Introduction to Wavelets and their applications in signal denoising

Year 2018, Volume: 8 Issue: 1, 1 - 10, 28.06.2018

Cigdem Polat , Mehmet Siraç Özerdem

https://doi.org/10.17678/beuscitech.349020

Cited By: 11

Abstract

 The aim of this study is providing a comprehensive background
information related to the roots of both Fourier Transform (FT) and Wavelet
Transform (WT) along with an experiment related to applications of WT
techniques. The paper describes several applications of WT and provides
background information on FT. Fourier Transform (FT) is a concept that has a
long history yet several issues related to resolution and uncertainty of time
–frequency. Even though there are several adapted forms of FT such as Short
Time Fourier Transform (STFT), which intend to solve the problems, certain
limitations remain. Wavelet Transform (WT) is an alternative transformation
technique emerged in order to fully tackle these diverse and complicated
issues. In this paper, the background information related to the roots of FT
and WT are given. Some of the problems that WT addresses are examined. WT is a
tool that has many advantages among them is noise reduction and compression. We
reviewed several studies that use the noise reduction capability of WT alone or
combined with other signal processing tools. Discrete Wavelet Transform (DWT)
based algorithm is also examined as a noise reduction technique and carried out
in MATLAB setting. Analysis on a speech signal which contaminated with keyboard
sound also a number spelling female voice containing unknown noise are
performed. Different types of thresholding and mother wavelets were in
consideration and it was revealed that Daubechies family along with the soft
thresholding technique suited our application the most.

Keywords

Fourier transform, Signal denoising, Short time Fourier transform, Wavelets

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