There's a whole area of signal processing dedicated to optimal filtering. In pretty much every case I've seen the filtering problem is formulated with a convex cost function. Here's a freely ...

I don't have a mathematical proof for you, but here are 2 issues to think about. The impulse response from the actuator (speaker) to the error measurement (microphone) is non-minimum phase. This is ...

This is just a guess, but it could be that you are getting these harmonics because you have inadequate acoustic coupling between the accelerometer and its mount point (i.e. tape isn't secure enough). ...

You're using a high order model so you might be running into numerical precision issues. Make sure the realization of model_state_space is minimal. You can do this with min_model_state_space = ...

You could try a Savitzky-Golay filter, followed by standard peak detection. The S-G filter will preserve the location of your peaks. If you're using Matlab it comes with the signal processing toolbox. ...

The way you wrote it, 1/f0 defines the -3dB cutoff frequency. This is easy to see if you let s = 1/f0. The numerator becomes 1 and the denominator becomes 2. A gain of 1/2 is -3dB. Since it's high-...

The eigenvector corresponding to the largest eigenvalue of the autocorrelation matrix indicates the direction of fastest change, while the eigenvector of the smallest eigenvalue indicates the ...

If I were to approach the problem here's what I might try... convert the images to greyscale as Andrey suggested, look at the normalized cross-correlation on a subregion of the images to find the ...

The equation error approach should have worked (assuming your model was the same order as the unknown system). While it's not as efficient as QRD-RLS algorithms you can always use a Kalman filter to ...

It means u and v are orthogonal. If u or v or both have zero mean then they are also uncorrelated. If they are uncorrelated and jointly gaussian then they are also independent.