UTN synthetic noise generator

1
UTN synthetic noise generator

• M. Hueller
• LTPDA meeting, Barcelona 26/06/2007

2
Purpose

• Simulate noise data with given continuous
  spectrum
• Choose between
• input the model parameters (developing and
  modeling)
• fit experimental data
• Use as a tool for system identification data
  simulation

3
The approach (1)

• x(t) is the output of a filter, with transfer
  function H(w), with a white noise e(t) at input,
  with PSDS0

• Assuming that the transfer function H(w) has the
  form

• then the process x(t) can be seen as

• the process x(t) is equivalent to Np correlated
  processes

4
The approach (2)

• A powerful recursive formula

• Once defined

• One can calculate cross correlation of the
  innovation processes

• And for the starting values

5
Matlab implementation (1)

• Vector of starting values, with the given
  statistics
• Propagate through time evolution, adding
  contributions from innovation processes
• Innovations are evaluated starting from Np
  uncorrelated random variables, transformed
  according to
• Eventually, add up the contribution from all
  correlated processes

6
Matlab implementation (2)

• The base changing matrix Akj contains the
  eigenvectors of the cross-correlation matrix
  (diagonalization)
• Additionally, a phase factor must be applied to
  each eigenvector, to allow the sum of all the Np
  contribution to be real
• ?
• Force the first element of each eigenvector to be
  real

7

• Major problems solved, minor remaining
• Associated with the initial rotation of the
  eigenvalues
• Visible as a residual imaginary part
• Arising with complex poles too near or too far in
  frequency
• Converted into AOs class
• Parameters passed with a plist
• Spectral data to be fitted passed through an AO
  containing fsdata
• Merged into the LTPDA GUI
• Problem passing the poles list (a Nx2 matrix),
  possible workaround through some class (miir?)

8
Input parameters available features

• LP filters
• HP filters
• f -2 noise, by a LP filter with roll-off at very
  low frequency
• Mechanical resonances
• Mechanical forcing lines (not yet implemented)

9
Some results noise

• Poles
• 10 mHz

10
Some results time series

• Poles
• 10 mHz

11
Some results noise

• Poles
• 2 mHz, Q 3300
• 0.5 Hz, Q10000
• 1Hz2 Hz

12
Some results time series

• Poles
• 2 mHz, Q 3300
• 0.5 Hz, Q10000
• 1Hz2 Hz

13
Some results noise

• Poles
• 10 mHz, Q 3000
• 1 Hz, Q10000
• 1.3 Hz, Q1000

14
Some results noise

• Poles
• 10 mHz, Q 3000
• 1 Hz, Q10000
• 1.3 Hz, Q1000

15

• What comes next
• Get the fitting features to work
• Compare with AEI noise generator
• Use it as the tools for system identification