TY - JOUR
T1 - A limitation of the kernel method for joint distributions of arbitrary variables
AU - Baraniuk, Richard G.
N1 - Funding Information:
Manuscript received May 10, 1995. This work was supported by the National Science Foundation, grant no. MI€'-9457438, the Office of Naval Research, grant no. N00014-95-1-0849, and the Texas Advanced Technology Program, graut no. TX-ATP 003604-002. The associate editor coordinating the review of this letter and approving it for publication was Prof. G. F. Boudreaux-Bartels. The author is with the Department of Electrical and Computer Engineering, Rice University, Houston, TX 77251-1892, USA (email: [email protected]). Publisher Item Identifier S 1070-9908(96)01831-7.
PY - 1996/2
Y1 - 1996/2
N2 - Recently, Cohen has proposed a construction for joint distributions of arbitrary physical quantities, in direct generalization of joint time-frequency representations. Actually, this method encompasses two approaches: one based on operator correspondences and one based on weighting kernels. The literature has emphasized the kernel method due to its ease of analysis; however, its simplicity comes at a price. In this letter, we use a simple example to demonstrate that the kernel method cannot generate all possible bilinear joint distributions. Our results suggest that the relationship between the operator method and the kernel method merits closer scrutiny.
AB - Recently, Cohen has proposed a construction for joint distributions of arbitrary physical quantities, in direct generalization of joint time-frequency representations. Actually, this method encompasses two approaches: one based on operator correspondences and one based on weighting kernels. The literature has emphasized the kernel method due to its ease of analysis; however, its simplicity comes at a price. In this letter, we use a simple example to demonstrate that the kernel method cannot generate all possible bilinear joint distributions. Our results suggest that the relationship between the operator method and the kernel method merits closer scrutiny.
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U2 - 10.1109/97.484215
DO - 10.1109/97.484215
M3 - Article
AN - SCOPUS:0030081465
SN - 1070-9908
VL - 3
SP - 51
EP - 53
JO - IEEE Signal Processing Letters
JF - IEEE Signal Processing Letters
IS - 2
ER -