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数字水印文件和数字水印命令是数字水印技术在军事应用的两个重要应用。本文以一种基于分数阶傅里叶变换
(FRFT)的数字水印算法，使用chirp信号作为水印信息，嵌入到图像的分数阶傅里叶的加密域中。该算法有效地利用水印的
嵌入位置和FRFT的阶次作为密钥的同时，还利用chirp信号在分数阶傅里叶域的特点，可以很方便的检测到水印，具有良好
的不可见性和安全性的同时，还能够抵抗很强的JPEG压缩和噪声的攻击，对剪切、滤波等操作也有一定的鲁棒性。-Watermarking files and digital watermarking command are two important applications of digital watermarking technology for military applications in. In this paper, based on fractional Fourier transform
(FRFT) digital watermarking algorithm using chirp signal as the watermark information is embedded into the image encryption fractional Fourier domain. The effective use of watermarking algorithm
FRFT embedding position and at the same time as the order of the keys, but also take advantage of the characteristics of chirp signals in fractional Fourier domain, and can easily detect the watermark, with good
Invisibility and safety, it is also highly resistant to JPEG compression and noise attacks, shear, filtering and other operations also has certain robustness.
(FRFT)的数字水印算法，使用chirp信号作为水印信息，嵌入到图像的分数阶傅里叶的加密域中。该算法有效地利用水印的
嵌入位置和FRFT的阶次作为密钥的同时，还利用chirp信号在分数阶傅里叶域的特点，可以很方便的检测到水印，具有良好
的不可见性和安全性的同时，还能够抵抗很强的JPEG压缩和噪声的攻击，对剪切、滤波等操作也有一定的鲁棒性。-Watermarking files and digital watermarking command are two important applications of digital watermarking technology for military applications in. In this paper, based on fractional Fourier transform
(FRFT) digital watermarking algorithm using chirp signal as the watermark information is embedded into the image encryption fractional Fourier domain. The effective use of watermarking algorithm
FRFT embedding position and at the same time as the order of the keys, but also take advantage of the characteristics of chirp signals in fractional Fourier domain, and can easily detect the watermark, with good
Invisibility and safety, it is also highly resistant to JPEG compression and noise attacks, shear, filtering and other operations also has certain robustness.
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分数阶傅里叶变换在数字水印的军事应用研究.pdf