Signals and Systems - Electrical Engineering

504 C H A P T E R 8: Discrete-Time Signals and Systems 8.6. Generation of periodic discrete-time signals—MATLAB Periodic signals ...

Problems 505 8.10. Periodicity of discrete-time signals Consider periodic signalsx[n], of periodN 1 = 4 , andy[n], of periodN 2 ...

506 C H A P T E R 8: Discrete-Time Signals and Systems 8.14. LTI of ADCs An ADC can be thought of as composed of three subsystem ...

Problems 507 8.18. FIR filter—MATLAB An FIR filter has a nonrecursive input–output relation y[n]= ∑^5 k= 0 kx[n−k] (a) Find and ...

508 C H A P T E R 8: Discrete-Time Signals and Systems (a) Consider the case of averaging an input signalx[n]under real-time con ...

Problems 509 absolute value of the input, and a second one that low-pass filters its input. A circuit that is used as an envelop ...

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CHAPTER 9 The Z-Transform...................................................................................... I was born not k ...

512 C H A P T E R 9: The Z-Transform localization of poles and zeros determines the type of filter. However, in the discrete dom ...

9.2 Laplace Transform of Sampled Signals 513 with Laplace transform X(s)= ∑N n= 0 e−nsTs= 1 −e−(N+^1 )sTs 1 −e−sTs The poles are ...

514 C H A P T E R 9: The Z-Transform Letting r=eσTsandω=Ts, we have that z=rejω which is a complex variable in polar form, with ...

9.3 Two-Sided Z-Transform 515 9.3 Two-Sided Z-Transform Given a discrete-time signalx[n],−∞<n<∞, its two-sided Z-transform ...

516 C H A P T E R 9: The Z-Transform causal. To express the two-sided Z-transform in terms of the one-sided Z-transform we separ ...

9.3 Two-Sided Z-Transform 517 Solution To see the poles and the zeros more clearly let us expressX 1 (z)as a function of positiv ...

518 C H A P T E R 9: The Z-Transform nExample 9.3 Find the Z-transform of a discrete-time pulse x[n]= { 1 0≤n≤ 9 0 otherwise Det ...

9.3 Two-Sided Z-Transform 519 an exponentialRn 1 u[n] such that|xc[n]|<MRn 1 forn≥0 for some valueM>0. Then, forX(z)to con ...

520 C H A P T E R 9: The Z-Transform n {R 2 :|z|<0.5}—the inside of a circle of radius 0.5, an anti-causal signalx 2 [n] can ...

9.4 One-Sided Z-Transform 521 RemarksThe uniqueness of the Z-transform requires that the Z-transform of a signal be accompanied ...

522 C H A P T E R 9: The Z-Transform in terms of one-sided Z-transforms. Another valid reason to study the one-sided Z-transform ...

9.4 One-Sided Z-Transform 523 The Z-transform is a linear transformation, meaning that Z(ax[n]+by[n])=aZ(x[n])+bZ(y[n]) (9.10) f ...