Qualitative Analysis of a Zero Autocorrelation Noise Generator

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Qualitative Analysis of a Zero Autocorrelation
Noise Generator

• by Donald Hersey
• Northeastern Illinois University
• April 20, 2007

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Qualitative Analysis of a Zero Autocorrelation
Noise Generator

• The purpose of this project is to create a noise
  generator (for analyzing digital filters).
• Depending on the test being done the noise must
  meet certain requirements Whiteness and Zero
  Autocorrelation.
• After creation, Analysis is needed to verify
  these qualities exist in the noise generator.

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What are Digital Filters?

• Digital Filters affect the amplitude of the
  specific frequencies that make up a signal
• These changes are called the Frequency Response
• The frequency response describes how a Digital
  Filter affects a signal

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What are Digital Filters? Cont.

• Applying a Digital Filter affects the
  interference that is a part of every input signal
• This is called the Noise Amplification Figure
• The theoretical Noise Amplification Figure can be
  calculated if the interference has no correlation

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DF Example - Stereo System

• High Quality stereos contain Tweeter, Midrange
  and Woofer speakers.
• Tweeters reproduce High Frequency signals
• Midrange speakers reproduce Medium Frequency
  signals
• Woofers reproduce Low Frequency signals

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Digital Filters For Speakers

• Three Digital Filters are used to separate the
  song into the three ranges
• Each speaker receives only the frequencies that
  it can recreate as sound

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Tweeter - High Pass Filter
Frequency Response
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Midrange - Band Pass Filter
Frequency Response
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Woofer Low Pass Filter
Frequency Response
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Other Examples of Digital Filters

• Curve fitting
• Smoothing
• Missing data interpolation
• Numerical Integration
• Numerical Differentiation

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Testing Digital Filters

• Want to verify Filters Frequency Response (Does
  the DF do what we want?)
• Need to verify response at all frequencies.

How do we do this?
WHITE NOISE
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Testing Digital Filters

• Want to verify Filters Noise Amplification
  Figure (Does the DF do what we want cleanly?)
• NAF model applies to uncorrelated input

What makes this?
ZERO AUTOCORELLATION NOISE
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What is Noise?

• The output of a noise signal can only be
  predicted in terms of statistical likelihood(it
  does not correspond to a function).
• White noise contains equal amounts of every
  frequency and phase.
• Zero autocorrelation noise is non repetitive
  Future output does not mimic prior output

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(No Transcript)
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Where does our noise come from?
Our Noise is created by the NC302L Zener Noise
Diode produced by the Noise/Com company
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How does a diode make noise?

• Zener (Avalanche breakdown) Noise
• Electrons are particles, therefore conduction is
  marked by discrete events of differing magnitudes
• Near the breakdown voltage reverse conduction
  happens sporadically due to weaknesses in the
  diodes construction
• These two processes are random and create
  broadband noise

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Microsoft Excel Pseudorandom Number Generator

• Easily acquirable source of digital numbers
• Not actually random
• Useful to condition true noise
• "Anyone who uses arithmetic methods to produce
  random numbers is in a state of sin." John von
  Neumann

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Noise Generator Tests

• White Noise Test
• Spectrum Analysis using the Fourier Transform
• Fourier Transform graphs noise signal in terms of
  component frequencies
• Tested with Analog Devices ADC_Analyzer software
• FIPS PUB 140-2 Tests
• From the Information Technology Laboratory at the
  National Institute of Standards and Technology
• Describes statistical tests of autocorrelation
  for random number generators
• Tests implemented with C program

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FIPS PUB 140-2 Tests

• Monobit
• Count the number of 1s in a 20,000 bit stream.
• Denote this quantity by X. Pass if 9,725 10,275.
• Poker
• Divide 20,000 bits into 5,000 consecutive
  nibbles, count the number of occurrences of the
  16 possible patterns (0000, 0001, 0010) in an
  array Fn
• X(16/5000)(F02F1 2F15 2)- 5000
• Pass if 2.16

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FIPS PUB 140-2 Tests

• Short Runs
• Store the length of each run
• Do the number of runs of each length conform to
  their statistical likelihood?
• Long Runs
• Test is failed if there are more than 25
  continuous 1s or 0s

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FFT Results

• Broadband white noise from 5 Megahertz to at
  least 50 Megahertz

• Pass!

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Autocorrelation Results

• Raw Sample
• Monobit Fail
• Poker Fail
• Short Runs Fail
• Long runs Pass

• Pseudorandom Sample
• Monobit Fail
• Poker Fail
• Short Runs Fail
• Long runs Pass

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Autocorrelation Results

• Post Processing Sample
• (Raw Noise Sample Pseudorandom) Modulo 65535

• Monobit Pass
• Poker Pass
• Short Runs Fail
• Long runs Pass

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Conclusions

• The noise generator is ready for Frequency
  Response tests in the 5 Megahertz to 50Megahertz
  band.
• Further post-processing research and development
  needed to determine suitability for Noise
  Amplification Figure tests.

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Qualitative Analysis of a Zero Autocorrelation
Noise Generator

• For more information and these slides visit
• http//DigitalFilters.blogspot.com