Lecture 21: Nonparametric spectral estimation

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Lecture 21Non-parametric spectral estimation

• Svetoslav NikolovØrstedDTU, Building 349

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Spectral estimation in ultrasound
Received signal -
Speed of blood
Transducer freq.
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Power spectrum

• The power density spectrum of a stationary random
  process is the Fourier transform of the
  auto-correlation function

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Periodogram
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Performance

• Bias
• Variance

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Modified periodogram
Segmentation
L independent segments
50 overlap
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DFT as a filter bank
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Frequencyresolution
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f/fs
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Example L1
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Example L2
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Example L 4
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Example L16
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Mini problem

• A random signal is observed for time 0.1 seconds.
  Determine if it is possible to calculate the
  spectrum with a frequency resolution and
  relative precision