hw2 - x = [1,1,1,0,0,0,0,0,0,0,0] and input time ni = 0:10...

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BME 311 PROBLEM SET #2 January 18, 2006 DUE DATE: January 25, 2006 Show work on separate sheets of paper. Include all hand plots, Matlab plots, and Matlab code. 1. [15] Using the approximation δ Δ ( t ) = 1 Δ rect ( t Δ ) as Δ 0, show that δ (2 t ) = 1 2 δ ( t ) and u ( t ) = Z t -∞ δ ( τ ) d τ. 3. [20] Download the three functions f1.m , f2.m , and f3.m from the CTools web site. Each of these functions can be called as follows: [y,no] = f1(x,ni); where x is a vector representing the discrete-time (DT) input x [ n ], y is the system output y [ n ], ni is the input time vector ( e.g. , ni = 1:10 ), and no is the output time vector. For each of these systems: (a) Choose sample inputs to test if the system is linear. (b) Choose sample inputs to test if the system is time-invariant. (c) Determine and plot the impulse response. Label all axes and title the plot. (d) Determine and plot the output for the input signal
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Unformatted text preview: x = [1,1,1,0,0,0,0,0,0,0,0] and input time ni = 0:10 . Label all axes and title the plot. 4. [15] O&W, 1.41. 5. [15] O&W, 1.43. 6. [15] O&W, 1.44(a). 7. [20] Use the Matlab function conv to determine the convolution of the following DT signals. Plot the results for each, and label all axes and title the plots. Pay attention to the time axis! (a) x [ n ] = h [ n ] = ± 1 , n = 0 , 1 , 2 , otherwise . (b) x [ n ] = ± 1 , n = 0 , 1 , 2 , otherwise and h [ n ] = ± n, n = 0 , 1 , 2 , otherwise . (c) x [ n ] = ± 1 , n = 0 , 1 , 2 , otherwise and h [ n ] = ± . 5 n , ≤ n ≤ 5 , otherwise . (d) x [ n ] = ± 1 , n = 0 , 1 , 2 , otherwise and h [ n ] = ± . 5 | n | ,-5 ≤ n ≤ 5 , otherwise . 8. [15] O&W, 2.21. 9. [15] O&W, 2.26. 1...
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This note was uploaded on 04/30/2008 for the course BIOMEDE 311 taught by Professor Steel during the Winter '06 term at University of Michigan.

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