Hello, I have several questions to ask regarding the expected behaviour of a linear adaptive filter applied in a system identification arrangement using two uncorrelated sequences for both the reference and desired signals. I'll describe the experiment, the observed results, and then put forward my questions. In Matlab I create two uncorrelated sequences using the following code: SIZE = 4096; randn('seed', 0); desired=randn(1,SIZE); randn('seed', 4); reference=randn(1,SIZE); These two sequences form the desired and reference sequences for a FIR-based, linear adaptive filter configured in a system identification arrangement with the weights updated using both the conventional RLS and QR-decomposition RLS algorithms. In this case, the adaptive filter's estimate of the desired sequence should theoretical be zero due to the uncorrelated relationship between the desired and reference sequences; the weights should go to zero. This behaviour is roughly observed when the forgetting-factor is larger than 0.9; significantly greater than zero and less than unity, as stated in all standard references. However, if the forgetting factor is mid-range, for example, say 0.5, the adaptive filter's estimate becomes significant and the resulting error tends to zero. Why is this occurring? Are there strict limits for the forgetting-factor? Should it always be larger than 0.9? Is there a working ballpark range for sequences like speech? Any insights would be greatly appreciated. Thank you, Michael.

# Opinion - Adaptive Filtering of Uncorrelated Sequences

Started by ●February 16, 2006