step_whitening_filter

  STEP_WHITENING_FILTER - Compute the optimal FIR filter for Wiener filtering a step 

   [RINV,R] = STEP_WHITENING_FILTER(ALPHA, N, M)

    Computes the inverse of the correlation matrix of a STEP signal for a Wiener filter.

    Suppose we have a signal d[n], and we wish to make the best linear projection
    y[n] from a signal x[n] onto d[n]. What is the optimal filter h[n] such that

    y[n] = sum( h[1:M] . * x[n-[1:M]] ) 

    Suppose further that we know that x[n] is comprised of STEPs of
    -1, 0, or 1, with probability alpha, 1-2*alpha, and alpha, respectively, and
    exhibits duration N.

    Then the auto-correlation matrix of the signal x[n] is returned in R.
    R(i+1,j+1) = expectation( x[n-i] x[n-j] )
    And Rinv is the inverse of this matrix.

    This matrix can be used to find the optimal filter h[n]:

    h[n] = Rinv * P, where P is the correlation of d[n] with x[n].