How to proof a noise signal change its pattern over time?

Question

I have a 600 data point signal which is noisy and not perfectly generate from one of two filters. The first 200 output data points generate from the filter A or B should be identical. If the rest 400 data point is generated by filter A, then the signal pattern should be the same as the first 200 points. However, if the signal is generate by filter B, then the concavity of the signal will change a little bit.

I have another 600 point signal which is the perfect expectation of the output of filter A.

How to find out which is the filter to generate the data signal??

How can I know whether the signal

Answer 1

The statistical way to do this is correlation.  You could correlate the sample data with the expected data.  If the signal was unknown and you wanted to see if it was repetitive you could do auto-correlation, i.e. compare time t data to time t + w data (w represents the anticipated period of the data).

If your data is sampled amplitudes of noise or you just don't know what it is, then you have multiple frequencies and thus multiple periods.  Auto-correlation is going to be fixed on a particular period of repetition so you would have to transform the data to accommodate this possibly by using a discrete Fourier transform (this transforms the time domain data into frequency domain data)and auto-correlating the frequency mix over time.

If you want to dynamically have the system develop the "best" result from the two filters, you could use a numerical technique like a Kalman filter to merge the data from the two filters.