Four channels of sequentially acquired data from a single input signal
Figure 7 shows the outputs from the four subfilters, all fed with the samples of Figure 6, implemented using the Digital Filter Block in the PSoC3. Remember that the four filters have identical magnitude responses, and differ only in that their group delays are spread apart by units of a quarter of a sample time. Passage through these filters rather magically reshapes the applied waveforms so that the output signals are all identical, to within very close tolerances.
Are there downsides to this approach? Well, we’ve put each channel’s data through a 32-tap filter, and the average group delay experienced by the channels is that of a 32-tap linear phase filter running at Fs, and that’s 16/Fs. You might want that to be rather lower, especially at lower sample rates or in a closed-loop system. If you don’t need such a wide band of flat frequency response, you can reduce the number of taps in the initial filter to reduce the delay. If you really do need the bandwidth, another approach is to use a minimum-phase FIR filter as your starting point. In sacrificing linear phase response, the low frequency group delay can be greatly reduced. The technique still works perfectly (I’ve tried it in simulation). Sophisticated filter design programs such as FilterShop from LinearX can produce minimum-phase FIR filters.
The four channels after passage through their ‘realignment filters’
This work was done to support our electricity metering analysis, but it has quite a few other applications. If you’re analyzing structures, the cross-correlation terms in the vibration will be useless unless you can rely on simultaneity in the data sets. One intriguing application I looked at recently was a gunfire detection system sampling eight microphones at 60k samples per second each, with the Digital Filter Block implementing eight 12-tap subfilters derived from a minimum phase