CU-Boulder MCEN 3037 - 19R (18 pages)

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19R



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19R

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Pages:
18
School:
University of Colorado at Boulder
Course:
Mcen 3037 - Data Analysis
Data Analysis Documents

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STATIC AND DYNAMIC CHARACTERISTICS OF SIGNALS INPUT sensor transducer Signal A MEASUREMENT SYSTEM Signal B OUTPUT Signal C Signal just associated with transmission of information Important Questions What is the dynamic range of the measurement system What is the frequency response of the measurement system What are the characteristic of the signal from your sensor transducer Are you looking for a static or dynamic response Classification of some basic types of signals based on acquisition representation 1200 Price dollars 1000 800 600 400 200 0 0 1000 2000 Days Ago Reminder How many discrete quantization levels are there in a signal digitized by an 8 bit analog to digital converter 256 How do we analyze signals Magnitude and Phase single frequency Frequency Content Fourier analysis Apply signal processing techniques filtering time averaging Very simple signal analysis may be suitable for some tasks What is the mean value of a signal For discrete data this is simply t2 y y t dt t1 t2 N Area under curve dt t1 Time window y y n 1 N n The average value is a function of the time window select the time window based on measurement plan If you are interested in the AC component of a signal the simple operation of subtracting out the DC component can be useful for analysis Another useful quantity for characterizing the dynamic portion of a signal is the Root Mean Square Value RMS t2 yRMS 1 2 y dt t2 t1 t1 yRMS 1 N N 2 y n n 1 What does this look like Let s look at a mass spring system d2y m 2 ky 0 dt Where does this come from The general solution is y A cos t B sin t How do you find these y C cos t harmonic oscillation k resonance m Using some trig we can C Also write the solution as A2 B 2 B A tan A What s going on here We are splitting light into it s individual frequency components f Low spatial frequency filter Lower spatial frequency filter Block low frequencies Block more low frequencies What is a periodic function f x T f x period If f x and g x are periodic with the



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