Discrete cosine transform(离散余弦转换)

Posted 2021-01-01 2008nmj

A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. DCTs are important to numerous applications in science and engineering, from lossy compression of audio (e.g. MP3) and images (e.g. JPEG) (where small high-frequency components can be discarded), to spectral methods for the numerical solution of partial differential equations. The use of cosine rather than sine functions is critical for compression, since it turns out (as described below) that fewer cosine functions are needed to approximate a typical signal, whereas for differential equations the cosines express a particular choice of boundary conditions.

离散余弦变换（DCT）以不同频率振荡的余弦函数之和来表示数据点的有限序列。DCT对科学和工程中的很多应用都很重要，从音频(例如MP3)和图像(例如JPEG)的有损压缩（其中可以丢弃小的高频分量），到偏微分方程数值解的谱方法。