mae 3113_6

# mae 3113_6 - MAE 3113 3-1 Measurements and Instrumentations...

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School of Mechanical and Aerospace Engineering MAE 3113 3-1 Measurements and Instrumentations Analog to Digital

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School of Mechanical and Aerospace Engineering MAE 3113 3-2 Sample Rate 0 1 2 3 4 5 6 x 10 -3 -6 -4 -2 0 2 4 6 Time (sec) Voltage Lets examine the following cases and see what happens as we increase the sample rate. Consider the following cases, where a waveform with frequency ( f ) of 500 Hz and is sampled at increasing rates ( f s ).
School of Mechanical and Aerospace Engineering MAE 3113 3-3 Sample Rate Result: The input waveform now appears to be DC, or a waveform with a constant value. This will result regardless of when you start the sampling. The only thing that will change is the apparent value of the waveform. Case 1: The sampling frequency matches the frequency of the waveform. f f s = 0 1 2 3 4 5 6 x 10 -3 -6 -4 -2 0 2 4 6

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School of Mechanical and Aerospace Engineering MAE 3113 3-4 Sample Rate Case 2: The sampling frequency is greater then the frequency of the waveform, but less then twice the frequency of the waveform. f f f s 2 0 1 2 3 4 5 6 x 10 -3 -6 -4 -2 0 2 4 6 Result: The input waveform does appear as a varying waveform, however it is at a lower frequency.
School of Mechanical and Aerospace Engineering MAE 3113 3-5 Sampling Theorem and Aliasing According to sampling theorem, an analog signal can be exactly reconstructed from its samples if the sampling rate is at least twice the highest frequency component present in the signal. Otherwise aliasing can occur. Sampling Java Applet Demo: http://www.jhu.edu/~signals/sampling/index.html

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School of Mechanical and Aerospace Engineering MAE 3113 3-6 Sample Rate Case 3: The sampling frequency is twice the frequency of the waveform. Result: The output waveform has the same frequency and amplitude of the input waveform. However, if the sampling is not correctly timed then the signal again appears to be constant. s f f = 2 0 1 2 3 4 5 6 x 10 -3 -6 -4 -2 0 2 4 6
School of Mechanical and Aerospace Engineering MAE 3113 3-7 Sample Rate Case 4: The sampling frequency is twice the frequency of the waveform. Result: Only when the sampling rate is greater then twice the input waveforms frequency, do we obtain a correct discrete representation of the waveform. 0 1 2 3 4 5 6 x 10 -3 -6 -4 -2 0 2 4 6 s f f < 2

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School of Mechanical and Aerospace Engineering MAE 3113 3-8 Sample Rate Recommended Sample Rate: s f f < 10 0 2 4 6 x 10 -3 -6 -4 -2 0 2 4 6 No delay 0 2 4 6 x 10 -3 -6 -4 -2 0 2 4 6 1/4 delay 0 2 4 6 x 10 -3 -6 -4 -2 0 2 4 6 1/2 delay T ime (sec) Voltage 0 2 4 6 x 10 -3 -6 -4 -2 0 2 4 6 T ime (sec) 3/4 delay
and Aerospace Engineering MAE 3113 3-9 Nyquist Frequency The highest frequency that can be resolved is called the Nyquist frequency and is defined by; Any waveform that has a frequency, which is lower, then the Nyquist frequency is accurately sampled. Waveforms above the Nyquist frequency will appear as lower frequencies. 2

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mae 3113_6 - MAE 3113 3-1 Measurements and Instrumentations...

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