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D. Rocchesso: Sound Processing
parabolic interpolation
phase following
Figure 8: Sonogram representation of the signal (15). N = 128 and R = 128.
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DFT magnitude
Figure 9: DFT image (magnitude) of a sinusoidal component.
· The sinusoidal component "leaks" some of its energy into bins that stay
within a neighborhood of its theoretical position;
· It is difficult to determine the exact frequency of the component from
visual inspection.
To overcome the latter problem, we describe two techniques: parabolic interpo-
lation and phase following.
Parabolic interpolation
Any kind of interpolation can be applied to estimate the value and position of a
frequency peak in the magnitude spectrum of a signal. Degree-two polynomial
interpolation, i.e. parabolic interpolation, is particularly convenient as it uses
only three bins of the magnitude spectrum.