in JMPs Time Series Analysis Platform Jerry Fish President, - - PowerPoint PPT Presentation

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A JMP Script to Enhance Spectral Density Analysis in JMPs Time Series Analysis Platform Jerry Fish President, Experistats LLC Footer Text 8/15/2014 1 A Quick Intro on Fourier Transforms Fourier Transform fits a number of sine waves

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SLIDE 1

A JMP Script to Enhance Spectral Density Analysis in JMP’s Time Series Analysis Platform

Jerry Fish President, Experistats LLC

8/15/2014 1 Footer Text

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SLIDE 2

A Quick Intro on Fourier Transforms

  • Fourier Transform fits a number of sine waves to a

time-based signal.

  • Each sine wave has an associated Frequency, Amplitude, and Phase
  • Amplitudes plotted against Frequency are called a

Frequency Spectrum

8/15/2014 Footer Text 2

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SLIDE 3

A Quick Intro on Fourier Transforms

8/15/2014 Footer Text 3

𝑔 𝑒 = 𝐡 + πΆπ‘œsin(π‘œπ‘’ βˆ’ πœ’π‘œ)

∞ π‘œ=1

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SLIDE 4

Discrete Sampling Effects

  • A Discrete Fourier Series operates on a Discrete Time

Series

  • Discrete Time Series Parameters
  • Sampling Interval (or Sampling Frequency)
  • Total Number of Sampled Points

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Sample 17 βˆ†t=0.04 sec Sample 1 Sample 2

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SLIDE 5

Effect of Sampling Frequency

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18 samples per cycle

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SLIDE 6

Effect of Sampling Frequency

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18 samples per cycle 3 samples per cycle

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SLIDE 7

Effect of Sampling Frequency

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18 samples per cycle 3 samples per cycle 2 samples per cycle

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SLIDE 8

Effect of Sampling Frequency

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18 samples per cycle 3 samples per cycle 2 samples per cycle 1.33 samples per cycle

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SLIDE 9

Discrete Sampling Effects – Nyquist Freq

  • The maximum frequency that can be accurately fit

to the sampled data is the Nyquist Frequency

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𝑔𝑛𝑏𝑦 = π‘”π‘‚π‘§π‘Ÿπ‘£π‘—π‘‘π‘’ = 1 2βˆ†π‘’

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SLIDE 10

Discrete Sampling Effects – Nlines

  • A discrete frequency spectrum has a finite number
  • f frequency β€œlines”, depending on the sample size.

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π‘‚π‘šπ‘—π‘œπ‘“π‘‘ = 𝑂 2

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SLIDE 11

Discrete Sampling Effects – Frequency Resolution

  • Frequency Resolution is the distance between

spectral lines

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𝑔𝑠𝑓𝑑 = 𝑔𝑛𝑏𝑦 π‘‚π‘šπ‘—π‘œπ‘“π‘‘ = 1/(2βˆ†π‘’) 𝑂/2 = 1 π‘‚βˆ†π‘’

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SLIDE 12

Discrete Sampling Effects – Summary

8/15/2014 Footer Text 12

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SLIDE 13

What’s an FFT

  • Fast Fourier Transform
  • Very fast software algorithm for computing sine wave amplitudes and

frequencies.

  • Limited to sample sizes that are powers of 2 (32, 64, 128, …)
  • This limits spectral lines to 16, 32, 64, …
  • JMP does not use FFT.
  • No limits on sample size
  • Frequency Analysis Script uses JMP methods

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SLIDE 14

The Frequency Analysis Script

  • A live demo of the script.
  • See submitted paper for more information.

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SLIDE 15

Future Script Features

  • Amplitude Axis Options
  • A-Weighting Function
  • Coherence Function
  • Power Between Cursors
  • Periodogram
  • Additional Windowing Options
  • Save data to table
  • Collect data from external instruments
  • Add an β€œAbout” Button
  • Use Column Names on Plots

8/15/2014 Footer Text 15

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SLIDE 16

About the Author

  • Jerry Fish is owner and President of Experistats LLC.

He is a trained Lean Six Sigma Black Belt, and has many years of experience in statistics and DOE while working for Caterpillar Tractor, Cummins Engine, GE Aircraft Engines, and Lexmark

  • International. He and his wife live in Lexington, KY.
  • Contact Info:

Jerry Fish Experistats LLC experistats@gmail.com 859-433-6231

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