The electrocardiogram (ECG) is the recording of the electrical potential of the heart versus time. The analysis of ECG signals has been widely used in cardiac pathology to detect heart disease. The ECGs are non-stationary signals which are often contaminated by different types of noises from different sources. In this study, simulated noise models were proposed for the power-line interference (PLI), electromyogram (EMG) noise, base line wander (BW), white Gaussian noise (WGN) and composite noise. For suppressing noises and extracting the efficient morphology of an ECG signal, various processing techniques have been recently proposed. In this paper, wavelet transform (WT) is performed for noisy ECG signals. The graphical user interface (GUI) system is developed for visual representation and adaptive enhancement on noise modeling in ECG-based signal processing. Percentage root mean square difference (PRD) was measured between the modeled noisy signals and the samples of the original ECG. Moreover, cross correlation (XCorr) and root mean square error (RMSE) were performed between the noisy ECG signals and the denoised ones which resulted from WT denoising technique initially to evaluate the effectiveness of the WT denoising technique. The results show that the WT was successfully removed different types of proposed models of noises. The PRD was reasonable and are within the acceptable range, which is less than 50%, with 17% for BW and 47% for PLI indicating that the models and methods used for prediction are ideal for high precision signal applications. This study will help medical doctors, clinicians, physicians, and technicians to eliminate different types of noise.