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Wdigfiltreview - ECE 421 - Sum 2010 Detailed Solutions -...

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Unformatted text preview: ECE 421 - Sum 2010 Detailed Solutions - Set 1: Digital Filtering 1 1-1. An analog signal x t = e 5 t u t is sampled using a sampling interval T s = : 1 seconds. The digital signal which results can be written in the form x [ m ℄= x mT s = A m u [ m ℄ where A is a constant. Compute A . DETAILED SOLUTION: Use the definition of the digital signal obtained from an analog signal: x [ m ℄= x mT s = x t ¬ ¬ ¬ t = mT s a With x t as given in the problem statement, equation a gives x [ m ℄= e 5 t u t ¬ ¬ ¬ t = mT s = e 5 mT s u mT s = e 5 mT s u [ m ℄ b Using the T s from the problem statement, the exponential in b may be evaluated as follows: e 5 mT s = e 5 m : 1 = e : 5 m = h e : 5 i m c Substitute the result from c into b , obtaining x [ m ℄= h e : 5 i m u [ m ℄ d Numerically evaluating the exponential in d then gives the result x [ m ℄= h e : 5 i m u [ m ℄= : 6065 m u [ m ℄ e From e we therefore see that the value of A for this problem is given by...
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This note was uploaded on 09/07/2010 for the course ECE 421 taught by Professor Hallen during the Summer '08 term at N.C. State.

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Wdigfiltreview - ECE 421 - Sum 2010 Detailed Solutions -...

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