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A FEW IMPORTANT NOTES The following practical tutorial is designed to give the student a more practical, or hands-on, approach to the theoretical engineering course. This method allows the student to explore the concepts that was given in the reference book as well as to reinforce the techniques that was taught. For this practical a personal computer is a necessity, as computer programs will have to be written. The computer language or simulation tools to use are solely the student's choice. The following list will give the student an idea of what computer simulation tools are available on the market. Some of them are free and others are expensive. Tools Type of license Platform Matlab Commercial PC/Unix/M ac - Matlab (Student version) Commercial PC/Unix/M ac Most Universities (±R300) (RAU) Mathcad Commercial PC/Mac - SciLab - matrixbased scientific software package GNU Unix Internet - Octave - MATLAB lookalike GNU Unix Internet - ftp.che.utexas.edu/pub/octave R-Lab - MATLABlike matrix-oriented programming language GNU Unix Internet - evans.ee.adfa.oz.au /pub/RLaB SciLab, Octave and R-Lab are available on the internet for the Linux version of Unix. Normal C, Pascal or Basic could also be used. PRACTICUM 1 Generate the following signals with a computer program: 1.1 5 Hz sinusoidal 1.2 25 Hz sinusoidal 1.3 5 Hz + 25 Hz sinusoidal 1.4 Random noise in the amplitude interval (0,0 1,0) 1.5 Random noise in 1,4 but with a zero mean Each signal must contain one thousand (1 000) data-points per second. Generate the signals for a time-span of 2 s but only plot the first 0,5-second of data. (Hand in the plots as well as the computer code) 2 Write a computer program to simulate an Analog to Digital converter. The A/D must have the following specifications: Full-Range input of ± x Volt y Bit resolution z Sampling frequency 3 Use a summation of 5 Hz, 10 Hz and 15 Hz sinusoidal signals to represent an analogue signal. Use 1 000 data points per second. Scale the signal to an amplitude of ±12. To digitise this signal use the model of the A/D converter with the following specifications and plot the input and digitised signal on top of each other for the first 0,2 seconds. (Hand in the plots as well as the computer code). ±12 Volt full-range input, 12 Bit resolution, 100 Hz sampling frequency. ±12Volt full-range input, 2 Bit resolution, 200 Hz sampling frequency. 4 Use a 15 Hz sinusoidal signal to represent an analogue signal. Use 1 000 data points per second. Scale the signal to an amplitude of ±12. To digitise this signal, use the model of the A/D converter with the following specifications and plot the input and digitised signal on top of each other for the first 0,5 seconds: ±12 Volt full-range input, 12 Bit resolution, 20 Hz sampling frequency. What happened in this digitisation process? (Hand in the plots as well as the computer code) 5 Write a computer program to determine the DFT or FFT of a signal x = {4; 3; 5, 6; 2; 3; 5}. [Test with the following: DFT({1; 0; 0; 1})={2,1+j; 0,1-j}] (Hand in the computer code as well) 6 Write a computer program to determine the inverse DFT or inverse FFT of a signal Y1 = {20,0000; -1,1180 + 7,6942j; 1,1180 – 1,8164j; 1,1180 + 1,8164j; -1,1180 – 7,6942j}. [Test with the following: IDFT({3;j;0;-j})={1;0;1;1}] (Hand in the computer code as well)

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function [ UD ] = ADConvert( t, UA,range, resolution, sampleRate )
%UNTITLED Summary of this function goes here
%   Detailed explanation goes here

    if (size(t) == size(UA))
       OneBitVoltage = 2 * range /(2^resolution - 1) % calculate the voltage of one bit
       overValue = find(UA < -range) % Check if there is a value outside of negative range
       if ~isempty(overValue)
            UA(overValue) = -range
       end
       clear overValue
       overValue = find(UA > range) % Check if there is a value outside of range
       if ~isempty(overValue)
            UA(overValue) = range
       end      
       samplingTime = 0
       k = size(t)
       for i = 1:k(2)
            if (t(i) >= samplingTime)
                UD(i) = round(UA(i) / OneBitVoltage) * OneBitVoltage % Quantizicide digital value
                samplingTime = samplingTime + 1 / sampleRate
            else
                UD(i) = UD(i - 1)
            end
       end
    end
end...
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