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 PSD=S0 • 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, Q=10000; 1Hz;2 Hz

12. Some results: time series Poles: 2 mHz, Q = 3300; 0.5 Hz, Q=10000; 1Hz;2 Hz

13. Some results: noise Poles: 10 mHz, Q = 3000; 1 Hz, Q=10000; 1.3 Hz, Q=1000;

14. Some results: noise Poles: 10 mHz, Q = 3000; 1 Hz, Q=10000; 1.3 Hz, Q=1000;

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