Table 1 List of commonly used terms for filters of length M

d _k

IR

Desired output of unknown system

w

IR^M×1

Impulse response of unknown system

w _k

IR^M×1

Estimate of w

u _k

IR^M×1

Regression vector

u _k

IR^1×1

Elements of the regression vector

v _k

IR

Additive noise

R _uu

IR^M×M

Autocorrelation matrix of u _k

Λ _u

IR^M×M

Diagonal matrix =Q R _uu Q ^T

K _k

IR^M×M

Covariance matrix of w−w _k

x _k

IR

White generating process

\(m_{\mathrm {x}}^{(2)}\)

IR

Second-order moment of x _k

\(m_{\mathrm {x}}^{(2,2)}\)

IR

Joint fourth-order moment of x _k

μ

IR

Step-size

A

IR^M×(M+P)

upper right Toeplitz matrix

I

IR^M×M

Identity matrix of dimension M

I _P

IR^P×P

Identity matrix of dimension P

1

IR^M×1

Vector with ones as entries