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

它将变换与深度神经网络结合，因此基于深度的超分辨率。

The Fourier transform of an intensity vs.

强度与强度的变换。

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

以下是快速变换如何允许您压缩图像。

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

这就是什么今天每当有人进行变换时，几乎是以快速变换的形式完成。

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

这就是快速变换如何将 N 平方计算减少到 NlogN。

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

对于任何询问变换与量子计算有何关系的人来说，都是如此。

The Fourier transform is just the integral part of this.

变换只是其中的组成部分。

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，快速变换。

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，在该频率下变换的值就越大。

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

这是一个地震仪信号及其变换的示例。

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

那么离散变换将有八个频率仓。

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

整个图就是我所说的原始信号的“几乎变换”。

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的、诚实的变换之间的最后一个区别。

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

你可以对这个非常简单的信号进行离散变换。

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变换的工作原理，请观看 3Blue1Brown 的精彩视频。

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

这系数的离散变换。

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变换。

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， 这是变换和级数的核心思想，以及随之而来的无穷无尽的主题。