Homework5_Sol

Homework5_Sol - MCE311 Homework # 4 Due on Wed Nov 30th,...

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MCE311 Homework # 4 Due on Wed Nov 30 th , 2011 Question 1 (5.16): A function has the form ݂ሺݐሻ ൌ 3 sin 10ߨݐ ൅ 5 cos 40ߨݐ and is sampled at a rate of 30 samples per second. What false alias frequency(ies) would you expect in the discrete data? Solution: ݂ሺݐሻൌ3sinሺ2ߨ 5 ሻݐ൅5cosሺ2ߨ 20 ሻݐ The function has frequencies of 5 and 20 Hz. The minimum sampling rate would then be 40 Hz to avoid aliasing. Sampling at 30 Hz would not produce aliases for the 5 Hz signal but would for the 20 Hz signal. The alias frequency can be evaluated using the folding diagram in Section 5.1. f a =30-20=10Hz Or we can use the folding diagram: f N = 30/2 = 15 Hz. f/f N = 20/15 = 1.3333. From the folding diagram, f a /f N = 0.666. Thus f a = 0.666 15 = 10 Hz. This is the difference between the sampling rate and the signal frequency. Question 2 (5.17) : A function has the form ݂ሺݐሻ ൌ 6 sin 20ߨݐ ൅ 5 cos 30ߨݐ and is sampled at a rate of 50 samples per second. What false alias frequency(ies) would you expect in the
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Homework5_Sol - MCE311 Homework # 4 Due on Wed Nov 30th,...

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