Hi Christoph,
I understand that you are looking for an explanation of how the initial condition calculation in MATLAB's "filtfilt" function relates to the method described in the IEEE article on forward-backward filtering, and how the extrapolation by reflection works.
- The "filtfilt" function is designed to perform zero-phase digital filtering by processing the input data in both forward and reverse directions. This is done to minimize phase distortion and achieve a more accurate filtered result.
- According to the article, the initial conditions for the filter are determined by minimizing the difference between the results of forward-backward and backward-forward filtering. This is achieved by carefully selecting initial conditions that account for the filter's memory of previous samples.
- In "filtfilt", the extrapolation by reflection is a technique used to handle edge effects and ensure that the filter has sufficient data to initialize its internal states. By reflecting the data at the boundaries, the algorithm effectively extends the input signal, providing a more stable initial condition for the filter. This reflection helps in reducing edge artifacts that might occur due to the lack of data beyond the signal boundaries.
- The initial condition calculation in "filtfilt" involves solving a linear system to determine the state of the filter at the start of the data. This is done using the filter's state-space representation and the reflected data.
- While the reflection method is effective, it is theoretically possible to use alternative methods for setting initial conditions. However, any alternative approach must still ensure that the filter's internal states are appropriately initialized to minimize transients and achieve the desired zero-phase response.
Refer to the documentation of MATLAB's "filtfilt" function for more details on its implementation: https://www.mathworks.com/help/signal/ref/filtfilt.html
Refer to the documentation on digital filters in MATLAB: https://www.mathworks.com/help/signal/digital-filters.html
Hope this helps!
