1. Digital Measurements AOE 3054 Lowe 3.14.2011 Credits: Some excerpts developed by Devenport and Edwards, extracted from the course manual. 1

2. Announcements Report 2 - 1st submission is due this week LabVIEW and Digital Measurements Instrumentation Sessions in Rm 26 this week. – Bring your tablet – Make sure you have NI-DAQmx installed: http://joule.ni.com/nidu/cds/view/p/id/2214/lang/en 2

3. Sampling Measuring a signal at a well known time. Goal: Obtain the appropriate amount of information to represent the original signal with the samples Requires temporal and vertical resolution 3

4. Temporal resolution Sampling the signal quickly enough to capture the frequency content. Nyquist frequency: The maximum frequency which is resolved by a given sampling rate: Sampling rate must exceed the Nyquist frequency 4

5. Aliasing Energy in high frequencies sampled at low frequencies can look like low frequency energy. Solutions: – Sample at higher frequencies – Install an anti-aliasing filter before data acquisition. 5

6. Temporal resolution The Nyquist-Shannon Sampling Theorem guarantees that if you sample your signal at a frequency greater than twice the largest frequencies, you may perfectly reconstruct the original signals from the samples. – Caveat: Requires an infinite number of samples – In practice: The sampling theorem still works well in practice, but Signals always contain some aliased information Also a rule of thumb is sample at 2.56 times the greatest expected frequencies 6

7. Vertical resolution Integral to the ‘digitization’ of a signal. Digitized signals are represented by bits in the computer – A bit is a single binary switch (0 or 1) A quantum of information – Let’s sample our earlier signal at 1 bit resolution: 7

8. Analog signalPerfect vertical sampling1 bit sampling (blue) Amplitude resolution require more bits 8

9. 9 2 bit sampling

10. Resolution in binary data 8 bit resolution is common in high frequency applications (digital oscilloscopes) 12, 14, and 16 bit resolution is common in basic systems Systems up to 24bits are available (maybe higher…) 10

11. Examples: 4 bit binary to integer conversion 0101 1001 1111 11

12. Examples: Signed 4 bit binary to integer conversion 0101 1001 1111 12

13. The “LSB” Least-significant bit: Value of the bit at the far right relative to the total number of digital states – Total number of possibilities: 2 N, where N is the resolution of the device in bits. – The LSB is 1/ 2 N, 000….0001 The LSB defines the resolution of the instrument. – Take a 4bit DAQ operated over a range of 1V, resolution in voltage is 13

14. Signal-to-noise ratio 14