I know that sampling in one domian [time or frequency] gives raise to replicas in another domain[frequency / time]. How replicas are formed. What is this Time domain periodicity and frequency domain periodicity here in sampling.


Question: Will dismissal from one graduate school affect me applying to another?
Answer: 
  Is there hope for me in applying to grad schools in the future? 


Yes, but you will need a convincing argument for why graduate school will go better next time than it did the first time you tried it.  It's easy to say "I didn't care about grades and didn't work very hard, but I'll work harder this time," while actually working harder is much more difficult, so vague excuses may be discounted.

You could get lucky and find a school that is happy to give you another chance (perhaps a less prestigious department, which sees potential in you beyond what's typical for their students).  You might also be able to give a more concrete excuse for your past grades (for example, if there were external factors in your life that troubled you last time but won't apply this time).  Otherwise, the best way to demonstrate that things have changed is probably to succeed at something else.  Finding a job and doing well at it can show that you are now more mature and responsible than when you were a student, and successfully taking a few classes part-time can also look good.

So I'd suggest following a two-part strategy.  Try applying again with the best explanations/excuses you can offer, and see whether it works.  If it doesn't, then you should start thinking about longer-term methods to demonstrate that you've changed.