0

I have a base signal which is a wave with (fairly) consistent shape and known frequency. On top of that signal is some uniformly distributed additive noise (wave goes from -1 to 1, noise is uniformly distributed from -0.025 to +0.025 on any given sample)

We sample at a specified rate (48K frames/second).

Our goal is to determine the index of the frame in the wave's period at which it reaches its maximum. (The shape of the waveform varies in a somewhat non-deterministic fashion, so curve fitting is out, but the maximum/minimum are fixed at a specified point in the period)

We can sample an arbitrary number of complete waveforms, but want to keep it as short as necessary to get reach some arbitrary confidence level.

One proposed method is to simply sample n periods, average the sample data for each frame in the period, and find the index of the maximum frame.

The other proposed method is more complicated. We divide our n waveforms into x (probably 2 or 3) groups. For each group of n/x periods, we average and obtain the index of the maximum frame (as above, but with fewer periods).

We then compare the indices for each of these x groups, and if they match, we're done. If they don't, we sample another n/x periods, and get the index of the maximum frame, and continue this until we get x consecutive groups that give us the same index.

We don't have stats training (obviously), and I'm suspicious about whether the second method actually buys us anything over the first, although it 'feels' like we're getting some verification that we chose the right maximum frame and that we're getting more samples only when we 'need' it.

Does checking for consistency among multiple groups of a smaller number of waveforms actually help us here? I'm not looking for a lot of mathematics here, just some discussion whether the general technique is valid or not.

(And yes, if it's worthwhile, we can use the minimum as well for additional validation.)

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
Tom West
  • 1
  • 1
    Closely related: http://stats.stackexchange.com/questions/22974 and http://stats.stackexchange.com/questions/21718. And this one appears to be an exact duplicate: http://stats.stackexchange.com/questions/36309. Does that answer your questions, Tom? – whuber Dec 04 '12 at 18:32
  • Thanks you for the references (I did look, but turned up nothing.) I'll look at these tonight and reply. – Tom West Dec 04 '12 at 21:36
  • Your last reference was very useful vis-a-vis finding a maximum using methods other than a straight average. Many thanks for your pointer (and your answer to those previous questions!) However, my primary question was whether there's any benefit to dividing my samples into smaller groups and comparing individual results from each group to ensure they come up with the same value, and for that I am still hoping for some input. – Tom West Dec 04 '12 at 23:05

0 Answers0