April 2014
Beginner to intermediate
830 pages
15h 21m
Chinese
Content preview from Mathematica 錦囊妙計
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448
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第十一章
Z 轉換為離散訊 號處理常見的 無窮級數，其定義為：
Sum[f[n]z^-n,{n,0,Infinity}]
。
Mathematica 內建的
ZTransform
指令可直接支援 Z 轉換。[Page-450]
以下提供一個較少見的
Sum
指令應用，其概念來自於離散數學的生成函數（generating
function）。 藉 由
Sum
指 令 可 以 建 構 一 個 生 成 函 數， 解 決 以 下 問 題： 找 出 所 有 滿 足
n1+n2+n3 == 12
的正整數解，其中
n1 >= 4、n2 >= 2
及
5 >= n3 >= 2
。由於每個變數都
有下限，稍微心算一下可得到
n1
與
n2
的上限分別為 8 以及 6。使用
Expand
指令將生成
函數展開，並使用
Cases
找出指數和為 12 的項次，這些項即是方程式的解。
若只想知道解的個數，只需使用一個變數，並求出 x
12
項的係數即可。
延伸資訊
關於 Mathematica 中生成函數的運算，請參考訣竅 11.11。
ch11.indd 448 2014/4/2 下午 01:03:53
11.10 差分方程式（Difference equations）求解
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449
讀者若需進一步了解與無窮級數相關的演算法，可以參考由 Marko P
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