延 安大学数字信号处理课件Chapter 1 Discrete-Time Signals and Systems.pptVIP

* Discrete-time * Discrete-time * Discrete-time * Discrete-time * Discrete-time * Discrete-time 1.3 Discrete-time systems Cascade Connection Parallel Connection Simple Interconnection Schemes 1.4 Time-domain characterization of LTI discrete-time systems An important subclass of LTI discrete-time systems is characterized by a linear constant coefficient difference equation of the from The output y[n] can be computed for all , knowing x[n] and the initial conditions Linear constant coefficient difference equation 1.4 Time-domain characterization of LTI discrete-time systems Classical Solution The procedure for computing the solution of the constant coefficient difference equation is very similar to that employed in solving the constant differential equation in the case of an LTI continuous-time system. 1.4 Time-domain characterization of LTI discrete-time systems Zero-Input Response Zero-State Response Total Solution Classical Solution Impulse Response Calculation? It is simply the zero-state response with x[n]=δ[n] 1.4 Time-domain characterization of LTI discrete-time systems Recursive Solution If we assume the system to be causal, then we can rewrite the linear constant coefficient difference equation to express y(n) explicitly as a function of x(n): The output y(n) can be computed recursively. 1.4 Time-domain characterization of LTI discrete-time systems Z-Transform Solution 1.4 Time-domain characterization of LTI discrete-time systems MATLAB Solution yn=filter(B,A,xn) %ep141.m A=0.8;ys=1; xn=[1, zeros(1,30)]; B=1;A=[1,-a]; xi=filtic(B,A,ys); yn=filter(B,A,xn,xi) N=0:length(yn)-1; subplot(3,2,1);stem(n,yn,’.’) title(‘(a)’);xlable((‘n’);ylable(‘y(n)’) 1.4 Time-domain characterization of LTI discrete-time systems MATLAB Solution The impulse and step responses of a causal LTI discrete-time system can be computed using MATLAB M-files impz and stepz, respectively 1.4 Time-domain characterization of LTI discrete-time systems MATLAB Solution Example: Dete