The z - transform of the time function $$\sum\limits_{k = 0}^\infty {\delta \left( {n - k} \right)} $$ is

The transfer function of a zero - order - hold system is

The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system to an excitation e^-at u(t), a>0 will be

Consider a rectangular pulse g(t) existing between $$t = \, - {T \over 2}\,and\,{T \over 2}$$. Find and sketch the pulse obtained by convolving g(t) with itself. The Fourier transform of g(t) is a sinc function. Write down the Fourier transform of the pulse obtained by the above convolution.