Question

Q5: Consider the system in Figure 1. Assume that X (F) 0 for lfl> F /2 and that How is the output of the discrete-time system y(n) related to the input signal x (t)? LA

Answer 1

A discrete-time system is defined mathematically as a transformation or operator that maps an input sequence with values can be denoted as [n into an output sequence with values yIn]. This y[n] = T(x[n]} (2.19) and is indicated pictorially in Figure 2.6. Equation (2.19) represents a rule or formula for computing the output sequence values from the input sequence values. It should be emphasized that the value of the output sequence at each value of the index n may depend on input samples [n] for all values of n, i.e., y at time n can depend on all or part of the entire sequence x. The following examples illustrate some simple and useful systems Figure 2.6 Representation of a discrete-time system, i.e., a transformation that maps an input x[n Tsequence x[n] into a unique output sequence yin

though the abscissa is drawn as a continuous line,-it is important to recognize that x[n is defined only for integer values of . It is not correct to think of [n] as being zero when n is not an integer; x[n] is simply undefined for noninteger values of n. x 기 ₩ȚITT-n 78 910 11 Figure 2.1 Graphic representation of a discrete-time signal. 9-8-7-6-5-4-3-2-1 01 2 3456