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9.6.1 Partial Fraction Expansion .....................................................................9−259.6.2 The Inversion Integral............................................................................9−329.6.3 Long Division of Polynomials ................................................................9−369.7 The Transfer Function of Discrete−Time Systems ............................................9−389.8 State Equations for Discrete−Time Systems ......................................................9−459.9 Summary.............................................................................................................9−489.10 Exercises .............................................................................................................9−539.11 Solutions to End−of−Chapter Exercises.............................................................9−55MATLAB ComputingPages 9−35, 9−37, 9−38, 9−41, 9−42, 9−59, 9−61Simulink ModelingPage 9−44Excel PlotsPages 9−35, 9−4410 The DFT and the FFT Algorithm 10−110.1 The Discrete Fourier Transform (DFT) ............................................................10−110.2 Even and Odd Properties of the DFT................................................................10−910.3 Common Properties and Theorems of the DFT ..............................................10−1010.3.1 Linearity ...............................................................................................10−1010.3.2 Time Shift ............................................................................................10−1110.3.3 Frequency Shift....................................................................................10−1210.3.4 Time Convolution ...............................................................................10−1210.3.5 Frequency Convolution .......................................................................10−1310.4 The Sampling Theorem ...................................................................................10−1310.5 Number of Operations Required to Compute the DFT ..................................10−1610.6 The Fast Fourier Transform (FFT)..................................................................10−1710.7 Summary...........................................................................................................10−2810.8 Exercises ...........................................................................................................10−3110.9 Solutions to End−of−Chapter Exercises...........................................................10−33MATLAB ComputingPages 10−5, 10−7, 10−34Excel Analysis ToolPakPages 10−6, 10−811 Analog and Digital Filters11.1 Filter Types and Classifications......................................................................... 11−111.2 Basic Analog Filters........................................................................................... 11−2Signals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fourth EditionCopyright © Orchard Publicationsvii