Signals and Systems - Electrical Engineering

564 C H A P T E R 9: The Z-Transform 9.6 What Have We Accomplished? Where Do We Go from Here?.................... Although the h ...

Problems 565 (d) From the above results, indicate the region in thes-plane to which the wholez-plane is mapped into. Sinceω=ω+ 2 ...

566 C H A P T E R 9: The Z-Transform (c) Compute the Laplace transform of the sampled signal (i.e.,Xs(s)=L[xs(t]). (d) Determine ...

Problems 567 (a) Use the given Z-transform to find a difference equation for which the outputy[n]is a discrete-time cosineAcos(ω ...

568 C H A P T E R 9: The Z-Transform 9.18. Inverse Z-transform Find the inverse Z-transform of X(z)= 8 − 4 z−^1 z−^2 + 6 z−^1 + ...

Problems 569 (a) Find a matrix equation that would allow us to find the coefficients ofB(z)andA(z). (b) Leth[n]=0.5n(u[n]−u[n−10 ...

570 C H A P T E R 9: The Z-Transform 9.25. Prony method and Z-Transform—MATLAB Consider finding the Z-transform of a noncausal s ...

CHAPTER 10 Fourier Analysis of Discrete-Time Signals and Systems........................... Diligence is the mother of good luck ...

572 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems In this chapter, we will see that a great deal of th ...

10.2 Discrete-Time Fourier Transform 573 or that x[n]be absolutely summable. This means that only for those signals we can use t ...

574 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems n Eigenfunctions and the DTFT.The frequency represen ...

10.2 Discrete-Time Fourier Transform 575 According to the formula for the DTFT atω=0, we have that X(ej^0 )= ∑∞ n=−∞ x[n]ej^0 n= ...

576 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems a sinusoidx[n]=cos(ω 0 n+θ), which is not absolutely ...

10.2 Discrete-Time Fourier Transform 577 so thatx[n]=A+0.5Bcos((ω 0 +ω 1 )n)+0.5Bcos((ω 1 −ω 0 )n). Lettingω 2 =ω 0 +ω 1 andω 3 ...

578 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems n The functionabscomputes the magnitude and the func ...

10.2 Discrete-Time Fourier Transform 579 (^00102030405060708090100) 0.5 1 n x[ n] − 1 −0.8 −0.6 −0.4 −0.2^0 0.2 0.4 0.6 0.8 0 10 ...

580 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems FIGURE 10.2 DTFT of (a) a sampled signal, and (b) th ...

10.2 Discrete-Time Fourier Transform 581 Solution Sincep[n] has a finite support, its Z-transform has as region of convergence t ...

582 C H A P T E R 10: Fourier Analysis of Discrete-Time Signals and Systems Downsampling and Upsampling Although the expanding a ...

10.2 Discrete-Time Fourier Transform 583 nExample 10.4 Consider the frequency response of an ideal low-pass filter, H(ejω)= { 1 ...