*Article* **The Optimal Selection of Mother Wavelet Function and Decomposition Level for Denoising of DCG Signal**

**Young In Jang , Jae Young Sim, Jong-Ryul Yang \* and Nam Kyu Kwon \***

Department of Electronic Engineering, Yeungnam University, Gyeongsan, Gyeongbuk 38541, Korea; owlisie@yu.ac.kr (Y.I.J.); ja2922@yu.ac.kr (J.Y.S.)

**\*** Correspondence: jryang@yu.ac.kr (J.-R.Y.); namkyu@yu.ac.kr (N.K.K.); Tel.: +82-53-810-2495 (J.-R.Y.); +82-53-3095 (N.K.K.)

**Abstract:** The aim of this paper is to find the optimal mother wavelet function and wavelet decomposition level when denoising the Doppler cardiogram (DCG), the heart signal obtained by the Doppler radar sensor system. To select the best suited mother wavelet function and wavelet decomposition level, this paper presents the quantitative analysis results. Both the optimal mother wavelet and decomposition level are selected by evaluating signal-to-noise-ratio (SNR) efficiency of the denoised signals obtained by using the wavelet thresholding method. A total of 115 potential functions from six wavelet families were examined for the selection of the optimal mother wavelet function and 10 levels (1 to 10) were evaluated for the choice of the best decomposition level. According to the experimental results, the most efficient selections of the mother wavelet function are "db9" and "sym9" from Daubechies and Symlets families, and the most suitable decomposition level for the used signal is seven. As the evaluation criterion in this study rates the efficiency of the denoising process, it was found that a mother wavelet function longer than 22 is excessive. The experiment also revealed that the decomposition level can be predictable based on the frequency features of the DCG signal. The proposed selection of the mother wavelet function and the decomposition level could reduce noise effectively so as to improve the quality of the DCG signal in information field.

**Keywords:** doppler cardiogram; wavelet transform; denoising; mother wavelet function; decomposition level; signal decomposition; signal-to-noise-ratio
