ece 313 hw 6 - 1. 2. Problem 7.19, p. 230. 3. ECE...

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Unformatted text preview: 1. 2. Problem 7.19, p. 230. 3. ECE 313 Fall 2010 Homework 6 – Due Thursday, October 21 Problem 7.14, p. 229. Consider the DT LTI system defined by the input ­output difference equation y [ n ] + y [ n − 1] = x [ n ] − x [ n − 1] . (a) Find the system’s transfer function H ( z) . ȹ π n ȹ (b) Find y [ n ] if the input is x [ n ] = cosȹ ȹ . ȹ 2 Ⱥ € € Problem 7.21, p. 230. € € Suppose we want to implement a DT LTI system having transfer function 1 1 H ( z) = 1 − z −1 + z −2 − z −3 . 2 2 4. 5. (a) Find the system’s input ­output difference equation. € (b) Draw a Direct Form II system implementation. n (c) Find the system output y [ n ] if the input is x [ n ] = 1 + ( −1) . 6. € (d) Find and plot the system’s impulse response h [ n ] . (Hint: You can find the answer by comparing the input ­o€tput difference equation of part (a) and u € the input ­output convolution equation y [ n ] = h [ n ] * x [ n ] . € Let h [ n ] be the impulse response of a DT LTI system. € (a) Show that the system is causal if h [ n ] = 0 for all n < 0 , and that the system is noncausal if h [ n ] ≠ 0 for some n < 0 . ∞ € € (b) Show that the system is stable if ∑ h [ n ] < ∞ , and that the system is € € n = −∞ unstable if ∞ ∑ h[ n] = ∞ . n = −∞ 7. Problem 6.19, p. 194. € € Problems from Textbook ...
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