Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605246 | Applied and Computational Harmonic Analysis | 2013 | 9 Pages |
Abstract
To determine the instantaneous amplitude and frequency of a nonstationary signal, it is equivalent to determine the imaginary operator ℑ. Vakman argued that ℑ must be the Hilbert transform if the demodulation is subject to certain fundamental physical conditions. But the proof provided by Vakman lacks rigor. To rigorously prove Vakmanʼs statements, we construct a weighted space that includes , the p-th integrable periodic function space, and Lp(R), the p-th integrable function space on R. On an extension of the classical Hilbert transforms H and is defined and a rigorous Vakmanʼs theory is established on this space.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis