Department of Electrical and Computer Engineering 
                        
                        
           ELEC 442 Discrete-Time Signal Processing  
                   Lab Manual 
                        
                        
              William E. Lynch and Maria Amer 
                        
                    June 2019  
                 
                Table of Contents 
                Submission Instructions .................................................................................................................. 1 
                Lab 1.   Linear Constant Coefficient Difference Equations (LCCDE) ......................................... 2 
                  Objectives ................................................................................................................................... 2 
                  Introduction ................................................................................................................................. 2 
                  LTI System as a Filter ................................................................................................................. 3 
                     The Impulse Response ............................................................................................................ 3 
                     Finite Impulse Response (FIR) Systems ................................................................................. 3 
                     Infinite Impulse Response (IIR) Systems ............................................................................... 4 
                     Solution of an LCCDE Using MATLAB ............................................................................... 4 
                  Lab Problems .............................................................................................................................. 6 
                Lab 2.   The Fourier Transform and the Z-Transform ................................................................. 10 
                  Objectives ................................................................................................................................. 10 
                  Signal Acquisition ..................................................................................................................... 10 
                  The Fourier Transform: The Spectrum of a Signal ................................................................... 11 
                  Lab Problems I .......................................................................................................................... 14 
                  The Z-Transform ....................................................................................................................... 14 
                  Lab Problems II......................................................................................................................... 15 
                  The Frequency Response from the Z-Transform ...................................................................... 18 
                  Lab Problems III ....................................................................................................................... 22 
                Lab 3.   The Sampling Theorem .................................................................................................. 24 
                  Objectives ................................................................................................................................. 24 
                  Sampling Issues ........................................................................................................................ 24 
                  Periodic Sampling ..................................................................................................................... 25 
                  Nyquist Theorem ...................................................................................................................... 27 
                  Reconstruction .......................................................................................................................... 28 
                  Lab Problems ............................................................................................................................ 31 
                Lab 4.   Multirate Digital Signal Processing ............................................................................... 34 
                  Objectives ................................................................................................................................. 34 
                  Key Issues ................................................................................................................................. 34 
                  Downsampling and Decimation ................................................................................................ 35 
                  Upsampling and Interpolation................................................................................................... 39 
                  Sampling Rate Conversion ....................................................................................................... 41 
                  Lab Problems ............................................................................................................................ 42 
                Lab 5.   Signal Restoration and Filter Design ............................................................................. 48 
                  Objectives ................................................................................................................................. 48 
                  Signal Restoration ..................................................................................................................... 48 
                  Objective Quality Measurement ............................................................................................... 48 
                  MATLAB’s Filter Designer tool .............................................................................................. 49 
                  Lab Problems ............................................................................................................................ 49 
                References ..................................................................................................................................... 53 
                Acknowledgment .......................................................................................................................... 53 
                 
                 
                                                                                                 
                 Submission Instructions 
                     •   For each lab problem, create MATLAB script files. 
                     •   Include your name and ID as comments in each script file.  
                     •   For each lab problem, submit as part of the written lab report, the script file and any 
                         required plots. 
                     •   It is suggested to save the script file under meaningful name, such as Lab1_Prob1.m. 
                                                   
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