Nerve signals were recorded from the sciatic nerve of the rabbits in the acute experiments with multi-channel thin-film longitudinal intrafascicular electrodes. 5.5 s sequences of quiescent and high-level nerve activity were spectrally decomposed by applying a ten-level stationary wavelet transform with the Daubechies 10 (Db10) mother wavelet. Then, the statistical distributions of the raw and subband-decomposed sequences were estimated and used to fit a fourth-order Pearson distribution as well as check for normality. The results indicated that the raw and decomposed background and high-level nerve activity distributions were nearly zero-mean and non-skew. All distributions with the frequency content above 187.5 Hz were leptokurtic except for the first-level decomposition representing frequencies in the subband between 12 and 24 kHz, which was Gaussian. This suggests that nerve activity acts to change the statistical distribution of the recording. The results further demonstrated that quiescent recording contained a mixture of an underlying pink noise and low-level nerve activity that could not be silenced. The signal-to-noise ratios based upon the standard deviation (SD) and kurtosis were estimated, and the latter was found as an effective measure for monitoring the nerve activity residing in different frequency subbands. The nerve activity modulated kurtosis along with SD, suggesting that the joint use of SD and kurtosis could improve the stability and detection accuracy of spike-detection algorithms. Finally, synthesizing the reconstructed subband signals following denoising based upon the higher order statistics of the subband-decomposed coefficient sequences allowed us to effectively purify the signal without distorting spike shape.