线性[tex=26.429x5.071]a0s3MH7cLIdmiBRR0YN063iA+CHfdqeR+QqfxBdlcdEigoWrkP6yfeUHal3rD89aw10ZSYiut/3G9wzQbE0AK5ioMmJO0sGfo3icxUxXz5AtY7DPJ0aw8MF9XUi1qKJ59QM1WoZmUac+L1QMnzZRC48W9iI2dQ5Ns4EdEfV5mAUGEha4qIL1zf29IFHf5vJ5KYyLwgKdFnziDJfdUOb1x0WWwXyXLcBSErgqB0/OJKwPxueOI5BXm0Pf2mUusGsSDdkgnFek206D8+zSYCIyEz9RiFp+JID3beODsIe0E4U=[/tex]序列移位[tex=31.429x3.357]0np/EwHzbJ63NI0iy4J0meiy9eeGHlSxRp7hpWzUjO5nXF0EmuOq7iKx8AqdYYFbizI30gyHJZQKO9LQqcaufVeweZyvwOgBkaNBBl1YgWKGxT7JRp8YEiylBhqU/qCh6V0eEb7U/SLp+Wc3SAAHyGYg71ylg4NCFntvpUrirVbUY6fhutDhpv58LeVGEsED5PTxkUQ731fWiI4XAL8Mvwfapk4RTA7s45NgBwoAvA+SmZITZeLW0SyF+J17yO2dpM7l21EqV7kA43q4t2aKqByOpzjKsqz5+mSWpZWA8YXAZVTLF++RSLa6JIKbFWG4BnvmQuIYPZynDzD2ly7FQw==[/tex]乘以指数序列[tex=21.643x3.286]0np/EwHzbJ63NI0iy4J0mR8br80JuQiKcUWmkaNtK7ej0JiyZp1EnXdQlLNLN5fdQz2u1KD6ZKOlCDE3uri4fgn36GjgLvjlfQXIcg44z17ONDNFSN3GkWofG+mgcdjr4gcyAfg4jGlmNHgXr2Wdz6r1hX6+6yiw9ZxlBZ8Vq6KwWJISQLIvXxoP3CUyyRaf[/tex]序列折叠[tex=20.286x3.286]0np/EwHzbJ63NI0iy4J0mbtkWArNyzuaU275CgYU6k64hJrP8I9EjImS52sBIgmzwS7oQn9pg3hREE3EyqymPOlSNwHJ9vx7MXgTxoCi8L9YkTEohYtJcB/7Y5KErVlrkcA/zbpDy2Wk4A6QBg7OlmbJPA1RgEUhHLrd91Ib7tjnAtXZDbe1UHqqaFPfTdpM[/tex]复共轭序列[tex=20.0x3.429]0np/EwHzbJ63NI0iy4J0meamxbRIBa2vn2UG6d8+wOdooPy0v3tapKkZ26pFAjB2hualeZgUlkcXLq6liS/vtCrke5G/88h5Y/OG5beXpxlOlrzKmZwszp6S8//ypTPRtfYi2KMP4Wwu7DJpIujdM/A7kK11FXVVHeJEsK88A/LHx9Avmt584WdqGLIp8RZ3[/tex]与[tex=0.643x0.786]SBMIs+VUk7//BOpfqlQl0w==[/tex]相乘[tex=23.643x7.071]a0s3MH7cLIdmiBRR0YN064fIl1LPZuX8ZmchIUd2nCLl9a9W2I3GP5QZ5PfwkJTzryHy8WYXq4PQPcsSyoovtWjUQ9LxLsE4co5a8rM5JNW4taKdIA6XXdZsEZSrQCO9riSPlktSchOSbXvJPk3CSyPXExqgmBmTlYvw04xm5jOcA+Lyjg2cik8G0FoyVdfJ46O5bT2u3UqTNAUcR9q3WVv2u3gmAr71l1LNCyecBCZjnSGIkeggj55FG/H/nm4QJTmqbCxEJr1iEtTa3zYadZWw6hztzaokG2KazkfDXjdPh6QtIm/rb9xUw3Vxdhn2c9y0KEqJ/EMdIY4om0UrnFHK3v03g4Ez/nR2r6zq+cFhKiON+vaBpL2XrWtt2jSa[/tex]由此得到[tex=12.143x3.286]0np/EwHzbJ63NI0iy4J0mQ952/ZstNthtkbQgcZXdV+uWo65cy8FFDighTfiXnWKJcq2Dd2GoFdNgLzBC2/rUtsfGA+HZqhcw+xhMy7pWn8=[/tex]初值定理对于因果序列：[tex=6.0x1.357]BjUkiYoc89X4Fz0zzHRdwQ==[/tex][tex=26.571x3.357]Qif26GWhqPUM/Yz2V8uxeIf1ERiW/k9fTwon5C+cfd/fClg7Au9Pc7EvVedvvmgPGlQc0BmQf3uK+NCokNQjOtLza23WDlgYPz/y7/g1WMxApeVmvtk7vuUFwcs821NuhSEd5ALmA1gBAMoBwC10n42vvus90hm5ejbeBPsQyCqAbuzXDIY8wTqQUj8KDcSc/W4zClXTArz4jDj63oaQDVO7tTL3B/0mFVXHHpF+of2x1m151uyYdDQYBc9XJell[/tex]对于逆因果序列：[tex=6.0x1.357]fwhMgH1zfzHfUWrpBIvfzA==[/tex][tex=27.071x3.5]Qif26GWhqPUM/Yz2V8uxeBEn0q9Izo3474dg0XEFjZMSUTKvT6xqzoNV3r/KLDzu/2Wpj9H2+ee41nS/iSwrcWcG/S2mhPQrLGEdYZcaka1OMgMqVnBPPZkqB1vfSFr32TZrS2A26R1vxj1pVX1wf3DNlDzDz8ormSJ6GTc09qJ/Y1Ukn6GNiso84H7oKbd71R1iVnYwVUrvopx5R0E6tOGPDioTGYMRRNGpbTTcuko=[/tex]终值定理[tex=10.786x1.357]LDMA7xwjEraBdpy2mXWhV8k95qG9FCtbSB20srvhxrY=[/tex]根据序列移位性质,[tex=2.571x1.357]66TFR8y716S6kNd4xkcKJw==[/tex]是[tex=3.286x1.357]eOumrkNBwZJRT8pdgJpRZQ==[/tex]的[tex=0.5x0.786]gdMkE6SnyZedYLxpUxdkaQ==[/tex]变换,所以[tex=15.786x3.286]u6tf7HUjryikpxQimLu2JscfwhobwFJ9OF/MafY/S7MIKI0Mw4lrjV4er/C+G27MMG0mM/j+hc4mjhUSQ77Fcg==[/tex]对于因果序列[tex=17.429x3.357]M0/f0EHMocNCznEFjX01c6foJqhD8hTS/SpA/G+uSYkRBniR4L3CxLUMsrJrjLWz0x7WGjAvkDfT9rlQmkMV4PFexFR4SDYGj/q4DtJqTG0=[/tex][tex=2.071x1.357]0MhZ1zsXck4LsHGlZK0EQA==[/tex]在单位圆上只有在[tex=1.786x1.0]5KB+jUnt4Otf5O87DVSdKg==[/tex]处可能有一阶极点,函数[tex=4.643x1.357]+oUSdHPKJ+zDS5KjOEa8Ig==[/tex]能够抵消这个可能的极点,因此,[tex=4.643x1.357]+oUSdHPKJ+zDS5KjOEa8Ig==[/tex]的收敛域包括单位圆,所以,允许对等式两端取极限[tex=2.0x1.0]zCit3U71RRRhKIZOsRuYVA==[/tex],即[tex=29.214x7.5]a0s3MH7cLIdmiBRR0YN06y2S4DDph6U9AbQcv09BD3VfeFO7E++3K0Mno/rjn0xpH+B3araHexAiikowCc0qWhotf6NbzghmRKRPT01dSGSLfzbJtC4AGE4y0ReL8jSUYRHPjNg/9U0mBWjpFadt+4YwOct4OJmWuvK2FIc91Z5j2qUN13+TjvomMgyJB6BgzDSKkWZ45UZHfxu7adpF9gexf6yByynquNDAbRyZ8lZGcOUySVB9JW813Bnyj2++peoX3+j+WMmnYZhsWsnVARst/PBhUyNojefBQbToxQ14ht+l+gUqf5YDFbCn6VvI1qFqb2IEhULBTFdGVQG5M8s6r9balpbMa6SGCS8vj0IpifOWgZK+Z9MSutc9aUKP[/tex]由于[tex=2.071x1.357]0MhZ1zsXck4LsHGlZK0EQA==[/tex]在[tex=1.786x1.0]5KB+jUnt4Otf5O87DVSdKg==[/tex]上的留数为[tex=12.071x1.857]BIloFusPrBF+XgL1twUxa3X0y0NfcRYnTtnWHVDEsPGLCt7mufPcBxxDPj5gKveXNchYLmzt0cp5hZ5iAl1E5Q==[/tex]所以[tex=9.929x1.786]8vJYfWnQRBqJWdmg/yoyrH0o2wmnIyTBf87uoOcbfZSi5fQHU2ycugEn0CEaA6wzyVkxtSsQJiEkLlOp/mNXzw==[/tex]序列卷积[tex=30.857x12.071]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[/tex]复卷积定理[tex=21.714x3.286]0np/EwHzbJ63NI0iy4J0mfHLfAj3Ayt5k6fzOYInejnH5b53bVkcOxvb9DLyxKe6TI6wfDQwJ+EpuGDL2PHDFiBajka84NnJqKbwfnVpjx1zV605zmF2YOxoG6p5ldY+iu8tUr0WHdW2Ih522aRLhvFE6P8D8JY9DtG+FMx0Md4=[/tex][tex=16.5x3.286]sq9BO+5WiVlP0/AmAY1YD1V+3DZU6mR4zD796ZSFEZmpNIJhhDVo0LQHTYfD7y6B8UDbGIxbfoyGszFxnpIfgFtC08aqb2BNDEC3N5u+BWyIRQrQ6bc26Gs6OVWu0/yujNSBk1zkP8Yb1lbbigEKCA==[/tex]在收敛域[tex=8.0x1.357]ommIQA8VoECio7y0lQwWGJ5dsY0kWuHRl+9fILohwlA=[/tex]内，上式中的和式为[tex=11.0x3.286]0np/EwHzbJ63NI0iy4J0mTOyISVrEduCwqYiD8rntWeg7puCoq8EY0CSbUrr74VG+DtUyNkVf+7XlGHbZ4BH1NNj0m9JsX7uuVNlJbagGnKQDt9uo+WKSpkquPWJyvAQ[/tex]故[tex=19.786x3.286]0np/EwHzbJ63NI0iy4J0mfHLfAj3Ayt5k6fzOYInejnH5b53bVkcOxvb9DLyxKe6Ku+/c4qtZOP0paVixK6gsLgnTx6HbAd1yX4UPs3vGhPQbuAnGmOQKMaNhb9mA7H6JnJGUjrvSKkNXl9w/8Zotfh2Ru94LgzF+fRlLoBaZQ0=[/tex]复序列的实部[tex=24.857x9.643]a0s3MH7cLIdmiBRR0YN063iA+CHfdqeR+QqfxBdlcdFrARniThCMNzI9eYoLtImYvYlcOkxWTZ3GPvve7qNoMzo/i5c2W1qTOucPGh/1uVoJza9bSSDtcK2z2rbGPXfFsn299XENt4SJYQhzca8+Eo2fbZn+4LHLt9zWsX3qElVHm+uSMDj2enqJts1BpYOvrsN8A5rL7oYsIN1jLzghIil8Vt2wDZZ56XkAOumJpSysmOLw25E2EBK4GzXf2R02orwjQBoP/0aMXKRbRTQCYGSFT4I5BVvWUOm554nV/0wjz6jGbfsN7wVExABnvyrI1yXpyUKwsxHJjoJynh87YzFAhOewHu7TepDhZmt1eH47j99c3Uu7Ztub9cTwCbBf8nQJOjZtzsReUjwdbDaXYnqUG81hXi/PDqUVAYffevr3TBWE7FFpnyLYBD/4Vqr5qa3CcaxqiI5XcThBOfnR9Q==[/tex]复序列的虚部[tex=24.929x9.643]a0s3MH7cLIdmiBRR0YN063iA+CHfdqeR+QqfxBdlcdFrARniThCMNzI9eYoLtImYJdB1f6hae+/l4FBsGgFdJ/lLagrzfw1GoM0jeoBiOAmJOCSk/A4Qn27VZXC049o0f+oxV7mxNmEnd6/WG+TGTHOj09yZt3WG/CqbfEqOTzOBIDDV2mt0V9QDLn2nSiOiKAhSTcMuYVTUU9IYudfZSJxyxgHaGcowTzcGM23rZxLI+c8HowdOqcWmNpG6Q1FmwGtAM8P57dK15EJ1LxTkcTzUtLZs3YwZZ3r8W/ImHzagGmsM6fgojR3PgPO2Vh2l05BnqBsChSY+a8ZWbHa43ttplJKI64xPvKHe3lnUAXAeDH91npCVUslD6hVgIQncwcF5ttSJ8pbf4vRLH3tBmkGLbLteKcVXMUpIRclTeI9ZHIKTitlS8NeJoHayoAKRef2ivom5FjHHIMofVgQuDQ==[/tex]Parseval定理利用前面已经证明过的复卷积定理和复共轭序列,得到[tex=25.0x3.286]N3emATICIIqZVYLLtteBvU7PRUkrJl8C3MCPusGRncoTY1wDkGV8XXfEqrbVuMMcHjbrm+Vn+0UM2fIThfRv/B6RD2Xipf7cGlQKt1YWH6St5HW7oG9eHC0H76fRlr6HWbCqqcWq5EDfOAdkE1B0hFXTvBJQDEfAAI+ubGADkgz4P5njWkdzoJXGBTNnG0smijl+LxrnqXj6vC0xad7zAw==[/tex]由于收敛域为[tex=10.429x1.357]IybmZuK5S7kRWXY5IDREg4vi2jeLrdt7KQ6XPH0jgBs=[/tex]，且收敛域应包含单位圆，即应当满足关系[tex=9.929x1.286]piCJHOzqUokJ22qEbsHIsDha1BFL6cKayKWp1nuVuas=[/tex]，这说明[tex=2.357x1.357]G8WDVf+fQj0euQoa/uL93Q==[/tex]在收敛域内，即[tex=2.214x1.357]SIK+oxcN6jzGbAzWyNsFbQ==[/tex]在单位圆上收敛，因此[tex=3.714x1.357]bZ1Ay1r/09ixxq7jMhLMCM9Ojblk7BFJYeqI/6gUwmg=[/tex]存在，[tex=22.786x3.286]ug3wsgaBAdS+HoHOm0UMCx5Wb9d9V9BIHhOqS5qQ7ILANUwGYR9Msn6U8LsOiWnqMgkkM7FrbsScCL21ipJFwg8kYYbbuBIt4entToMjji+WCZHr6kn7iNwjSPmQgekQIbKVbXAEsQ9OL3xg3pKrbqKjyCq040x/frmVlwFCcBQ=[/tex]