The present paper deals with the performance and the reliability of a Wavelet Denoising method for Doppler ultrasound Fetal Heart Rate (FHR) recordings. It displays strong evidence that the denoising process extracts the actual noise components. The analysis is approached with three methods. First, the power spectrum of the denoised FHR displays more clearly an l/fa scaling law, i.e. the characteristic of fractal time series. Second, the rescaled scale analysis technique reveals a Hurst exponent at the range of 0.7-0.8 that corresponds to a long memory persistent process. Moreover, the variance of the Hurst exponent across time scales is smaller at the denoised signal. Third, a chaotic attractor reconstructed with the embedding dimension technique becomes evident at the denoised signals, while it is completely obscured at the unfiltered ones.