Removing DC trends before calculating power spectral densities is a necessary operation, but the choice of the method is probably one of the most difficult problems in electrochemical noise measurements. The procedure must be simple and straightforward, must effectively attenuate the low frequency components without eliminating useful information or create artifacts. Several procedures will be presented, including moving average removal, linear detrending, polynomial fitting, analog or digital high-pass filtering, and their effect on electronic and electrochemical signals discussed. The results show that the best technique appears to be polynomial detrending On the contrary, the recently proposed moving average removal method was found to have considerable drawbacks and its use should not be recommended.
In the analysis of electrochemical noise (EN), when extracting statistical information from the time records of the fluctuations of the electrical quantities (current or voltage), one is often confronted with the problem that the signal sampled does not appear to be stationary, at least within the measurement time T. The signal is said to be drifting, and since the calculation of the power spectral density (PSD) or even of the standard deviation presupposes a stationary process, it is necessary to apply some procedure to the incoming signal so as to eliminate the contribution of what is commonly called its drift. The reasons for this behavior may be different and hard to know: for example, the signal may be stationary, but it may contain frequency components lower than fo = l/T, or there may be some slow alteration of the system under study that causes the drift, whether linear or not. In corrosion studies, progressive deterioration of the electrodes and therefore lack of stationarity, is to be expected in many c a s e s . An illustrative example is given by a random signal superimposed to a linear drift. In the implementation employed to generate Fig. la, white noise (2 mV p-p) in the range from 0 to 300 Hz, produced by a signal generator was added to a ramp with a 1.6 mV/min slope. Both time records in Fig. la and lb consist of 2048 points, but in the first the sampling rate is 10 Hz with a low-pass antialiasing filter at 3.3 Hz, while in the second it is 100 Hz, the cut-off frequency of the antialiasing filter being set at 33 Hz. For this case there is an analytical solution, and the expression for the PSD is:l, 2 a2T ~x, comp( f ) -- ~x (f) + ~ (1) 2~2f 2 where tPx~comp is the PSD of the composite signal, tPx that of the signal without drift, and the second term, which represents the effect of the drift, contains the slope, a, and the duration, T, of the time record. This component of the PSD, which gives a straight line of slope -2 in the logarithmic plot, is deterministic and not stochastic, so that the error is zero. For this reason, the low-frequency part of the spectra in Fig. 2, which are produced from the fast Fourier transform (FFT) of the two time records, is very smooth. Although the signal sampled in the two figures is the same, since Eq. 1 contains the total time T, which is different in the two cases, the PSD is different, as shown in Fig. 2. The fact that the two PSDs do not join is another indication that the signal is not stationary, so that one can only speak of pseudo-PSDs. If the sampling rate is increased to 1 kHz (antialiasing filter set at 330 Hz), curve c in Fig. 2 is a good representation of the PSD of white noise because the amplitude aT of the drift during the acquisition time is now small compared to the random fluctuations of 2 mV p-p. One has here the analytical proof of the experimentalist's common sense that if the drit~ is negligible during
