DFT在诸多多领域中有着重要应用，下面仅是颉取的几个例子。 需要指出的是，所有DFT的实际应用都依赖于计算离散傅里叶变换及其逆变换的快速算法，即 快速傅里叶变换。

3 days ago · DFT（离散傅里叶变换）将时域信号转换为频域表示，通过复指数展开实现信号与正弦/余弦基函数的内积运算。FFT算法大幅提升 ...

密度泛函理论（Density functional theory，DFT）是一种以电子密度为基本变量研究多电子体系电子结构的量子力学方法，广泛应用于化学、材料科学、凝聚态物理及核物理等领域，是计算材 …

这三条规律引出了DFT的一个重要性质：共轭对称性，即X (m)=X* (N-m)。 由于DFT的共轭对称性，因此DFT结果中的后N/2-1个元素是冗余的，因此我们也可以说DFT的输出是N/2+1个虚数。

DFT与理论工具DTFT（处理无限长离散信号）的关系在于：DFT是对有限长信号DTFT频谱的离散采样。 实际应用中，DFT/FFT已成为频谱分析、滤波和信号处理的工业标准。 _dft数学定义

The Fourier transform of a continuous-time signal may be defined as Thus, right off the bat, we need calculus. The DFT, on the other hand, replaces the infinite integral with a finite sum: …

The DFT is also used to efficiently solve partial differential equations, and to perform other operations such as convolutions or multiplying large integers. Since the DFT deals with a finite …

Dec 22, 2025 · Discrete Fourier transforms (DFTs) are extremely useful because they reveal periodicities in input data as well as the relative strengths of any periodic components. There …

Example (DFT Resolution): Two complex exponentials with two close frequencies F1 = 10 Hz and F2 = 12 Hz sampled with the sampling interval T = 0.02 seconds. Consider various data …

The discrete Fourier transform, or DFT, is the primary tool of digital signal processing. The foundation of the product is the fast Fourier transform (FFT), a method for computing the DFT …