For each sinusoidal component of a signal, we need to determine its frequency, amplitude, and phase (when needed). As a starting point, consider the windowed complex sinusoid with complex amplitude and frequency :
As discussed in Chapter 5, the transform (DTFT) of this windowed signal is the convolution of a frequency domain delta function at [ ], and the transform of the window function, , resulting in a shifted version of the window transform . Assuming is odd, we can show this as follows:
At , we have
If we use a zero-phase (even) window, the phase at the peak equals the phase of the sinusoid, i.e., .
Tracking Sinusoidal Peaks in a Sequence of FFTs
Following Spectral Peaks