Analog signal can be discrete time?
This sounds like a confusion in terminology. See http://en.wikipedia.org/wiki/Digitizing

Digitization basically involves two steps: 


Discretization: Sampling the signal at discrete times
Quantization: Turning the samples from (in theory) infinite resolution to finite resolution


Look at all possible combinations you can have 4 different types of signal:


continuous time, continous amplitude
discrete time, continous amplitude
continuous time, discrete amplitude
discrete time, discrete amplitude


Typically we refer to #1 as "analog" and #4 as "digital". #2 and #3 are of little practical relevance, other than getting the mathematical models right. Quantization and Discretization are really quite different mathematically so it doesn't make a lot of sense to analyze them in combination. In other words: the theory of time discretization applies equally to continuous amplitude and discrete amplitude signals.