How do the English pronunciations of "tiu" and "tou" differ?
First of all, don't expect an answer like "Compute such and such well-known function on the data and if the result is above such or such value it's tiuuu otherwise it's tou". You won't get anything robust or reliable with approaches like that.

The good representations of sound which can be used for this kind of discrimination task are either the Mel Frequency Cepstral Coefficients (MFCC) or the linear prediction coefficients (Compute the first 20 or so autocorrelation coefficients and use the Levinson-Durbin recursion to get the AR coefficients). Both are somehow independent of pitch (good), moderately robust to noise (good but can be better), but are still somewhat speaker and gender dependent. It's still a vast improvement over trying to guess formants from a spectrum and matching that to a per-phoneme table.

Does your application tolerate a training phase? If so, get your user to record a dozen of utterances of each word ; and use this as a training set for a simple bayesian classifier using a gaussian model. Use this classifier to discriminate new utterances.

Does your application need realtime processing? If not, you can get by with clustering. Record the whole "sentence", split it into "words" ; compute average feature vectors over each word ; and run K-means clustering to get 2 class out of it. One class will be "tou" and the other "tiu". The class whose "words" have the lowest average spectral centroid are likely to be the "tou".

A last word on speech recognition: if you have a vocabulary of two words, the cost of running a decent speech recognition toolchain will be that of:
* Computing the MFCC features (which you have to do anyway no matter what).
* Scoring a dozen of gaussians (which you have to do anyway).
* Finding the lowest cost paths in a FST with less than a dozen states.

This is quite pedestrian and nowhere near the complexity of natural language speech recognition. Since you have no experience in digital signal processing, doing so will probably be faster than whatever custom code you might write. Thus I very strongly suggest you to collect a small training corpus of utterances from people around you and start looking into "off the shelf" speech recognition toolboxes like HTK. Just using the built-in tools you will be able to train a model evaluate it on your data without writing code.