Fourier Transform of Untransformable Signals Using Pattern Recognition Technique

Abstract

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.