A method and apparatus are provided for the removal of significant broad-band noise from waveforms acquired for time domain network analysis. The method may include the steps of providing the noisy waveform as an input waveform, determining a frequency domain noise shape associated with the input waveform, calculating a wavelet domain noise shape from the frequency domain noise shape, calculating a discrete wavelet transform of the input waveform to form a wavelet domain waveform, and estimating the noise statistics from the wavelet domain waveform. A threshold may be calculated from the estimated noise statistics and the wavelet domain noise shape, and the threshold may be applied to the wavelet domain waveform to form a denoised wavelet domain waveform. Finally, an inverse discrete wavelet transform of the denoised wavelet domain waveform may be calculated to form a denoised waveform.