Multidelay Block Frequency Domain Adaptive Filter - Variable Definitions

Variable Definitions

Let be the length of the processing blocks, be the number of blocks and denote the 2Nx2N Fourier transform matrix. The variables are defined as:

With normalisation matrices and :

\mathbf{G}_1 = \mathbf{F}\begin{bmatrix} \mathbf{0}_{NxN} & \mathbf{0}_{NxN} \\ \mathbf{0}_{NxN} & \mathbf{I}_{NxN} \\ \end{bmatrix}\mathbf{F}^{-1}
\tilde{\mathbf{G}}_2 = \mathbf{F}\begin{bmatrix} \mathbf{I}_{NxN} & \mathbf{0}_{NxN} \\ \mathbf{0}_{NxN} & \mathbf{0}_{NxN} \\ \end{bmatrix}\mathbf{F}^{-1}

In practice, when multiplying a column vector by, we take the inverse FFT of, set the first values in the result to zero and then take the FFT. This is meant to remove the effects of the circular convolution.

Read more about this topic:  Multidelay Block Frequency Domain Adaptive Filter

Famous quotes containing the words variable and/or definitions:

    “Walked forth to ease my pain
    Along the shore of silver streaming Thames,
    Whose rutty bank, the which his river hems,
    Was painted all with variable flowers,”
    —Edmund Spenser (1552?–1599)

    “The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.”
    —Pamela Patrick Novotny (20th century)