tivg7[/tex][tex=19.786x6.214]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[/tex]

举一反三

内容

0
已知某离散时间系统函数[tex=2.143x1.357]oUUJfCD5beKNaWD9gue2xw==[/tex]的零极点分布图如题图所示，试定性画出各系统单位脉冲响应[tex=1.714x1.357]+mi6z4gh7vxqDBBtQ2ZcBQ==[/tex]的系统的幅频特性曲线。[img=678x859]17dade07c62387b.png[/img]
1
已知某系统函数 H(s)的零、极点分布如题图所示, 若冲激响应的初值 [tex=3.714x1.357]L+tLhJnQ09HSDv22FuHU0Q==[/tex], 求系统函数 H(s), 并求出 h(t) 。[img=401x342]17d4c3130c4562b.png[/img]
2
图表示一个因果时不变离散系统。试求该系统的系数函数 [tex=2.143x1.357]oUUJfCD5beKNaWD9gue2xw==[/tex] 和频率响应 [tex=3.143x1.571]C/R/2fwB8OIhSRFaanE7W/1y0Fvl3h7gua/fPZexJjq1aqqdgH/o54aJy9zRwrOP[/tex][img=394x131]17a3713a32829c9.png[/img]
3
已知离散 LTI 因果系统的零极,点如图 6-13 所示, 且系统的 [tex=4.5x1.357]Fmy8wovuJw5q0ksU9YiB9Q==[/tex], 求系统单位样值响应h(n)[br][/br] [img=360x144]17ae77245ec2d1e.png[/img]
4
某 LTI 离散系统如题图所示, 已知激励[tex=5.286x1.5]D17R4Hcu7j87cOqQ6jJhoEzph6lyTZFDJh2Pu6E3Py8=[/tex], 响应初始值[tex=6.571x1.357]KwKAKtInfye44ax7xkNY8JlhdGH1Ymie0/6aJgADo9Q=[/tex] 。试求该系统的自甴响应、强迫响应和完全响应。[img=435x210]17b010711824178.png[/img]