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  Computer Explorations in Discrete-Time Signals and Systemsand Digital Signal Processing Using MATLAB –A Laboratory Manual–  Dr. Mateo AboyOctober 22, 2005  SUMMARY TABLE OF CONTENTS 1 Introduction to Sampling and Aliasing 102 Discrete-Time Signals 183 Discrete-Time Systems and Convolution 254 DTFT, DFT, and FFT 335 Sampling and Aliasing 426 The Z-Transform 527 Digital Filtering 628 Digital Filtering 779 Project: Design of an Automatic Beat Detection Algorithm 9210 Appendix 99 1  CONTENTS 1 Introduction to Sampling and Aliasing 10 1.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.2 Theoretical Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.2.1 Sampling and aliasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.3 Computer Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.3.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.3.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.4 Example MATLAB code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.5 Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 Discrete-Time Signals 18 2.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Theoretical Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.1 Unit Sample Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.2 Unit Step Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.3 Real– and Complex–Valued Exponential Sequences . . . . . . . . . . . . 202  2.2.4 Other Functions and Operations . . . . . . . . . . . . . . . . . . . . . . 212.3 Computer Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4 Example MATLAB code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3 Discrete-Time Systems and Convolution 25 3.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2 Theoretical Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2.1 Development of the Convolution Sum . . . . . . . . . . . . . . . . . . . 273.2.2 Stability and Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3 Computer Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.4 Example MATLAB code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4 DTFT, DFT, and FFT 33 4.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2 Theoretical Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2.2 Zero Padding, Windowing and Other Considerations . . . . . . . . . . . 364.3 Computer Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.3.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.3.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.4 Example MATLAB code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
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