What does "real time" signal processing mean? I thought this was supposed to be an obvious question, until I finally set up my real time system.

So basically I have a transmitter that sends 128 samples/second to a receiver. The transmitted information is stored as an object in MATLAB and continuously updated.

When people talk about real time signal processing, I'm really confused as to what they mean by real time. 

For example, say I want to extract the "mean" feature of this signal. Do I compute the mean when I receive one sample, two samples, all 128 samples, or ...what is this mean value?

More intriguing for me is the prospect of doing real time wavelet transform for joint time frequency analysis. Again, the question of "real time" comes up. How many samples do I need to reliable compute the wavelet (or fourier) coefficients so I could get a good view of the energy contained in this signal. 

Can anyone who is knowledgeable on this topic please elaborate how when and under what condition do you compute "features" or perform frequency domain analysis for a real time system.

Thanks!
'Real time' is a concept from computer engineering. A real time system is one that is guaranteed, by design, to execute a function or routine in a certain time T, or less. For example, a real-time avionics system is proven to react to signals coming from certain instruments in a time below a given threshold.

In your case, a more precise description (IMHO) of what you want is a "streaming system". You want a receiver that can process a stream of incoming samples without "dropping" samples; in other words, without its buffer overflowing. The easiest way to achieve that is to provide large enough computing power that the probability of dropping samples is very small.

This property is largely orthogonal to the problem of estimating signal features. Since the incoming signal is random, its features are going to vary. You may need to calculate, or find by experiment, how many samples do you need to process to have a useful feature estimate.

For example, these days most, if not all, transmitted signals have no DC component, so the mean will be close to zero all the time (barring imperfections in your analog front-end). I wouldn't worry about updating the mean estimate very often.

In modulation recognition, in contrast, you may need a few thousand samples, and the processing could take some time. You may decide to do something like gathering 5,000 samples (which in your case would take ~40 seconds), and you may take five second to process them, so you'll be updating that estimate every 45 seconds or so.

As you see, it really varies by estimate, and you'll need to figure out the best number in each case, given your requirements and your processing resources.