scholarly journals Derivation of Diagonalized Identical Equations for 3 by 3 Circulant and Quasi-Circulant Matrices and Their Application to Winograd 7-Point FFT

2022 ◽  
Vol 26 (1) ◽  
pp. 13-19
Author(s):  
Nobuaki Takahashi ◽  
Daisuke Takago
Keyword(s):  
Circulant Matrices

Compressed Sampling of Spectrally Sparse Signals Using Sparse Circulant Matrices

Frequenz ◽  
2014 ◽  
Vol 68 (11-12) ◽  
Author(s):  
Guangjie Xu ◽  
Huali Wang ◽  
Lei Sun ◽  
Weijun Zeng ◽  
Qingguo Wang
Keyword(s):  
Circulant Matrices ◽  
Noise Robustness ◽  
Sparse Signals ◽  
Measurement Matrix ◽  
Compressed Sampling ◽  
Random Measurement ◽  
Compressive Performance ◽  
Generating Sequence ◽  
Periodic Autocorrelation ◽  
Selection Of

AbstractCirculant measurement matrices constructed by partial cyclically shifts of one generating sequence, are easier to be implemented in hardware than widely used random measurement matrices; however, the diminishment of randomness makes it more sensitive to signal noise. Selecting a deterministic sequence with optimal periodic autocorrelation property (PACP) as generating sequence, would enhance the noise robustness of circulant measurement matrix, but this kind of deterministic circulant matrices only exists in the fixed periodic length. Actually, the selection of generating sequence doesn't affect the compressive performance of circulant measurement matrix but the subspace energy in spectrally sparse signals. Sparse circulant matrices, whose generating sequence is a sparse sequence, could keep the energy balance of subspaces and have similar noise robustness to deterministic circulant matrices. In addition, sparse circulant matrices have no restriction on length and are more suitable for the compressed sampling of spectrally sparse signals at arbitrary dimensionality.

On singular values of block circulant matrices

2019 ◽  
Vol 563 ◽  
pp. 400-410
Author(s):  
Marek Niezgoda
Keyword(s):  
Singular Values ◽  
Circulant Matrices

scholarly journals Block matrices and Guo's index for block circulant matrices with circulant blocks

2018 ◽  
Vol 556 ◽  
pp. 301-322 ◽  
Author(s):  
Enide Andrade ◽  
Cristina Manzaneda ◽  
Hans Nina ◽  
María Robbiano
Keyword(s):  
Circulant Matrices ◽  
Block Matrices

Study on Some New Properties of k-Circulant Matrices

2014 ◽  
Vol 536-537 ◽  
pp. 30-33
Author(s):  
Ying Mei
Keyword(s):  
Circulant Matrices

In this paper, we investigate the structure ofk-circulant matrices, and then present some new properties ofk-circulant matrices.

Circulant Matrices

2011 ◽  
pp. 23-25
Author(s):  
M. W. Wong
Keyword(s):  
Circulant Matrices
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