雙語暢銷書《艾倫圖靈傳》第7章:運轉起來(27)
The Delilah was based on these two ideas from the beginning, while in the X-system they had arrived by a back-door route.
The point about sampling was that it removed the redundancy of the continuous sound wave.
所謂採樣，就是去掉連續聲波的冗餘信息。Any sound signAl could be represented by a curve such as:
聲音信號可以表示成這樣的曲線：
The point was that it would be unnecessary to transmit the whole curve.
艾倫的想法是，沒必要傳輸整條曲線，只需要傳輸這條線的某些點就足夠了。It would be sufficient to communicate the knowledge of certain points on the curve, provided that the recipient could thereupon perform the exercise of 'joining the dots' to reconsitute the curve.
從理論上說，接受者可以通過這些點，來擬合出一條曲線。Since sharp wiggles would correspond to high frequencies, it followed that provided there was a limit on the frequencies contained in the signal, then a sequence of discrete points, or samples, of the curve, taken at regular intervals, would contain all the information of the signal.
因爲高頻信號的擺動過於劇烈，所以要在信號中限制高頻，然後每隔一定的時間進行採樣，得到一組離散的點，這些點就能夠包含信號所需的全部信息。Since telephone channels did in any case cut off high frequencies, the restriction on allowed 'wiggling' of the curve was no real restriction at all, and in fact a rather small number of samples could be shown to suffice to convey the signal.
因爲電話頻道本身就會削去高頻，所以並不需要對曲線進行更多的限制，因此只需要很少量的樣本，就能夠傳遞聲音信號。The idea was well-known to communication engineers. In the X-system, it was the practice to sample each of the twelve 25 Hz channels fifty times a second.
通信工程師們對這種想法很熟悉，比如說X系統就是每秒對12個25赫茲的頻道進行50次採樣。These figures were illustration of a general result, that it was necessary to sample at a rate of twice the maximum variation in frequency of the sound, or bandwidth.
一個普遍的規律是，採樣率必須達到最高頻率的2倍，There was an exact mathematical result to this effect, proved as early as 1915 but which Shannon had re-stated11 and discussed with Alan at Bell Labs.
這是一個精確的數學結論，最早是由香農在1915年證明的，並在貝爾實驗室與艾倫討論過。If, for instance, the sound signal were restricted to frequencies less than 2000 Hz, then a sample taken 4000 times a second would be exactly enough to reconstitute the signal. There would be precisely one curve of the stated frequency restriction that passed through all the sampled points.
例如，如果一個聲音信號的頻率不超過2000赫茲，那麼每秒4000次採樣就可以足夠精確地表徵該信號，並能得到一條通過所有采樣點的曲線。Alan described and proved this result to Don Bayley as the 'Bandwidth theorem'. His 'Why not?' had come in asking why this elegant fact could not be made the pivot on which to turn the whole encipherment process.
艾倫向唐·貝利描述並證明了這個結論，他的想法是，可以試着利用這個事實，來改變整個加密過程。
