April 2014
Beginner to intermediate
830 pages
15h 21m
Chinese
Content preview from Mathematica 錦囊妙計
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第九章
一般對分析人聲音訊來說，1 秒鐘的樣本太長了，只需想一下 1 秒鐘內你可以發出多少
個音節即可了解，1/10、1/20 甚或 1/30 秒是較合適的樣本長度，以較短的樣本長度，你
可以辨別各個不同的音節，例如以下樣本「yes we can」中的「yeh」與「sss」音節、單
母音「we」以及重音「c」與「an」。
以下顯示「we」音樣本，音波的重複性很高。
以上所示為時域空間的 9,600 樣本點（9,600/48,000=1/5 秒），傅立葉轉換後每個點的間
距為 48,000/9,600 = 5Hz，因此傅立葉分析必須在樣本點數目及輸出頻率間距之間取捨，
意即減少樣本點將導致解析度降低。
ch09.indd 404 2014/4/2 下午 12:52:16
9.18 實作短時距傅立葉變換
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405
若使用相同音訊範圍，但總樣本點數目減為 4,800，則每個頻譜點間距增為 10 Hz，比較
上下兩張圖，馬上可看出樣本數降低後，於 150-200 Hz 與 300-350 Hz 區間有些資訊遺
失了。
9.18 實作短時距傅立葉變換
問題點
你想隨著時間進行傅立葉分析。408
解決方案
你可以將資料分割為每 1/30 秒一小段，並對每一段分別進行傅立葉分析，則頻率空間的
間隔為 30
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