Modern research or study on patterns in nerve signals
You might want to read about event related potentials (recorded by EEG) or event related fields (recorder by MEG). The idea is simple:

1) Pick some stimulus, e.g. a person touching the hand of a subject. Pick another stimulus, e.g. the subject seeing a person touching the hand of another subject. Record EEG/MEG.

2) Repeat each condition for at least few hundred times. Throw away bad data, and average the repetitions. You do the averaging because the signal-to-noise ratio is low in all non-invasive electrical measurements, and the signals are always riddled with movement, cardiac, and eye-blink artefacts.

3) Compare the conditions in each sensor. Rest is statistics, though not very easy.

Actually, the experiment above would be about mirror neurons, a relatively hot topic in neuroscience. (See e.g. recent issue from Nature)

The more general situation is that using pattern recognition/machine learning algorithms to study brain signals is already a standard thing to do. There are for example graduate/undergraduate programs in computational neuroscience.

If you would study some other signal (e.g. measure from a hand, leg), they are going to dull. Very dull. Mostly because then you have 1 time-series, instead of several hundreds of time-series to analyse.


  For example I would want to know if applying hot/cold object to skin of both right and left limbs would cause the sensory neuron to send the same or similar signal (electrical impulse) to the spinal cord.


This you could too study with the event related fields/potentials.