And it mixes that with deep neural networks, and hence, this is called Deep Fourier-based super-resolution.

它将傅里叶变换与深度神经网络结合，因此被称为基于深度傅里叶的超分辨率。

Well, get this, it uses the Fourier transform, a mathematical technique for breaking down a signal, for instance, a song into its frequencies, like taking the bass guitar out of a song.

听好了，它使用了傅里叶变换，这是一种数学技术，用于分解信号，比如将一首歌分解成它的频率，就像从一首歌中取出贝斯吉他一样。

Today we can see that Gauss had figured out the discreet Fourier Transform before Joseph Fourier himself published it in 1807. And he had developed the same Fast Fourier Transform algorithm as Cooley and Tukey a century and a half earlier.

今天我们可以看到，在约瑟夫·傅里叶于 1807 离散傅里叶变换之前，高斯就已经出了离散傅里叶变换。并且他在一纪前就开了与库利和图基相同的快速傅里叶变换算法。

And most of the reason that it's a lie is that I still have yet to tell you what the actual Fourier Transform is, since it's a little more complex than this x-coordinate-of-the-center-of-mass idea.

而这说法之所以是谎言， 最主要的原因是我还没有告诉你傅里叶变换实际上是什么，因为它比这“质心的x坐标” 的想法要复杂一些。

So a lot of those kind of basic courses, if you do electrical engineering, you take signal processing, you'll learn about Fourier transforms.

所以很多这类基础课程，如果你学电气工程， 你会学习信号处理，会学到傅里叶变换。

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

这从波形到频率的转换是通过一非常酷的算法——快速傅里叶变换来完成的。

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。

Physically, this has the effect that when a certain frequency persists for a long time, then the magnitude of the Fourier transform at that frequency is scaled up more and more.

从物理上讲， 这意味着当某频率长时间持续存在时，傅里叶变换在该频率处的幅度会被放大得越来越多。

It's called the discrete fourier transform of the coefficients.

它被称为系数的离散傅里叶变换。

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。

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

你可以对这非常简单的信号进行离散傅里叶变换。

There's a couple small distinctions between this and the actual Fourier transform, which I'll get to in a couple minutes, but already, you might be able to see how this machine lets us pick out the frequency of a signal.

这与实际的傅里叶变换之间有一些小的区别，我稍后会讲到，但你可能已经能看出来， 这台机器是如何让我们挑出信号的频率的。

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

那么离散傅里叶变换将有八频率仓。

More generally, this is the core idea  that underlies Fourier transforms, and Fourier series, and the infinite  swell of topics that follow from those.

更一般地说， 这是傅里叶变换和傅里叶级数的核心思想，以及随之而来的无穷无尽的主题。

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。

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

但信号持续的时间越长，在该频率下的傅里叶变换的值就越大。

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。

The plot that I've been graphing for the Fourier transform, is just the real component of that output, the x-coordinate But you could also graph the imaginary component separately, if you wanted a fuller description.

我绘制的傅里叶变换图只是输出的实部，即x坐标。但如果你想获得更完整的描述，也可以单独绘制虚部。

Now, we can say, whenever you're given two long lists of numbers and you want to take their convolution, first, compute the fast fourier transform of each one of them.

现在我们可以这么说， 当你拿到两长长的数字列并且想要计算它们的卷积时，首先， 分别计算每列的快速傅里叶变换。

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

您获取图像每行的像素亮度值并执行快速傅里叶变换。