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Wdigfiltreview - ECE 421 Sum 2010 Detailed Solutions Set 1...

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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 0 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 0 1 e 0 5 m e 0 5 m c Substitute the result from c into b , obtaining x m e 0 5 m u m d Numerically evaluating the exponential in d then gives the result x m e 0 5 m u m 0 6065 m u m e From e we therefore see that the value of A for this problem is given by A 0 6065 f
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ECE 421 - Sum 2010 Detailed Solutions - Set 1: Digital Filtering 2 1-8. An FIR digital filter has the impulse response h m 0 9 m u m u m 4 . The filter
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