1. UTN synthetic noise generator M. Hueller LTPDA meeting, Barcelona 26/06/2007

2. 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. 3 The approach (1) x(t) is the output of a filter, with transfer function H(  ), with a white noise  (t) at input, with PSD=S 0 Assuming that the transfer function H(  ) has the form then the process x(t) can be seen as the process x(t) is equivalent to N p correlated processes

4. 4 The approach (2) Once defined A powerful recursive formula One can calculate cross correlation of the innovation processes And for the starting values

5. 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 N p uncorrelated random variables, transformed according to: Eventually, add up the contribution from all correlated processes:

6. 6 Matlab implementation (2) The base changing matrix A kj 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. 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. 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. 9 Some results: noise Poles: 10 mHz

10. 10 Some results: time series Poles: 10 mHz

11. 11 Some results: noise Poles: 2 mHz, Q = 3300; 0.5 Hz, Q=10000; 1Hz;2 Hz

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

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

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

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