4. Give an example of a periodic function (either CT or DT) and demonstrate that this function is periodic. Give an example of a non-periodic function (either CT or DT) and demonstrate that this function is not periodic. Post your answers on Rhea.
Periodic and Non-Periodic functions
Definition
A function is defined as periodic if it can be moved along the x axis to a place where it exactly matches its original form. In mathematical terms, x(t) is periodic if and only if:
$ \,\! x(t+T)=x(t) $
Examples of periodic and non-periodic functions
Periodic examples:Basically any trigonometric function:
$ \,\!cos(t)=cos(t+2\pi) $
$ \,\!sin(t)=sin(t+4\pi) $
also, any square, triangle, or sawtooth waves are periodic
Non-Periodic examples:
any algebraic function:
$ \,\!f(t)=2x+5 $
$ f(t)=\frac{2x^3+5}{4^x-x} $
$ \,\!f(t)=log(x)+e^{x+2} $
any power, exponential or logarithmic function, without a periodic portion, are non-periodic as well.
