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# hw5 - N of x n and what are its FS coeﬃcients(b Using...

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BME 311 PROBLEM SET #5 February 20, 2006 DUE DATE: March 8, 2006 Show work on separate sheets of paper. Include all hand plots, Matlab plots, and Matlab code. 1. [20] O&W 3.28. 2. [10] Consider the function shown in figure P3.28(b). (a) Use Matlab to numerically determine the Fourier series (FS) coefficients for 0 k 5. Compare to the analytical results of problem 1. (b) The Matlab function fft implements the following formula: X [ k ] = N - 1 n =0 x [ n ]e - j 2 π N nk . Use Matlab’s fft function to determine the FS coefficients and compare with the results from part (a). Note that the output of fft must be modified in some way in order to make the comparison. 3. [10] Convergence of the Fourier series: Consider the periodic signal in Example 3.7. Using Matlab, plot at least two periods of the FS expansion of this signal for k = 0, | k | ≤ 1, | k | ≤ 3, | k | ≤ 5, and | k | ≤ 21. 4. [15] O&W 3.31. 5. [15] O&W 3.35. 6. [10] O&W 3.36. 7. [20] O&W 3.40. 8. [15] O&W 3.46(a). 9. [25] Consider the function x [ n ] = cos[ ω 0 n ] + 2 cos[3 ω 0 n ], where ω 0 = 2 π/ 16. (a) What is the fundamental period,
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Unformatted text preview: N , of x [ n ], and what are its FS coeﬃcients? (b) Using Matlab, create several periods of x [ n ] and apply it as an input to f4.m . Plot the input and output signals. (c) Determine the impulse response of f4.m and, from that, determine the frequency response of the system, H (e jkω ), for k = 0 , 1 , 2 , 3. (d) Use the result of part (c) to determine the system output from x [ n ]. Plot several periods of the output, and compare the results to part (b). 10. [15] Consider a continuous-time system with impulse response h ( t ) = e-αt u ( t ), where α > 0, and a periodic input function: x ( t ) = ± 1 , < t < 1 , 1 ≤ t ≤ T, where T = 4. Determine the output of the system by ﬁrst determining the FS representation of the input signal and then determining the frequency response of the system, H ( jω ). Using Matlab, plot at least two periods of the input and output functions for | k | ≤ 21. 1...
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