No society could improve, Fourier believed, until women's lot improved.

傅里叶认为，除非女性的命运得以改善，否则整个社会难以得以发展。

It was radical when Fourier wrote it in 1808.

但1808年，傅里叶写下的这句话却显得尤为激进。

Gloomy as he looked in portraits, the Frenchman Charles Fourier concentrated on fun.

法国人查尔斯傅里叶关注于这其中的乐趣，尽管他在肖像画里看起来很忧伤。

Fourier was wounded, so he demanded a second duel.

傅里叶受伤了，所以他要求进行第二次决斗。

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。

This has aptly become known as the Fast Fourier Transform.

这已被恰当地 称为快速傅里叶变换。

I also put an advanced Fourier system on the main hallway chalkboard.

走廊黑板上有高级傅立叶算式。

Was it not always believed until Fourier that the temperature of the interplanetary spaces decreased perpetually?

直到傅立叶之前， 人们并不总是相信行星际空间的温度会永久下降？

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。

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。

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。

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。

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。

Instead, you have to perform something called a Discreet Fourier Transform.

相反，您必须执行称为离散傅立叶变换的操作。

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。

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。

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。

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。

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。

And one of the distinguishing features of a Discreet Fourier Transform is that the frequency spectrum is also discreet and finite.

离散傅立叶变换的显着特征之一是频谱也是离散且有限的。