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RecitationMATLAB

# RecitationMATLAB - y n = âŽ âŽ¨ âŽ© 1 3 sin(2 Ï€ Ã— 60 n/f...

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Rensselaer Electrical, Computer, and Systems Engineering Department ECSE 4500 Probability for Engineering Applications MATLAB Recitation Tuesday February 16, 2010 1. Before using MATLAB as a tool for various functions of interest in probability, we review a brief list of common commands: size , length , plot , axis , hold on , hold o ff and for ... end . Apart from these we also review how arrays and matrices are declared and used in MATLAB. 2. Next we look at the 3 M- fi les available on the course LMS page. These include DeterFreq.m , RelFreq.m , and RelativeFrequencies.m . Please run the code for several di ff erent parameter values and explain the results. 3. (Convolution and Fourier Transform) Consider the following two discrete-time signals: x [ n ] = 0 . 6 sin (2 π × 50 n/f s ) + 1 . 5 sin (2 π × 70 n/f s ) + 0 . 8 sin (2 π × 90 n/f s ) +1 . 2 sin (2 π × 110 n/f s ) + 0 . 7 sin (2 π × 130 n/f s ) , n = 1 , 2 , ..., 100 . 0 , otherwise.
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Unformatted text preview: y [ n ] = âŽ§ âŽ¨ âŽ© 1 . 3 sin (2 Ï€ Ã— 60 n/f s ) + 0 . 3 sin (2 Ï€ Ã— 80 n/f s ) + 1 . 4 sin (2 Ï€ Ã— 100 n/f s ) +0 . 6 sin (2 Ï€ Ã— 120 n/f s ) + 1 . 5 sin (2 Ï€ Ã— 140 n/f s ) , n = 1 , 2 , ..., 80 . , otherwise. where f s = 1000 . Please do the following using MATLAB: a. Compute the convolution w of the two sequences x and y . b. Compute the 179-point fast Fourier transform X of the sequence x . c. Compute the 179-point fast Fourier transform Y of the sequence y . d. Calculate the product Z of X and Y (using element-by-element multiplication). e. Compute the inverse Fourier transform z of Z . f. Plot the sequences w and z in the same f gure. Please verify w = z and explain why. (Hint: The following commands may be useful here: conv , f t , i f t ) 1...
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