In this paper we present a comparative simulation study of three denoising algorithms using wavelets. The denoising algorithms (i.e., universal threshold, minimax threshold and rigorous SURE threshold) have been used to remove white Gaussian noise from synthetic and real signals. The analysis is done by applying soft and hard thresholds to signals with different sample sizes. The mean squared error (MSE) is used to evaluate the performance of these algorithms. The results show that the rigorous SURE algorithm with a hard threshold has a better performance than other algorithms in synthetic signals. On the other hand, the universal threshold algorithm with a soft threshold shows the best performance in real signals when using the Daubechies wavelet with 5 vanishing moments.