Phase Shift Between two signals with different unknown frequencies

Question

    Time    Heave   Trim
40.228  -4.057  0.016
40.238  -3.253  0.182
40.248  -3.084  0.12
40.257  -2.957  0.161
40.267  -2.28   0.245
40.277  -2.66   -0.047
40.287  -1.899  0.265
40.297  -1.687  0.141
40.307  -1.349  0.141
40.317  -1.433  -0.026
40.327  -0.46   0.161
40.337  -0.333  0.12
40.347  -0.121  0.057
40.356  0.556   0.203
40.366  0.26    -0.047
40.376  0.26    -0.13
40.386  0.725   -0.067
40.396  1.191   -0.005
40.406  1.021   -0.088
40.416  1.445   -0.005
40.426  1.614   -0.067
40.436  1.529   -0.067
40.446  1.656   -0.109
40.455  1.614   -0.088
40.465  1.233   -0.275
40.475  1.402   -0.171
40.485  1.318   -0.275
40.495  1.825   -0.026
40.505  0.767   -0.358
40.515  0.471   -0.462
40.525  0.514   -0.317
40.535  0.048   -0.421
40.545  0.006   -0.379
40.554  0.387   -0.088
40.564  -0.502  -0.338
40.574  -0.925  -0.358
40.584  -1.306  -0.338
40.594  -1.56   -0.379
40.604  -2.872  -0.608
40.614  -2.534  -0.4
40.624  -3.211  -0.442
40.634  -3.126  -0.379
40.644  -3.422  -0.296
40.653  -3.718  -0.338
40.663  -4.015  -0.254
40.673  -4.65   -0.317
40.683  -4.988  -0.4
40.693  -4.269  0.037
40.703  -5.242  -0.254
40.713  -5.538  -0.275
40.723  -5.581  -0.213
40.733  -5.708  -0.067
40.743  -6.3    -0.296
40.752  -5.919  -0.15
40.762  -6.173  -0.15
40.772  -6.385  -0.15
40.782  -6.3    -0.067
40.792  -6.3    -0.109
40.802  -6.215  -0.067
40.812  -6.3    -0.067
40.822  -6.215  -0.026
40.832  -5.792  0.016
40.842  -5.919  -0.047
40.851  -5.2    0.099
40.861  -5.538  -0.005
40.871  -5.03   0.12
40.881  -4.734  0.078
40.891  -4.396  0.141
40.901  -4.353  0.057
40.911  -4.015  0.099
40.921  -3.338  0.224
40.931  -3.422  0.037
40.941  -2.787  0.182
40.95   -2.576  0.037
40.96   -2.364  0.12
40.97   -1.772  0.182
40.98   -2.026  -0.005
40.99   -1.433  0.057
41  -0.798  0.141
41.01   -0.798  0.12
41.02   -0.756  -0.088
41.03   -0.333  -0.088
41.04   0.344   0.141
41.05   -0.037  -0.067
41.059  1.064   0.224
41.069  0.598   0.037
41.079  0.175   -0.213
41.089  1.148   0.161
41.099  0.429   -0.171
41.109  0.006   -0.4
41.119  1.064   -0.005
41.129  0.725   -0.13
41.139  0.217   -0.317
41.149  -0.206  -0.421
41.158  0.006   -0.338
41.168  -0.248  -0.4
41.178  -0.671  -0.442
41.188  -0.841  -0.483
41.198  -0.925  -0.421
41.208  -0.248  -0.026
41.218  -0.756  -0.213
41.228  -1.772  -0.358
41.238  -2.195  -0.442
41.248  -2.237  -0.317
41.257  -2.407  -0.254
41.267  -3.38   -0.546
41.277  -3.211  -0.358
41.287  -3.507  -0.358
41.297  -4.226  -0.462
41.307  -4.099  -0.338
41.317  -4.311  -0.338
41.327  -4.861  -0.483
41.337  -4.988  -0.317
41.347  -5.03   -0.254
41.356  -4.438  0.078
41.366  -5.496  -0.275
41.376  -5.369  -0.192
41.386  -5.708  -0.192
41.396  -5.411  -0.067
41.406  -5.496  -0.13
41.416  -5.496  -0.026
41.426  -5.708  -0.13
41.436  -5.75   -0.13
41.446  -5.496  -0.13
41.455  -5.411  -0.026
41.465  -5.284  -0.005
41.475  -5.115  -0.005
41.485  -4.607  0.182
41.495  -4.607  0.078
41.505  -4.48   0.057
41.515  -4.057  0.12
41.525  -4.057  0.037
41.535  -3.507  0.078
41.545  -3.422  0.037
41.554  -2.703  0.245
41.564  -2.449  0.224
41.574  -2.026  0.141
41.584  -1.899  0.182
41.594  -1.179  0.265
41.604  -1.729  -0.005
41.614  -1.01   0.078
41.624  -0.46   0.161
41.634  -0.375  0.078
41.644  0.344   0.265
41.653  0.133   -0.005
41.663  0.048   -0.067
41.673  0.81    0.057
41.683  0.64    -0.047
41.693  0.979   -0.067
41.703  0.767   -0.13
41.713  0.894   -0.15
41.723  1.191   -0.109
41.733  1.402   -0.13
41.743  1.021   -0.275
41.752  1.402   -0.192
41.762  0.979   -0.254
41.772  1.106   -0.213
41.782  0.767   -0.317
41.792  0.344   -0.4
41.802  0.556   -0.275
41.812  0.26    -0.254
41.822  -0.037  -0.338
41.832  -0.418  -0.421
41.842  -0.46   -0.317
41.851  -0.121  -0.047
41.861  -1.391  -0.358
41.871  -1.983  -0.566
41.881  -2.153  -0.4
41.891  -2.026  -0.213
41.901  -2.364  -0.296
41.911  -2.787  -0.317
41.921  -3.422  -0.442
41.931  -3.888  -0.4
41.941  -3.93   -0.421
41.95   -3.972  -0.275
41.96   -4.353  -0.275
41.97   -4.819  -0.338
41.98   -4.396  -0.088
41.99   -5.115  -0.296
42  -4.819  -0.192
42.01   -5.369  -0.275
42.02   -5.2    -0.171
42.03   -5.581  -0.15
42.04   -5.454  -0.088
42.05   -5.327  -0.088
42.059  -5.496  -0.067
42.069  -5.623  -0.13
42.079  -4.946  0.057
42.089  -5.369  -0.109
42.099  -5.073  -0.005
42.109  -4.523  0.161
42.119  -4.734  0.016
42.129  -4.819  -0.088
42.139  -4.269  -0.047
42.149  -3.888  0.12
42.158  -3.845  0.078
42.168  -3.041  0.161
42.178  -2.83   0.265
42.188  -2.618  0.12
42.198  -1.983  0.307
42.208  -1.983  0.141
42.218  -1.306  0.224
42.228  -0.968  0.182
42.238  -0.841  0.078
42.248  -0.544  0.099
42.257  -0.671  -0.088
42.267  -0.418  -0.109
42.277  0.387   -0.026
42.287  0.725   0.037
42.297  1.021   0.057
42.307  1.318   0.037
42.317  0.387   -0.4
42.327  1.487   -0.026
42.337  1.487   -0.171
42.347  1.572   -0.213
42.356  1.275   -0.275
42.366  1.91    -0.047
42.376  1.868   -0.15
42.386  1.952   -0.15
42.396  1.995   -0.192
42.406  2.418   0.161
42.416  1.064   -0.442
42.426  1.318   -0.317
42.436  1.656   -0.047
42.446  0.683   -0.338
42.455  0.302   -0.462
42.465  0.387   -0.338
42.475  0.006   -0.338
42.485  -0.206  -0.234
42.495  -0.037  -0.067
42.505  -1.264  -0.504
42.515  -2.153  -0.67
42.525  -1.729  -0.317
42.535  -2.491  -0.462
42.545  -2.914  -0.525
42.554  -3.38   -0.483
42.564  -3.295  -0.317
42.574  -3.761  -0.317
42.584  -3.972  -0.254
42.594  -4.438  -0.338
42.604  -5.115  -0.442
42.614  -4.988  -0.254
42.624  -5.284  -0.296
42.634  -5.454  -0.296
42.644  -6.046  -0.338
42.653  -6.046  -0.358
42.663  -5.961  -0.171
42.673  -6.131  -0.213
42.683  -6.427  -0.213
42.693  -6.3    -0.15
42.703  -6.088  -0.005
42.713  -6.131  0.016
42.723  -6.173  0.016
42.733  -6.173  -0.047
42.743  -5.919  0.057
42.752  -6.258  -0.13
42.762  -5.623  0.078
42.772  -5.369  0.078
42.782  -5.581  -0.005
42.792  -5.242  0.057
42.802  -4.48   0.265
42.812  -4.903  -0.026
42.822  -4.353  0.078
42.832  -3.888  0.265
42.842  -3.845  0.12
42.851  -3.211  0.141
42.861  -2.576  0.265
42.871  -2.787  0.099
42.881  -2.66   0.057
42.891  -2.195  0.099
42.901  -1.518  0.12
42.911  -2.026  -0.109
42.921  -1.095  0.057
42.931  -0.925  0.057
42.941  -0.248  0.141
42.95   -0.544  -0.005
42.96   -0.037  0.016
42.97   0.09    -0.026
42.98   -0.037  -0.088
42.99   0.26    -0.067
43  0.09    -0.15
43.01   0.302   -0.171
43.02   0.598   -0.13
43.03   0.387   -0.171
43.04   0.26    -0.317
43.05   0.387   -0.192
43.059  -0.164  -0.421
43.069  0.26    -0.213
43.079  -0.248  -0.296
43.089  -0.291  -0.234
43.099  -0.418  -0.254
43.109  -0.418  -0.192
43.119  -1.306  -0.4
43.129  -1.391  -0.338
43.139  -2.11   -0.462
43.149  -1.899  -0.296
43.158  -2.28   -0.275
43.168  -2.83   -0.4
43.178  -2.957  -0.338
43.188  -3.422  -0.317
43.198  -3.93   -0.483
43.208  -3.803  -0.296
43.218  -4.396  -0.421
43.228  -4.903  -0.442
43.238  -4.607  -0.234
43.248  -4.861  -0.254
43.257  -5.073  -0.296
43.267  -5.496  -0.379
43.277  -5.454  -0.234
43.287  -5.877  -0.317
43.297  -5.792  -0.192
43.307  -5.708  -0.109
43.317  -5.919  -0.192
43.327  -5.877  -0.13
43.337  -5.75   -0.067
43.347  -6.131  -0.192
43.356  -5.834  -0.088
43.366  -5.708  -0.088
43.376  -5.327  0.057
43.386  -5.327  -0.005
43.396  -5.411  -0.109
43.406  -4.776  0.037
43.416  -4.396  0.037
43.426  -4.353  0.016
43.436  -4.142  0.099
43.446  -3.634  0.12
43.455  -3.211  0.161
43.465  -3.041  0.12
43.475  -2.703  0.099
43.485  -2.618  -0.005
43.495  -2.026  0.016
43.505  -1.476  0.078
43.515  -1.095  0.161
43.525  -1.01   0.037
43.535  -1.095  -0.13
43.545  0.217   0.349
43.554  0.471   0.161
43.564  0.344   0.016
43.574  -0.079  -0.254
43.584  0.852   -0.026
43.594  1.445   0.057
43.604  0.725   -0.234
43.614  1.106   -0.254
43.624  1.402   -0.213
43.634  2.122   -0.026
43.644  1.656   -0.213
43.653  1.825   -0.192
43.663  1.487   -0.4
43.673  2.037   -0.192
43.683  1.825   -0.213
43.693  2.206   0.099
43.703  1.445   -0.317
43.713  0.852   -0.483
43.723  0.598   -0.546
43.733  1.318   -0.234
43.743  0.556   -0.421
43.752  0.302   -0.358
43.762  0.048   -0.358
43.772  -0.714  -0.546
43.782  -0.714  -0.4
43.792  -0.968  -0.338
43.802  -1.687  -0.442
43.812  -1.729  -0.358
43.822  -2.745  -0.587
43.832  -2.787  -0.462
43.842  -2.83   -0.317
43.851  -2.914  -0.234
43.861  -3.718  -0.462
43.871  -3.93   -0.338
43.881  -4.057  -0.358
43.891  -4.48   -0.317
43.901  -4.353  -0.254
43.911  -4.819  -0.317
43.921  -4.819  -0.15
43.931  -4.692  -0.109
43.941  -5.327  -0.234
43.95   -5.411  -0.234
43.96   -5.961  -0.358
43.97   -5.242  -0.067
43.98   -5.496  -0.109
43.99   -5.665  -0.15
44  -5.073  0.057
44.01   -5.2    -0.047
44.02   -5.284  -0.047
44.03   -4.903  0.037
44.04   -4.776  0.037
44.05   -4.776  -0.005
44.059  -4.311  0.099
44.069  -4.226  0.037
44.079  -3.041  0.39
44.089  -3.803  0.057
44.099  -3.549  -0.005
44.109  -2.83   0.203
44.119  -2.364  0.265
44.129  -2.026  0.203
44.139  -1.983  0.161
44.149  -1.814  0.099
44.158  -1.433  0.078
44.168  -0.798  0.161
44.178  -0.502  0.099
44.188  -0.121  0.182
44.198  -0.291  -0.026
44.208  0.514   0.224
44.218  0.387   0.016
44.228  0.387   -0.047
44.238  0.767   0.016
44.248  0.64    -0.109
44.257  1.064   -0.067
44.267  1.233   -0.026
44.277  1.36    -0.047
44.287  1.36    -0.109
44.297  1.275   -0.088
44.307  1.106   -0.275
44.317  1.148   -0.192
44.327  0.852   -0.254
44.337  0.81    -0.296
44.347  0.81    -0.234
44.356  0.683   -0.234
44.366  0.514   -0.275
44.376  0.217   -0.296
44.386  0.006   -0.213
44.396  -0.671  -0.421
44.406  -0.925  -0.4
44.416  -1.222  -0.379
44.426  -1.687  -0.421
44.436  -1.729  -0.358
44.446  -2.237  -0.358
44.455  -2.491  -0.358
44.465  -2.872  -0.358
44.475  -3.507  -0.421
44.485  -3.888  -0.442
44.495  -4.311  -0.421
44.505  -4.269  -0.338
44.515  -4.65   -0.317
44.525  -4.861  -0.317
44.535  -4.988  -0.296
44.545  -5.284  -0.338
44.554  -5.327  -0.234
44.564  -5.327  -0.192
44.574  -6.004  -0.317
44.584  -5.877  -0.192
44.594  -6.173  -0.317
44.604  -5.961  -0.13
44.614  -6.3    -0.234
44.624  -6.046  -0.088
44.634  -5.792  -0.047
44.644  -5.919  -0.047
44.653  -5.708  -0.047
44.663  -5.496  0.016
44.673  -5.581  -0.026
44.683  -5.75   -0.254
44.693  -4.65   0.224
44.703  -4.776  0.037
44.713  -5.073  -0.13
44.723  -4.523  -0.026
44.733  -4.396  -0.088
44.743  -3.845  0.078
44.752  -3.761  0.016
44.762  -3.168  0.12
44.772  -2.576  0.078
44.782  -1.56   0.557
44.792  -2.237  0.057
44.802  -2.449  -0.171
44.812  -1.899  -0.109
44.822  -0.375  0.536
44.832  -0.418  0.203
44.842  -0.671  -0.005
44.851  -0.164  0.161
44.861  -0.248  -0.005
44.871  0.048   0.016
44.881  0.302   -0.067
44.891  0.217   -0.15
44.901  0.471   0.016
44.911  -0.164  -0.4
44.921  0.683   -0.109
44.931  0.09    -0.317
44.941  1.275   0.078
44.95   0.471   -0.296
44.96   0.767   -0.15
44.97   0.429   -0.254
44.98   0.429   -0.234
44.99   0.344   -0.234
45  -0.079  -0.275
45.01   -0.502  -0.483
45.02   -0.502  -0.379
45.03   -1.052  -0.462
45.04   -1.095  -0.421
45.05   -1.391  -0.4
45.059  -1.729  -0.442
45.069  -1.729  -0.317
45.079  -2.11   -0.338
45.089  -2.957  -0.525
45.099  -2.999  -0.462
45.109  -2.914  -0.234
45.119  -3.676  -0.4
45.129  -4.523  -0.608
45.139  -3.93   -0.317
45.149  -4.269  -0.317
45.158  -4.226  -0.234
45.168  -4.903  -0.379
45.178  -4.734  -0.13
45.188  -5.581  -0.421
45.198  -5.242  -0.213
45.208  -5.496  -0.213
45.218  -5.623  -0.234
45.228  -5.454  -0.109
45.238  -5.623  -0.13
45.248  -6.004  -0.254
45.257  -5.75   -0.15
45.267  -5.75   -0.13
45.277  -5.792  -0.192
45.287  -5.157  0.037
45.297  -5.369  -0.005
45.307  -5.454  -0.109
45.317  -5.073  -0.005
45.327  -4.269  0.099
45.337  -4.776  -0.109
45.347  -4.057  0.141
45.356  -4.142  -0.005
45.366  -4.015  -0.026
45.376  -3.084  0.224
45.386  -3.972  -0.254
45.396  -3.084  0.016
45.406  -2.449  0.12
45.416  -2.407  0.016
45.426  -1.772  0.182
45.436  -1.518  0.099
45.446  -1.306  0.037
45.455  -1.01   0.078
45.465  -0.756  0.099
45.475  -0.544  0.037
45.485  -0.46   -0.067
45.495  -0.121  -0.047
45.505  -0.121  -0.13
45.515  0.429   -0.005
45.525  0.64    0.016
45.535  0.387   -0.171
45.545  0.514   -0.15
45.554  0.683   -0.13
45.564  0.725   -0.13
45.574  0.429   -0.254
45.584  0.471   -0.275
45.594  0.81    -0.213
45.604  0.725   -0.15
45.614  0.175   -0.379
45.624  0.048   -0.338
45.634  0.133   -0.317
45.644  -0.206  -0.338
45.653  -0.671  -0.421
45.663  -0.841  -0.379
45.673  -0.671  -0.296
45.683  -1.095  -0.358
45.693  -1.687  -0.379
45.703  -1.814  -0.338
45.713  -2.068  -0.234
45.723  -2.491  -0.338
45.733  -2.999  -0.358
45.743  -3.253  -0.358
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51.228  -1.349  0.037
51.238  -1.179  -0.005
51.248  -0.883  -0.005
51.257  -0.841  -0.047
51.267  -0.883  -0.15
51.277  -0.671  -0.109
51.287  -0.798  -0.213
51.297  -0.629  -0.171
51.307  -0.587  -0.234
51.317  -0.46   -0.234
51.327  -0.756  -0.296
51.337  -0.798  -0.254
51.347  -0.544  -0.171
51.356  -0.798  -0.234
51.366  -0.841  -0.234
51.376  -1.264  -0.4
51.386  -1.687  -0.462
51.396  -1.687  -0.379
51.406  -2.237  -0.483
51.416  -2.237  -0.379
51.426  -2.618  -0.421
51.436  -2.449  -0.296
51.446  -2.618  -0.296
51.455  -3.676  -0.504
51.465  -3.168  -0.254
51.475  -3.422  -0.275
51.485  -3.888  -0.358
51.495  -4.057  -0.296
51.505  -4.311  -0.275
51.515  -4.946  -0.338
51.525  -5.157  -0.296
51.535  -5.538  -0.358
51.545  -5.157  -0.171
51.554  -5.2    -0.15
51.564  -5.708  -0.275
51.574  -5.708  -0.213
51.584  -5.623  -0.13

I've got two signals recorded from an experiment, plotted against the time. I'm trying to determine the phase shift between them, but I've only find example for similar frequency.

The two signals look like this:

I'm wondering if anyone would have a practical way to determine the phase shift in python? thanks excel data example

Answer 1

Let's first note that your signals do have the same frequency, just a different amplitude and phase.

You could try to perform a cross-correlation of your two curves with scipy.signal's correlate and correlation_lags:

correlation = signal.correlate(df['Heave'], [df['Trim'], df.index], mode='full')
lags = signal.correlation_lags(df['Heave'].size, df['Trim'].size, mode='full')
lag = lags[np.argmax(correlation)]

Output: 17 (units of time, which you need to multiply by the time step, here 0.01)

And indeed, if we shift the Trim by 17 units, it aligns with the Heave:

Answer 2

thank you for the answer, I'll try to correct my code.