And you have the discreet Fourier transform of this really simple signal.

你可以对这个非常简单的信号进行离散傅里叶变换。

They needed to know how much of different frequencies were present which meant they needed to take a Fourier transform.

他们需要知道存在多少不同的频率，这意味着他们需要进行傅立叶变换。

So you can't use the idealized Fourier transform.

所以你不能使用 理想化的傅里叶变换。

Here's an example seismometer signal and its Fourier transform.

这是一个地震仪信号及其傅里叶变换的示例。

This conversion from waveform to frequencies is done with a very cool algorithm called a Fast Fourier Transform.

这种从波形到频率的转换是通过一种非常酷的算法完成的，称为快速傅里叶变换。

Well, then the discrete Fourier transform will have eight frequency bins.

那么离散傅里叶变换将有八个频率仓。

Basically, anytime a signal is processed, there's a good chance that a Fast Fourier Transform is involved.

基本上， 每当处理信号时，很有可能涉及快速傅立叶变换。

There are some elegant ways to understand how Fourier transforms work, shout out to the awesome video by 3Blue1Brown.

有一些优雅的方法可以理解傅里叶变换的工作原理，请观看 3Blue1Brown 的精彩视频。

To complete one discrete Fourier transform requires multiplying N data points by N different frequency waves.

要完成一次离散傅立叶变换，需要将 N 个数据点乘以 N 个不同频率的波。

Now this process works fine in principle and you could use it to calculate all discrete Fourier transforms.

现在这个过程原则上工作得很好，您可以用它来计算所有离散傅里叶变换。

Garwin observed Tukey doodling throughout but what he was actually doing was working on discreet Fourier transforms.

加文自始至终都在观察图基的涂鸦，但他实际上所做的是离散傅里叶变换。

A Fourier transform is a way of decomposing a signal into pure sine waves, each with its own amplitude and frequency that add to make it up.

傅里叶变换是一种将信号分解为纯正弦波的方法，每个正弦波都有自己的振幅和频率， 相加而成。

Thus far I've been thinking about signals as infinite continuous waves and when you take their Fourier transform, you get an infinite continuous frequency spectrum.

到目前为止， 我一直将信号视为无限连续波， 当你对其进行傅里叶变换时，你会得到无限连续的频谱。

The real obstacle to detecting underground explosions wasn't the accuracy of the seismometers, it was the vast amounts of computation required to Fourier transform the seismometer signals.

探测地下爆炸的真正障碍不是地震仪的精度，而是对地震仪信号进行傅立叶变换所需的大量计算。

At the end of the meeting, Garwin asked Tukey what he had worked out and he was shocked to learn that Tukey knew a way to compute discreet Fourier transforms with many fewer computations.

会议结束时，加文问图基他已经解决了什么问题，他惊讶地发现图基知道一种用更少的计算量来计算离散傅里叶变换的方法。