AM/FM rate estimation for time-varying sinusoidal modeling

Due to its simplicity and accuracy, quadratic peak interpolation in a zero-padded fast Fourier transform (FFT) has been widely used for sinusoidal parameter estimation in audio applications. We propose, as its natural extension, a method to estimate the first order amplitude and frequency modulation rates of time-varying sinusoidal components, as well as to correct biases in conventional amplitude, frequency and phase estimates. We derive exact formulas for Gaussian windows and obtain approximate formulas for often-used windows by introducing a simple window adaptation scheme. Experimental results show the average estimation biases of the AM and FM rates with a 30 ms Hann window are below 1% for typical AM/FM rates in speech.