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This article deals with the estimation of sinusoidal parameters for non stationary sinusoids. It will be shown that for linear amplitude and frequency modulation only the frequency modulation creates additional estimation bias for the standard sinusoidal parameter estimator. Then a new algorithm for frequency domain demodulation of spectral peaks is proposed that can be used to obtain an approximate maximum likelihood estimate of the frequency slope, and an estimate of the amplitude, phase and frequency parameter with significantly reduced bias. An experimental evaluation compares the new estimation scheme with some previously existing methods. It shows that significant bias reduction is achieved for a large range of slopes and zero padding factors. A real world example demonstrates the benefits of the new method.