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Simulation of Discrete Systems Using MATLAB: Sinewave Generator and Z-Transform Analysis

This document outlines the methods for simulating discrete systems using MATLAB, particularly focusing on the Sinewave Generator and Z-Transform applications. It emphasizes the importance of correcting common bugs found in MATLAB 4.0 and provides a comprehensive guide for users to set up their environments. Detailed instructions are provided for creating M-files, generating sinewaves, and verifying Nyquist's theorem with sample frequency considerations. Additional exercises include computing output sequences and elliptical plots for hands-on practice in discrete system simulation.

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Simulation of Discrete Systems Using MATLAB: Sinewave Generator and Z-Transform Analysis

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  1. Unit 2 Discrete System 中華技術學院電子系 蔡樸生 副教授 林盈灝 副教授

  2. PROGRAM M-File • The method for custom user with common purpose for simulation is strongly recommended. • There are some bugs in Matlab 4.0 and be updated 1. Using ‘MD’ to set up ‘c:\matlab\simu’ 2. Update your ‘*.bat ’ 3. When you save M-file, Matlab4.0 notes the file name ~.txt automatically, rename ~.txt to ~.m. Matlab File New m-file Edit Save Run

  3. Sinewave Generator • For :Repeat statements a specific number of times. for i = 1:n, for j = 1:n, A( i , j ) = 1/(i + j - 1); end end • Sinewave Generator for k=1:100, x(k)=(k*2*pi)/100; y(k)=sin(x(k)); end plot(x,y,’y’);

  4. Digital Oscillator – Sinewave (I) • Principle: Continuous Function Discrete Function • Z Transform :

  5. Digital Oscillator – Sinewave (II) Impulse Function

  6. Digital Oscillator – Sinewave (II) • Formula: • Design Spec. :

  7. Matlab Program clear; a=1.62;b=-1;c=0.59;dt=0.0001; y(1)=c;y(2)=a*y(1); t(1)=1*dt;t(2)=2*dt; for k=3:200 t(k)=dt*k; y(k)=a*y(k-1)+b*y(k-2); end plot(t,y); grid;

  8. Homework ( I ) • Plot the diagram verify the Nyquist theorem (sampling theorem) by difference equation. Signal frequency is 10Hz. • The sampling frequency be at least twice the highest frequency in the signal for perfect reconstruction (2) Compute the output sequence of difference equation

  9. (3) Elliptical plot (4) Curve Equation

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