Answer the following questions about discrete signal processing.
(1) Show the definition of the -transform of a discrete signal sequence defined for where is a complex number.
(2) By using the definition, find the -transform of a geometric sequence where is a real number.
(3) We consider the zero state response of the discrete time system shown in the figure below ,where and are real numbers.
Give and by using the -tranform of the system's internal state . Here, and are the -tranforms of the system's input and output , respectively.
(4) Give the transfer function of the system.
(5) Next, we find the system's frequency response by using the transfer function .
Consider the input sequnence sampled at the interval from a complex exponential function . Derive and then find the output sequence .
