  The complex-pole frequency representation (COFRE) is introduced in this paper
as a new approach for spectrum modeling in biomedical signals. Our method
allows us to estimate the spectral power density at precise frequencies using
an array of narrow band-pass filters with single complex poles. Closed-form
expressions for the frequency resolution and transient time response of the
proposed filters have also been formulated. In addition, COFRE filters have a
constant time and space complexity allowing their use in real-time
environments. Our model was applied to identify frequency markers that
characterize tinnitus in very-low-frequency oscillations within functional
near-infrared spectroscopy (fNIRS) signals. We examined data from six patients
with subjective tinnitus and seven healthy participants as a control group. A
significant decrease in the spectrum power was observed in tinnitus patients in
the left temporal lobe. In particular, we identified several tinnitus
signatures in the spectral hemodynamic information, including (a.) a
significant spectrum difference in one specific harmonic in the
metabolic/endothelial frequency region, at 7mHz, for both chromophores and
hemispheres; and (b.) a significant differences in the range 30-50mHz in the
neurogenic/myogenic band.
