fast fourier transform

简明释义

快速傅里叶变换

英英释义

例句

1.We implemented the fast fourier transform 快速傅里叶变换 to analyze the frequency components of the audio signal.

我们实现了快速傅里叶变换 快速傅里叶变换来分析音频信号的频率成分。

2.In image processing, the fast fourier transform 快速傅里叶变换 is used for filtering and image enhancement.

在图像处理中，快速傅里叶变换 快速傅里叶变换用于滤波和图像增强。

3.Using the fast fourier transform 快速傅里叶变换, we can quickly identify periodic patterns in data.

使用快速傅里叶变换 快速傅里叶变换，我们可以快速识别数据中的周期性模式。

4.The algorithm for the fast fourier transform 快速傅里叶变换 significantly reduces the computation time for signal processing.

用于快速傅里叶变换 快速傅里叶变换的算法显著减少了信号处理的计算时间。

5.The fast fourier transform 快速傅里叶变换 allows us to convert a time-domain signal into its frequency-domain representation efficiently.

通过快速傅里叶变换 快速傅里叶变换，我们可以高效地将时域信号转换为其频域表示。

作文

The concept of fast fourier transform has revolutionized the field of signal processing and data analysis. This mathematical algorithm allows for the efficient computation of the Fourier transform, which is a technique used to convert signals from their original domain (often time or space) into the frequency domain. By using the fast fourier transform (快速傅里叶变换), we can analyze various types of signals, such as audio, images, and even financial data, in a much shorter amount of time than with traditional methods.To understand the significance of the fast fourier transform, it is essential to first grasp what the Fourier transform does. The Fourier transform decomposes a function or signal into its constituent frequencies. For instance, if you have a sound wave that is a combination of multiple tones, the Fourier transform will help identify the individual frequencies that make up that sound. This is crucial in many applications, including audio compression, image processing, and telecommunications.However, the traditional computation of the Fourier transform can be quite slow, especially for large datasets. This is where the fast fourier transform comes into play. Developed by Cooley and Tukey in 1965, this algorithm dramatically reduces the number of computations required to perform the Fourier transform. Instead of directly calculating the transform from scratch, the fast fourier transform takes advantage of symmetries and periodicities in the data, allowing for a more efficient calculation.One of the most notable applications of the fast fourier transform is in digital signal processing. For example, when you listen to music on your smartphone, the audio signal is processed using the fast fourier transform to compress the data and enhance sound quality. This algorithm enables the device to quickly analyze the sound waves and apply effects such as equalization and reverb, making the listening experience more enjoyable.In addition to audio applications, the fast fourier transform is widely used in image processing. Techniques such as image filtering, enhancement, and compression often rely on this algorithm. For instance, when an image is compressed using JPEG format, the fast fourier transform helps to reduce the file size by transforming the image data into the frequency domain, where less important information can be discarded without significantly affecting the visual quality.Moreover, the fast fourier transform is also utilized in various scientific fields, including physics and engineering. It aids in analyzing oscillations, vibrations, and other phenomena that can be modeled as waveforms. Researchers can use the fast fourier transform to study complex signals, extract meaningful patterns, and even predict future events based on historical data.In conclusion, the fast fourier transform is a powerful tool that has transformed how we process and analyze signals across multiple disciplines. Its ability to efficiently compute the Fourier transform has made it indispensable in modern technology, allowing for advancements in audio processing, image manipulation, and scientific research. As we continue to generate and collect vast amounts of data, the importance of the fast fourier transform will only grow, paving the way for further innovations and discoveries in the future.

“快速傅里叶变换”的概念彻底改变了信号处理和数据分析领域。这种数学算法能够高效计算傅里叶变换，这是一种将信号从其原始域（通常是时间或空间）转换到频率域的技术。通过使用“快速傅里叶变换”（fast fourier transform），我们可以在比传统方法更短的时间内分析各种类型的信号，例如音频、图像甚至金融数据。要理解“快速傅里叶变换”的重要性，首先必须掌握傅里叶变换的作用。傅里叶变换将一个函数或信号分解成其组成频率。例如，如果你有一个由多个音调组合而成的声波，傅里叶变换将帮助识别构成该声音的各个频率。这在许多应用中至关重要，包括音频压缩、图像处理和电信。然而，传统的傅里叶变换计算可能相当缓慢，特别是对于大型数据集。这就是“快速傅里叶变换”发挥作用的地方。由库利和图基于1965年开发的这一算法显著减少了执行傅里叶变换所需的计算次数。它并不是直接从头计算变换，而是利用数据中的对称性和周期性，从而实现更高效的计算。“快速傅里叶变换”的一个显著应用是在数字信号处理领域。例如，当你在智能手机上听音乐时，音频信号会使用“快速傅里叶变换”进行处理，以压缩数据并增强音质。这个算法使设备能够快速分析声波，并应用均衡和混响等效果，从而让听觉体验更加愉悦。除了音频应用外，“快速傅里叶变换”还广泛用于图像处理。图像过滤、增强和压缩等技术通常依赖于这个算法。例如，当一幅图像使用JPEG格式压缩时，“快速傅里叶变换”通过将图像数据转换为频率域来帮助减小文件大小，在不显著影响视觉质量的情况下丢弃不重要的信息。此外，“快速傅里叶变换”还被应用于物理和工程等多个科学领域。它有助于分析振荡、振动和其他可以建模为波形的现象。研究人员可以使用“快速傅里叶变换”研究复杂信号，提取有意义的模式，甚至基于历史数据预测未来事件。总之，“快速傅里叶变换”是一种强大的工具，彻底改变了我们在多个学科中处理和分析信号的方式。它高效计算傅里叶变换的能力使其在现代技术中不可或缺，推动了音频处理、图像操作和科学研究的进步。随着我们继续生成和收集大量数据，“快速傅里叶变换”的重要性将只会增加，为未来进一步的创新和发现铺平道路。