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Fourier Transform of Untransformable Signals Using Pattern Recognition Technique

机译:使用模式识别技术对不可变换信号进行傅立叶变换

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In this paper we are highlighting the signals that are not Fourier transformable and give its Fourier transform using PCA (Principle Component Analysis), lDA (linear Discriminant Analysis). Such signals are step signal, signum, etc. Basically Fourier transform transforms time domain signal into frequency domain and after transformation describes what frequencies original signal have. Principle Component Analysis is a way of identifying patterns (recognition) in the data and the differences of the data is highlighted. With the help of PCA & lDA we do the dimension reduction of the signal. lDA is used in statistics and machine learning to find a linear combination of features which characterize or separate two or more classes of objects or events. The resulting combination may be used as a linear classifier or, more commonly, for dimensionality reduction before later classification. lDA is closely related to anova (analysis of variance). PCA is used for analyzing. Main advantage of PCA is that once patterns are found and data is compressed that is by reducing the number of dimension without much loss of information. Dimension reduction is the process of reducing the number of random variables under consideration, and can be divided into feature selection and feature extraction. Feature selection approaches try to find a subset of the original variables and feature extraction transforms the data in the high-dimensional space to a space of fewer dimensions.
机译:在本文中,我们重点介绍了无法进行傅立叶变换的信号,并使用PCA(原理成分分析),lDA(线性判别分析)进行了傅里叶变换。这些信号是阶跃信号,信号等。基本上,傅立叶变换将时域信号转换为频域,并在变换后描述原始信号具有的频率。主成分分析是一种识别数据中的模式(识别)的方法,突出显示数据的差异。借助PCA和IDA,我们可以减小信号的尺寸。 lDA用于统计和机器学习中,以找到特征的线性组合,这些特征可表征或分离两类或更多类对象或事件。所得的组合可用作线性分类器,或更普遍地,用于稍后的分类之前的降维。 lDA与方差分析(方差分析)密切相关。 PCA用于分析。 PCA的主要优点是,一旦找到模式并压缩数据,即通过减少维数而不会丢失太多信息。降维是减少所考虑的随机变量数量的过程,可以分为特征选择和特征提取。特征选择方法尝试查找原始变量的子集,然后特征提取将高维空间中的数据转换为较少维空间。

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