  A recent study (Yong, Silva, and Polifke, Combust. Flame 228 (2021)) proposed
the use of phasor diagrams to categorize marginally stable modes in an ideal
resonator with a compact, velocity-sensitive flame. Modes with velocity phasors
that reverse direction across the flame were categorized as ITA modes. The
present study extends this concept to growing and decaying modes. In other
words, with the method proposed, it is possible to distinguish whether a given
thermoacoustic mode -- regardless of its stability -- should be categorized as
acoustic or ITA. The method proposed does not rely on any parametric sweep, but
on the angle relating the velocity phasors across the flame. This method of
categorization reveals distinct regions in the complex plane where acoustic and
ITA eigenfrequencies are localized. Additionally, we analyze the medium
oscillation at the flame location to construct a physically intuitive
understanding of the proposed categorization method.
