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.

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