This paper provides a detailed description of the spectral analysis front-end of a melody extraction algorithm. Our particular approach aims at extracting the sinusoidal components from the audio signal. It includes a novel technique for the efficient computation of STFT spectra in different time-frequency resolutions. Furthermore, we exploit the application of local sinusoidality criteria, in order to detect stable sinusoids in individual FFT frames. The evaluation results show that a multi resolution analysis improves the sinusoidal extraction in polyphonic audio.