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# hw1 - (b Are these signals periodic If so determine the...

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BME 311 PROBLEM SET #1 January 11, 2006 DUE DATE: January 18, 2006 Show work on separate sheets of paper. Include all hand plots, Matlab plots, and Matlab code. 1. [10] Consider the following two discrete-time signals: x [ n ] = 3 sin 2 π n 10 y [ n ] = sin 2 π n 20 0 n 10 0 otherwise . (a) Plot these signals in Matlab. Label all axes and give the plot a title. (b) Are these signals periodic? If so, determine the period. (c) Are these finite energy or finite power signals? If finite power, determine P , and if finite energy, determine E and P . 2. [10] Consider the following two continuous-time signals: x ( t ) = 3 sin 2 π t 10 y ( t ) = sin 2 π t 20 0 t 10 0 otherwise . (a) Plot these signals in Matlab using at least two different time increments, Δ t . Label all axes and give the plot a title.
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Unformatted text preview: (b) Are these signals periodic? If so, determine the period. (c) Are these ﬁnite energy or ﬁnite power signals? If ﬁnite power, determine P ∞ , and if ﬁnite energy, determine E ∞ and P ∞ . Determine these values both analytically and numerically. For numerical integration, use the approximation Z f ( t )d t ≈ X k f ( k Δ t )Δ t, and try at least two diﬀerent values of Δ t . 3. [10] Oppenheim and Wilsky (O&W), problem 1.21. 4. [10] O&W, 1.22. 5. [15] O&W, 1.27. 6. [15] O&W, 1.34. 7. [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. 8. [15] O&W, 1.44(a). 1...
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