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DESIGN & PRODUCTS aNalOG DESIGN Fig. 5: Stopband phase shift from an averager does affect the Fig. 4: The FFT of a seven sample averager goes negative signal this price has a consumption-driven pattern with a periodic- Such processing can cause problems with electrical signals ity of six days, for some reason. Expressed as a frequency, too. The problem is at its worst for very simple filters that don’t this is 0.1666 price wobbles per day. We can see from Figure have high attenuation in the regions where the phase is ‘wrong’. 2 that this frequency lies in a ‘jumped up’ region, and yet the It can particularly be a problem with some simple FIR notch magnitude of the response is only about 13 dB down. Build- filters, as well as the boxcar averager. It’s particularly signifi- ing up a spreadsheet to analyze the output of such a process cant when the shape of a waveform is subjectively evaluated is easy. Figure 3 shows the six day fluctuation on a daily scale for clues as to what processes are occurring. Interpretation of (the higher-amplitude trace) and the output of the seven day signals acquired from physiological activity can be affected by averager. It confirms the hypothesis: in the filtered data, the six the changes wrought by filtering. day trend is inverted. If you don’t take that into account when Figure 5 shows a synthesized neural potential signal (the reading the smoothed data, you will totally misinterpret any one that peaks first), and the somewhat different responses underlying causality in the six day cycle. through a normal seven sample averager, with a width of 1.43 The thing that misleads us so often with these frequency ms (the darkest, slowest trace), and the same filter but with response plots is that we conventionally only plot the magnitude the phase jump synthetically removed so that all components of the response, whether expressed in linear or dB form. Now, stay in phase. The difference is subtle but significant for nerve the frequency response is nothing other than the Fourier trans- conduction experiments. form of the time response, and if we plot the amplitude of the The moral of this part of the story is that under-filtering, either Fourier transform of one of these offending filters, we find that it through laziness, lack of processing power or a desire to have goes negative in these regions, as seen in Figure 4. minimal impact on the signal, may be a misplaced belief. You That makes sense, when you think about it; an amplifier with should use either a filter whose stopbands are deep enough a negative gain is an inverting amplifier, and those little bits of that your signal can’t be corrupted by unexpected phase jumps rogue stopband are no different – they are regions within which in stopband signals, or a filter that doesn’t have those phase the filter is inverting. jumps in the first place. See us at Hall A4, Stand 117 November 13 - 16, 2012 www.electronica.de rswww.com/electronics 42 Electronic Engineering Times Europe October 2012 www.electronics-eetimes.com


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