### Discrete-Time System Analysis in the z-Domain ppt课件介绍及下载

Discrete-Time System Analysis in the z-Domain ppt课件内容预览：§5-3 Stability of Discrete-timeSystems§5-4 Frequency Response of Discrete-TimeSystemsProblems§5-1 Transfer FunctionRepresentationIn this section the transfer function representation is generated for the class of causal linear time-invariant discrete-time systems. The development begins with discrete-time systems defined by an inputoutput difference equation. Systems given by a first-order inputoutput difference equation are considered first.(5.2)First-orderCaseConsider the linear time-invariant discrete-time system given by the first-order inputoutput difference equationy[n]+ay[n–1]=bx[n](5.1)where a and b are real numbers,y[n]is the output,and x[n]is the input. Taking the z-transform of both sides of (5.1)and using the right-shift property giveswhere Y(z)is the z-transform of the output response y[n]and X(z)is the z-transform of the input x[n]. Solving (5.2)for Y(z)yields(5.3)Equation (5.3)is the z-domain representation of the discrete-time system defined by the inputoutput difference equation (5.1). The first term on the right-hand side of (5.3)is the z-transform of the part of the output response resulting from the initial condition y[–1],and the second term on the right-hand side of (5.3)is the z-transform of the part of the output response resulting from the input x[n]applied for n=0,1,2,….The system given by (5.1)has no initial energy at time n=0if y[–1]=0,in which case (5.3)rces to(5.4)becomesppt(5.4)Defining(5.5)The function H(z)is called the transfer function of the system since it specifies the transfer from the input to output in the z-domain assuming no initial energy (y[–1]=0). Equation (5.5)is the transfer function representation of the system.n(5.6)Expandingand taking the inverse z-transform of both sides of (5.6)gives(5.7)If the initial condition y[–1]is zero,(5.8)rces toThe output y[n]given by (5.9)is called the step response since it is the output response when the input x[n]is the unit step u[n]with no initial energy prior to the application of u[n].n=0,1,2,…(5.8)(5.9)Second-orderCaseNow consider the discrete-time system given by the second-order inputoutput difference equationy[n]+a1y[n–1]+a2y[n–2]=b0x[n]+b1x[n –1](5.10)Taking the z-transform of both sides of (5.10)and using the right-shift property gives (assuming that x[–1]=0)Solving for Y(z)givesThe above equation can be rewritten as follows(5.11)Equation (5.11)is the z-domain representation of the discrete-time system given by the second-order inputoutput difference equation (5.10). The first term on the right-hand side of (5.11)is the z-transform of the part of the output response resulting from the initial condition y[–1]and y[–2],and the second term on the right-hand side of (5.11)is the z-transform of the part of the output response resulting from the input x[n]applied for n=0,1,2,….

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