Introduction to Wavelets and their applications in signal denoising

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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Aggarwal, R., Rathore, S., Singh, J. K., Tiwari, M., India, M. P., Gupta, V. K., & Khare, A. (2011). Noise Reduction of Speech Signal using Wavelet Transform with Modified Universal Threshold. International Journal of Computer Applications, 20(5), 975–8887.
Bouman, C. A. (2013). Continuous Time Fourier Transform ( CTFT ). Digital Image Processing, 1–5. Cengiz, Y., Doç, Y., & Arıöz, U. (2016). Ayrık Dalgacık Dönü ¸ sümü Kullanarak Konu ¸ sma Sinyallerinin Gürültüden Arındırılması için Uygulama An Application for Speech Denoising Using Discrete Wavelet Transform, 1–4.
Federico, A., & Kaufmann, G. H. (2009). Wavelet Transform, 34(15), 2336–2338. Guo, X., Li, Y., Suo, T., & Liang, J. (2017). De-noising of digital image correlation based on stationary wavelet transform. Optics and Lasers in Engineering, 90(July 2016), 161–172. https://doi.org/10.1016/j.optlaseng.2016.10.015
Hazas, M., & Hall, H. (1999). Processing of Non-Stationary Audio Signals. Science, (August). Huang, W., & Macfarlane, D. L. (2012). Fast Fourier Transform and MATLAB Implementation, 1–26.
Liu, C.-L. (2010). A Tutorial of the Wavelet Transform. National Taiwan University, Department of Electrical Engineering (NTUEE), Taiwan, 1–72. https://doi.org/10.1111/j.1600-0404.1995.tb01711.x
Misiti, M., Misiti, Y., Oppenheim, G., & Poggi, J.-M. (2009). Wavelet Toolbox TM 4 User ’ s Guide. The MathWorks Inc., …, 11–47. Retrieved from http://feihu.eng.ua.edu/NSF_TUES/w7_1a.pdf
Osgood, B. (2007). Lecture Notes for EE 261 The Fourier Transform and its Applications. Stanford University, 428.
Patil, R. (2015). Noise Reduction using Wavelet Transform and Singular Vector Decomposition. Procedia Computer Science, 54, 849–853. https://doi.org/10.1016/j.procs.2015.06.099
Patil, S. S., & Pawar, M. K. (2012). Quality advancement of EEG by wavelet denoising for biomedical analysis. Proceedings - 2012 International Conference on Communication, Information and Computing Technology, ICCICT 2012, 1–6. https://doi.org/10.1109/ICCICT.2012.6398151
Polikar, R. (1994). The Wavelet Tutorial. Internet Resources, 1–67. https://doi.org/10.1088/1751-8113/44/8/085201 Yadav, T. (2016). Denoising and SNR Improvement of ECG Signals Using Wavelet Based Techniques, (October), 678–682.