Classification of CT and DT signals

Periodic and non-periodic Signals  

    A periodic function is one which has been repeating an exact pattern for an infinite period of  time and will continue to repeat that exact pattern for an infinite time. That is, a periodic  function x(t) is one for which  

                                        x (t) = x(t+nT)  

for any integer value of n, where T >0 is the period of the function and −∞ < t <∞ . The  signal repeats itself every T sec. Of course, it also repeats every 2 T,3T and nT. Therefore,  2T, 3T and nT are all periods of the function because the function repeats over any of those  intervals. The minimum positive interval over which a function repeats itself is called the  fundamental period T0.T0 is the smallest value that satisfies the condition x ( t ) = x ( t+T0).  The fundamental frequency f 0 of a periodic function is the reciprocal of the fundamental  period f 0=1/T0. It is measured in Hertz and is the number of cycles (periods) per second.  The fundamental angular frequency ω0 measured in radians per second is ω0=2πT0= 2πf0. A signal that does not satisfy the condition in (2.1) is said to be periodic or non-periodic.  

Deterministic and Random Signals  

    Deterministic Signals are signals who are completely defined for any instant of time, there is  no uncertainty with respect to their value at any point of time. They can also be described  mathematically, at least approximately. Let a function be defined as  

    A random signal is one whose values cannot be predicted exactly and cannot be described by  any exact mathematical function, they can be approximately described.