Define Exponential, Ramp, Periodic and Aperiodic signal | Determine whether the signal x(t) = cos2(2πt) is periodic and if so, find its fundamental period.

Exponential Signal 

        The continuous time complex exponential signal is of the form 

                                    X(t) = b. eat

    Here b and a are in general complex numbers. Depending on the values of these parameters, the complex exponent can have several different characteristics.

Unit ramp Signal 

        

           A CT ramp signal is denoted by r(t). Mathematically it is represented as, 

                                R(t) = t for t ≥ 0 , 0 for t<0 

 Periodic Signal

            A signal is said to be periodic signal if it repeats at equal intervals. A CT signal which satisfies the equation x(t) = x(t+T0) is said to be periodic Example: Sine wave, Cosine wave, etc., 

Aperiodic signal

    Aperiodic signals do not repeat at regular intervals. A DT signal which satisfies the equation

                    x(n) = x(n+N) is said to be Aperiodic. 

            Example: Ramp signal, Exponential signal, etc., 

Given signal is X(t) = cos2(2πt) 

                Condition for periodicity is, the value of T= ω/2π should be ratio of two integers. For given signal,

                                                ω=2π,  T=2π/2π = 1 

    It is ratio of two integers. Therefore the given signal is a periodic signal.