It was radical when Fourier wrote it in 1808.

但1808年，傅里叶写下这句话却显得尤为激进。

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

傅里叶认为，除非女性命运得以改善，否则整个社会难以得以发展。

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。

Here's how the Fast Fourier Transform allows you to compress an image.

以下是快速傅里叶变换如何允许您压缩图像。

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

走廊黑板上有高傅立叶算式。

You take the pixel brightness values for each row of an image and perform a Fast Fourier transform.

您获取图像每行像素亮度值并执行快速傅里叶变换。

And that is how the Fast Fourier Transform reduces N squared calculations down to NlogN.

这就是快速傅里叶变换如何将 N 平方计算减少到 NlogN。

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 个不同频率波。

Same goes to whoever asked about what the Fourier transform has to do with quantum computing.

对于任何询问傅里叶变换与量子计算有何关来说，都是如此。

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

直到傅立叶之前， 们并不总是相信行星际空间温度会永久下降？

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

这种从波形到频率转换是通过一种非常酷算法完成，称为快速傅里叶变换。

And those of you who know about fourier transforms and the FFT algorithm, might see where this is going.

那些了解傅立叶变换和 FFT 算法可能会明白这是怎么回事。

The Fourier transform of an intensity vs.

强度与强度傅里叶变换。

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。

But the longer that signal persists, the larger the value of the Fourier transform, at that frequency.

但信号持续时间越长，在该频率下傅里叶变换值就越大。

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示例。

The Fourier transform is just the integral part of this.

傅里叶变换只是其中组成部分。

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操作。

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频率，这意味着他们需要进行傅立叶变换。

And now, there is only one final distinction to point out between this and the actual, honest-to-goodness Fourier transform.

现在，只需指出这一点与实际、诚实傅里叶变换之间最后一个区别。