Skip to main content


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

From: Asymptotic equivalent analysis of the LMS algorithm under linearly filtered processes

Variable Dimension Meaning
d k IR Desired output of unknown system
w IRM×1 Impulse response of unknown system
w k IRM×1 Estimate of w
u k IRM×1 Regression vector
u k IR1×1 Elements of the regression vector
v k IR Additive noise
R uu IRM×M Autocorrelation matrix of u k
Λ u IRM×M Diagonal matrix =Q R uu Q T
K k IRM×M Covariance matrix of ww 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 IRM×(M+P) upper right Toeplitz matrix
I IRM×M Identity matrix of dimension M
I P IRP×P Identity matrix of dimension P
1 IRM×1 Vector with ones as entries