Frequency, Phase and Amplitude Estimation of Overlapping Partials in Monaural Musical Signals
A method is described that simultaneously estimates the frequency, phase and amplitude of two overlapping partials in a monaural musical signal from the amplitudes and phases in three frequency bins of the signal’s Odd Discrete Fourier Transform (ODFT). From the transform of the analysis window in its analytical form, and given the frequencies of the two partials, an analytical solution for the amplitude and phase of the two overlapping partials was obtained. Furthermore, the frequencies are estimated numerically solving a system of two equations and two unknowns, since no analytical solution could be found. Although the estimation is done independently frame by frame, particular situations (e.g. extremely close frequencies, same phase in the time window) lead to errors, which can be partly corrected with a moving average filter over several time frames. Results are presented for artificial sinusoids with time varying frequencies and amplitudes, and with different levels of noise added. The system still performs well with a Signalto-Noise ratio of down to 30 dB, with moderately modulated frequencies, and time varying amplitudes.