# Convergence of LMS

I'm not really sure about the following question and don't know where exactly to look it up, so I'm asking here:

I have an adaptive filter and compute the coefficients iteratively using e.g. LMS or a gradients search algorithm. Do the coefficients converge faster if I use white input noise ($$x[n]=w[n]$$) or some low-pass-filtered noise (e.g $$x[n] = \frac{1}{\sqrt{2}}(w[n]+w[n-1])$$)?
My guess would be, that they converge faster for white noise input but I don't have any explanation. I would be very happy for any help...

Thanks! : )

• You won't be able to determine the channel at frequencies where your input signal doesn't occupy. So do not filter out your input signal where you want to measure the channel response! For this reason white noise is better. If you have no concern with a portion of the frequency band, then you can filter that portion out. – Dan Boschen Feb 18 at 13:23