A Nonlinear Method for Stochastic Spectrum Estimation in the Modeling of Musical Sounds

We propose an original technique for separating the spectrum of the noisy component from that of the sinusoidal, quasi-deterministic one, for the sinusoids + transients + noise modeling of musical sounds. It also enables estimation of the time-domain noise envelope and detection of transients with standard techniques. The algorithm for spectrum separation relies on nonlinear transformations of the amplitude spectrum of the sampled signal obtained via fast Fourier transform, which allow to eliminate the dominant partials without the need for precisely tuned notch filters. The envelope estimation is performed by calculating the energy of the signal in the frequency domain, over a sliding time window. Several transformations (such as pitch shifting, time stretching, etc.) can be performed on the so-obtained stochastic spectrum prior to resynthesis. The synthesized sound is built via inverse fast Fourier transform with overlap-add method. The performance of the proposed algorithm is assessed on synthetic, instrumental, and natural sounds in terms of different quality measures