Suppose I have three time series with the same length and the same temporal interval. If I upsample each of the three time series through interpolation, that will cause aliasing. However, if I'm interested in the information embedded in the average of the three time series, is such an upsampling justified? In other words, does the above upsamping and then averaging among three time series increase the Nyquist frequency by three times? Thanks!
Simple Answer: No. (At least I don't think so -- It's been 10 years since my EE classes).
In general, multiple samples with independent white noise will, when averaged, raise the signal to noise ratio. But they will not increase the Nyquist frequency.
Construct three cell towers equidistant from a point source. Make a cell call in the center and record it independently on each of the three towers at a common sampling rate, say the 450 MHz GSM band. Then average each sample across the three towers and viola, triple the S/N (assuming that local noise characteristics of each tower are independent and all received the same signal at exactly the same strength).
However, even though you upped the S/N by a factor of three, you didn't change the Nyquist frequency. Reference included for those interested.
Note: In my example, I'm assuming that the samples collected at the three towers are "in phase" -- equidistant -- if so, then what I've stated above is correct. If the samples you're collecting are out of phase, then this might in fact raise the Nyquist frequency. That said, you might want to ask this question somewhere else -- Unfortunately the corresponding Signal, Image, & Video Processing and Electronics & Electrical Engineering boards have yet to really take off. You might post your question there, but I'm not sure if it will ever be answered.