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超分辨率。

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。

This whole plot is what I'll call the " Almost Fourier Transform" of the original signal.

整个图就是我所说原信号“近似傅里叶变换”。

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

这个从波形到频率转换是通过一个非常酷算法——快速傅里叶变换来完成。

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

有一些优雅方法可以理解傅里叶变换工作原理，请观看 3Blue1Brown 精彩视频。

The Fourier transform is just the integral part of this.

傅里叶变换就是这个积分部分。

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。

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

而现在，只需要指出这一点与真正、货真价实傅里叶变换之间最后一个区别。

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

你可以对这个非常简单信号进行离散傅里叶变换。

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涂鸦，但他实际上所做是离散傅里叶变换。

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。

Also Veritasium recently did a really good video on FFTs so you've got lots of options.

另外，Veritasium 最近做了一个关于快速傅里叶变换非常好视频，所以你有很多选择。

And importantly, this FFT algorithm goes both ways.

而且重要是，这个快速傅里叶变换算法是可逆。

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。

And it's why today whenever anyone takes a Fourier transform, it's almost always done as a Fast Fourier Transform.

这就是为什么今天每当有人进行傅里叶变换时，几乎总是以快速傅里叶变换形式完成。

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。

Luckily, there's a notion of an inverse Fourier transform that tells you which signal would have produced this as its Fourier transform.

幸运是，有一种叫做傅里叶逆变换概念，它可以告诉你哪个信号会产生这个傅里叶变换。

The Fourier transform of an intensity vs.

强度与频率傅里叶变换。

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。