SYSTEM OPERATION

The overall structure of our system is similar to conventional sinusoidal modeling. First, each frame is read in to a buffer, which is FFT'd and then analyzed for peaks. A parabola is fit to the log of each magnitude peak, yielding accurate magnitude and frequency estimates. A phase estimate is also recorded, and is normalized by the chirp parameter after the latter is estimated. (This is necessary because of the nonlinear mapping of phase offsets to detected peak phase for chirp signals.) Next, we apply the estimator in eqns. 5 and 7 as appropriate to each peak, assigning a chirp parameter to each. When calculating the second order difference in eqn. 5, we use the $Y(k)$ values at the nearest frequency bin $k$ to the detected peak (and its neighbors $k\pm 1$) in the calculation. In the future, we may try to use linear or other interpolation of $Y(k)$ to use values corresponding more exactly to the interpolated peak center frequency of the component. We leave the task of frequency trajectory alignment across frames to future work. We note that since our chirp and phase parameters are detected with great accuracy, it may no longer be necessary to align such trajectories. Direct synthesis of the detected frequency components via IFFT or a bank of oscillators will be explored as an alternative to trajectory alignment.