Orthonormal bases with nonlinear phases

For adaptive representation of nonlinear signals, the bank ${\cal M}$ of real square integrable functions that have nonlinear phases and nonnegative instantaneous frequencies under the analytic signal method is investigated. A particular class of functions with explicit expressions in ${\cal M}$ is obtained using recent results on the Bedrosian identity. We then construct orthonormal bases for the Hilbert space of real square integrable functions with the basis functions from ${\cal M}$.

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