Discrete Chebyshev transform. A natural modification of the DCT
Discrete Chebyshev transform. A natural modification of the DCT
复制标题
离散切比雪夫变换。
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
F. J. Smith
中科院分区：
文献类型：
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作者：
P. Corr;D. Stewart;Philip Hanna;J. Ming;F. J. Smith
虽然离散余弦变换（DCT）被广泛用于模式识别中的特征提取，但它对大多数理论上光滑的函数收敛缓慢。一种修改的DCT描述，基于变量的变化，它改变它到一个新的变换，称为离散切比雪夫变换（DChT），它收敛非常迅速，为相同的平滑函数。虽然这种快速收敛在很大程度上被真实的实验数据中的噪声破坏，但当数据的采样可以选择在非等距点时，离散Chebyshev变换通常仍优于DCT。对DCT的改进给出了改进的语音识别使用梅尔特征倒谱系数获得的理论解释。这些选择DCT的采样频率以对应于人类对音高的感知。它示出，这种采样是类似于离散切比雪夫变换中使用的采样。
Although the discrete cosine transform (DCT) is widely used for feature extraction in pattern recognition, it is shown that it converges slowly for most theoretically smooth functions. A modification of the DCT is described, based on a change of variable, which changes it to a new transform, called the discrete Chebyshev transform (DChT), which converges very rapidly for the same smooth functions. Although this rapid convergence is largely destroyed by the noise in real experimental data, the discrete Chebyshev transform is still generally better than the DCT when the sampling of the data can be selected at nonequidistant points. The improvement over the DCT gives a theoretical explanation for improved speech recognition obtained using Mel feature cepstral coefficients. These choose the sampling frequencies of a DCT to correspond to the human perception of pitch. It is shown that this sampling is similar to the sampling used in the discrete Chebyshev transform.