NonParametric Power Spectrum Estimation Methods

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Non-ParametricPower Spectrum Estimation Methods

• Eric Hui
• SYDE 770 Course Project
• November 28, 2002

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Introduction

• Applications of Power Spectrum Estimation (PSE)
• Wiener Filter
• Feature Extraction
• Non-parametric PSE does NOT assume any
  data-generating process or model (e.g.
  autoregressive model).

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Motivation

• Ideal autocorrelation
• Actual autocorrelation
• Limited (finite length of) data due to
• Availability of data
• Assumption of stationary

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Periodogram Method
redefined as
DTFT
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Periodogram Method
N
0
-N
DTFT
DTFT
0
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Good Method?

• Necessary conditions for mean-square convergence
• Asymptotically Unbiased
• Zero Variance

as N ?
as N ?
k
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Evaluation of Methods

• Resolution
• How much blurring effect is there on the power
  spectrum?
• Bias (Asymptotic)
• Does the estimation approach the true value with
  more data (i.e. as N increases)?
• Variance
• Does the amount of deviation from the true value
  depend on the data length (i.e. N)?

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Different PSE Methods

• Periodogram Method
• Apply rectangular window to x(n) to get xN(n).
• Modified Periodogram Method
• Apply non-rectangular window to x(n) to get
  xN(n).
• Bartletts Method
• Average the Periodogram estimate of
  non-overlapping sub-intervals of x(n).
• Welchs Method
• Average the Modified Periodogram estimate of
  overlapping sub-intervals of x(n).
• Blackman-Turkey Method
• Apply non-triangular window to r(x).

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Application Feature Extraction
PSD
linearize
repeat for whole image
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Questions or Comments?