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CE105 – DIGITAL SIGNAL PROCESSING LAB 2A: Discrete-Time Systems in the Time Domain Instructors: Phan Quoc Huy (huypq@uit.edu.vn) Nguyen Dang Nhan (nhannd@uit.edu.vn) Goal: The aim of this lab session is to illustrate the simulation of some simple discretetime systems on the computer using MATLAB and investigate their time domain properties Instructions: Students are required to go through the steps explained below and then complete the exercises given at the end of the lab I Background Review R2A.1 For a linear discrete-time system, if y1[n] and y2[n] are the responses to the input sequences x1[n] and x2[n], respectively, then for an input the response is given by It must hold for any arbitrary constants α and β and for all possible inputs x1[n] and x2[n] If it does not hold for at least one set of nonzero values of α and β, or one set of nonzero input sequences x1[n] and x2[n], then the system is nonlinear R2A.2 For a time-invariant discrete-time system, if y1[n] is the response to an input x1[n], then the response to an input x[n]=x1[n-n0] is simply y[n]=y1[n-n0] where no is any positive or negative integer The above relation between the input and output must hold for any arbitrary input sequence and its corresponding output If it does not hold for at least one input sequence and its corresponding output sequence, the system is time-varying R2A.3 A linear time-invariant (LTI) discrete-time system satisfies both the linearity and the time-invariance properties R2A.4 If y1[n] and y2[n] are the responses of a causal discrete-time system to the inputs u1[n] and u2[n], respectively, then u1[n]=u2[n] for n