## Computational methods for real-time adaptive multichannel signal processing |

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Page 103

Subgraph 1: This subgraph consists of four principal stages; the dependence

graphs for each of these stages are

stages can be connected together in the k direction to form a 3-D graph. Note that

the resulting 3-D graph is directionally shift invariant in the i direction. Because of

this, we will proceed as follows: 1. project the 3-D dependence graph in the i

direction to create a 2-D signal flow graph 2. project this 2-D signal flow graph in

the k ...

Subgraph 1: This subgraph consists of four principal stages; the dependence

graphs for each of these stages are

**shown Figure**4.4 - Figure 4.7. These fourstages can be connected together in the k direction to form a 3-D graph. Note that

the resulting 3-D graph is directionally shift invariant in the i direction. Because of

this, we will proceed as follows: 1. project the 3-D dependence graph in the i

direction to create a 2-D signal flow graph 2. project this 2-D signal flow graph in

the k ...

Page 142

Since wavefronts of the next stage are slow compared with the normalization of w

, the total added cost for normalizing w is only: t^+t^+X^+t^ (4.12) Next, we begin

the deflation of R as

processor 0 will become free to work on removing fill (as

From here onward, these two stages operate concurrently. The execution time,

thus, depends on the slower of the two stages. During the first r + 1 steps, stage

3A is ...

Since wavefronts of the next stage are slow compared with the normalization of w

, the total added cost for normalizing w is only: t^+t^+X^+t^ (4.12) Next, we begin

the deflation of R as

**shown in Figure**4.10. After the fourth wavefront of stage 3A,processor 0 will become free to work on removing fill (as

**shown in Figure**4.11).From here onward, these two stages operate concurrently. The execution time,

thus, depends on the slower of the two stages. During the first r + 1 steps, stage

3A is ...

Page 150

Daniel Joseph Rabideau. Note that the reflection H; only effects columns i...n.

Furthermore, the application of H, to each of these columns is independent. Thus,

the graph for a single hyperbolic Householder transformation, H, , is as

amount of computation it requires. For the "compute" vertex, this is (4k + 3) • tmult

+ (2k + 2) + t ^ + tdiu {k = number of new rows} . For the "apply" vertices, the

weights are 4k ...

Daniel Joseph Rabideau. Note that the reflection H; only effects columns i...n.

Furthermore, the application of H, to each of these columns is independent. Thus,

the graph for a single hyperbolic Householder transformation, H, , is as

**shown in****Figure**5.1. Each vertex in this graph is assigned a weight that denotes theamount of computation it requires. For the "compute" vertex, this is (4k + 3) • tmult

+ (2k + 2) + t ^ + tdiu {k = number of new rows} . For the "apply" vertices, the

weights are 4k ...

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### Contents

Introduction | 1 |

Review of Multisensor Processing and Parallel Mapping | 16 |

Fast Subspace Tracking Algorithms | 39 |

Copyright | |

4 other sections not shown

### Common terms and phrases

algorithm graph algorithm HHT app comm array processing automated mapping automating the mapping beamforming bearing estimation cells CG-FST coarse grain mapping column communication complexity compute condition estimation convergence correlation matrix cost functions deflation dependence graph double precision DSP algorithms edges eigenvalues Fast Subspace Tracking Furthermore global sum Grain FST grain partitioning Householder transformation hyperbolic Householder hypercube Idle cost function IEEE Transactions Intel iPSC/860 Intel Paragon iWarp linear speedup Minimax multiprocessors node processors noise subspace Number of Processors operations optimization orthonormal parameters performance plane rotations preserve the signal processor q QR algorithm QR decomposition QR factorization rank increase rank revealing real-time recursive least squares refinement step RO-FST sensor array processing shown in Figure signal eigenstructure signal flow graph signal processing signal subspace simulated annealing singular value decomposition singular values snapshot stage 4A subgraph subspace tracking algorithms target machine tasks techniques tmult TQR-SVD upper triangular wavefronts