American Journal of Engineering Research (AJER) 2017 American Journal of Engineering Research (AJER) e-ISSN: 2320-0847 p-ISSN : 2320-0936 Volume-6, Issue-8, pp-01-07 www.ajer.org Research Paper Open Access www.ajer.org Page 1 Comparison on Fourier and Wavelet Transformation for an ECG Signal Mahamudul Hassan Milon (Department of Mathematics, Khulna University, Bangladesh) Corresponding Author: Mahamudul Hassan Milon ABSTRACT: Wavelet analysis is a new method for solving difficult problems in mathematics, physics, and engineering, with modern applications as diverse as wave propagation, data compression, signal processing, image processing, pattern recognition, computer graphics, the detection of aircraft and submarines and other medical image technology. Wavelets allow complex information such as music, speech, images and patterns to be decomposed into elementary forms at different positions and scales and subsequently reconstructed with high precision. Signal transmission is based on transmission of a series of numbers. The series representation of a function is important in all types of signal transmission. The wavelet representation of a function is a new technique. Wavelet transform of a function is the improved version of Fourier transform because Fourier transform is a powerful tool for analyzing the components of a stationary signal. But it is failed for analyzing the non stationary signal where as wavelet transform allows the components of a non-stationary signal to be analyzed. In this study our main goal is to compare an ECG signal for Fourier transformation and Wavelet transformation. Keywords: ECG Signal, Fourier transformation, Wavelet transformation, Haar Wavelet transform. --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 19-07-2017 Date of acceptance: 01-08-2017 --------------------------------------------------------------------------------------------------------------------------------------- I. INTRODUCTION Historically, the concept of "Ondelettes" or "Wavelets" started to appear more frequently only in theearly 1980’s.One of the main reasons for the discovery of wavelets and wavelet transforms is that the Fourier transform does not contain the local information of signals. So the Fourier transform cannot be used for analyzing signals in a joint time and frequency domain. In 1982, Jean Morlet, in collaboration with a group of French engineers, first introduced the idea of wavelets as a family of functions constructed by using translation and dilation of a single function, called the mother wavelet, for the analysis of nonstationary sgnals. However this new concept can be viwed as the synthesis of various ideas originating from different disciplines including mathematics (Calderon-Zygmund operators and Littlewood-Paley theory), physics (coherent states in quantum mechanics and the renormalization group), and engineering (quadratic mirror filters, sideband coding in signal processing, and pyramidal algorithms in image processing)[1,2]. The Wavelets conference series was started by Andrew Laine in 1993. Under the leadership of Laine, Michael Unser, and Akram Aldroubi, it grew to be the leading venue for the dissemination of research on wavelets and their applications. Manos Papadakis replaced Akram Aldroubi as a conference chair in 2005, and since then the remainder of the leadership team has turned over, with the addition of Dimitri Van De Ville and Vivek Goyal[5,6]. Wavelets are mathematical functions that cut up data into different frequency components and then study each component with a resolution matched to its scale. They have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. The wavelet representation of a function is a new technique and it does not loss time information. Keeping these things in mind, our main goal in this thesis has been to provide both a systematic exposition of the basic ideas and results of wavelet transforms and some applications in time- frequency signal analysis.