Spectral decompositions of neural voltage recordings are susceptible to model misspecifications that cause meaningful estimation error

The power spectra of neural voltage recordings vary systematically across brain states and contain both narrowband (rhythmic) and broadband components. A large class of algorithms seeks to parametrize these spectra by separating rhythms from broadband structure, enabling many robust empirical findings. Here we show that two common assumptions underlying popular spectral decomposition methods are incompatible with standard physical and statistical properties of neural recordings: (1) field potentials arise from additive (linear) superposition of biophysical processes, yet several methods implicitly impose multiplicative structure; (2) power estimates are Gamma distributed, with variance proportional to squared power (heteroscedasticity), yet many methods assume Gaussian, homoscedastic errors across frequencies. Using simulations with known ground truth, we demonstrate how these misspecifications bias estimates of rhythm amplitude and broadband height/slope, even under well-behaved conditions. We introduce a corrected decomposition framework, released as the open-source package SL_specdecomp. Relative to the most widely used method, specparam, our approach recovers rhythms and broadband parameters accurately, while specparam decompositions are biased and can confound rhythmic peaks with broadband slope. We then apply these methods to monkey electrocorticography during propofol anesthesia. SL_specdecomp estimates a substantially steeper (more negative) 40--60~Hz broadband slope during anesthesia than during wakefulness, whereas specparam shows a smaller state difference. We show using simulation that the differences in the two decompositions can arise directly from specparam's model misspecification. We also introduce a formal method based on cross-validated log likelihood to compare candidate power spectral decompositions and show that it favors SL_specdecomp. These results suggest that misspecified decompositions can attenuate or distort broadband slope changes in the presence of strong rhythms, and motivate the use of SL_specdecomp as a more reliable decomposition tool.