Instantaneous magnitudes and frequencies of signals with positivity constraints

This paper proposes an optimization approach for representing instantaneous magnitudes and frequencies of signals. Signals are represented as the products of their magnitudes and the cosines of their phases. Also, both their instantaneous magnitudes and frequencies are positive. These two conditions are posed as linear functional inequality constraints. To have smooth signals, the sum of the total absolute values of the p th order derivatives of the magnitudes is minimized. To solve the optimization problem, the objective function is first converted to a linear objective function subject to linear functional inequality constraints. Finally, the functional inequality constraints are converted to the conventional linear equality constraints via the constraint transcription method. Experimental results show that the magnitudes obtained by our proposed method are much smoother than those obtained by existing methods.