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I've got a question regarding an adaptive filter for interference calcellation:

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Here, the interference is a periodic signal: $x[n] = \cos(\pi/4\cdot n + \varphi_1) + \cos(3\pi/4\cdot n + \varphi_2)$
where $\varphi_1$ and $\varphi_2$ are independent and uniformly distributed between 0 and $2 \pi$.
The signal is filtered by an IIR filter with impulse response: $h[n] = (\frac{1}{3})^n$

I should design an adaptive filter which minimizes the error in a MSE sense.

Now my first question is the following: what is the maximum filter length N I can choose for my adaptive filter? Here I am not quite sure how to answer this question and I would be very happy for some help! : )

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    $\begingroup$ Can you please clarify the diagram a bit? Is this a "homework" type question? Also, how comfortable are you with the "ideal" low pass filter in the time domain? $\endgroup$ – A_A Feb 11 at 9:26
  • $\begingroup$ Yes it is a homework. I know that the ideal lowpass filter in time domain is a sinc-function... $\endgroup$ – Phinie Feb 11 at 9:34
  • $\begingroup$ If I have a single sinusoid as an input signal, my autocorrelation matrix is only invertible for N <= 2. We have learned in class that the autocorrellation matrix of signals with discrete lines (#lines = L) in frequency spectrum is only invertible for a filter order N <= L. Therefore the maximum filter order Nmax in my case is 4, as I have 2 sinusoidal functions as an input signal? $\endgroup$ – Phinie Feb 11 at 9:44
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    $\begingroup$ Matt's answer at this link may help you: dsp.stackexchange.com/questions/37902/… but typically the filter needn't be longer than the delay spread of the channel (and ends up adding more noise if too long). $\endgroup$ – Dan Boschen Feb 11 at 17:58

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