Chapter 7 Notes - Chapter 7 Sampling, Digital Devices, and...

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1 Chapter 7 Sampling, Digital Devices, and Data Acquisition Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition Introduction ± “Integrating analog electrical transducers with digital data-acquisitions systems is cost effective and commonplace on the factory floor, the testing lab, and even in our homes. There are many advantages to this hybrid arrangement, including the efficient handling and rapid processing of large amounts of data and varying degrees of artificial intelligence by using digital microprocessor systems.” Analog Signal and Discrete Time Series Common Questions: Frequency content of measured signal? Size of time increment? Total sample period? How often should we sample? Figliola, 2000
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2 Notes: ± A continuous dynamic signal can be represented by a fourier series. ± The discrete fourier transform can reconstruct a dynamic signal from a discrete set of data. Sample Rate ± Sample time increment τ f = δ t (seconds) ± Sample Frequency f s = 1/ δ t (hertz) ± The sample rate has a significant effect on our perception and reconstruction of the continuous analog signal in the time domain. Figliola, 2000 f m is the maximum frequency component in a signal. ± Note the decrease in frequency of signal estimated by the slower sampling frequency. ± The sampling theorem states that to reconstruct the frequency content of a measured signal accurately, the sample rate must be more than twice the highest frequency contained in the measured signal. ± Sampling theorem: f s > 2f m ± Then, δ t < 1/(2f m ) should always give accurate DFT frequency determination.
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3 Alias Frequency ± If f s < 2f m , the high frequency content will be falsely represented by a low frequency component. False frequency is called alias frequency and results from discrete sampling of a signal at f s < 2f m ± The alias phenomenon is an inherent consequence of a discrete sampling process. ± Refer to the discussion of folding frequency for more detail in the text. Alias Frequency ± By following sampling theorem f s > 2f m , all aliases are eliminated. ± The concepts apply to complex periodic, aperiodic and non-deterministic that are represented by fourier transform Alias Frequency ± Nyquist frequency: f N = f s /2 = 1/(2 δ t) ± This represents a folding point for the aliasing phenomenon. ± All actual frequency content in the analog signal that is at frequencies above f N will appear as alias frequencies of less than f N ; that is, such frequencies will be folded back and superimposed on the signal at lower frequencies. ± An alias frequency, f a , can be computed from the folding diagram, in which the original frequency axis is folded back over itself at the folding point of f N and its harmonics, mf N , where m = 1, 2, …
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4 Alias Frequency ± For example, as noted by solid arrows in this figure, the frequencies of f = 0.5f N , 1.5f N , 2.5f N ,… will all appear as 0.5f N in the discrete series y(r δ t) Alias Frequency
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This note was uploaded on 11/22/2011 for the course ABE 6031 taught by Professor Burks during the Summer '11 term at University of Florida.

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Chapter 7 Notes - Chapter 7 Sampling, Digital Devices, and...

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