It has been challenged that FFT and JTFA give “completely” different results when applied to the same data, and that it is therefore not acceptable to use FFT-based norms when computing z-scores from an instantaneous JTFA (Quadrature Filter) calculation. This is not correct, and the equivalence of the two outputs is demonstrated below. Anyone can repeat this exercise with the BrainMaster software. The BrainAvatar software is used for this demonstration because it automatically produces an Excel file output with 8/second data, showing the instantaneous results. These results show clearly that the two computations, FFT (Fast Fourier Transform) and JTFA (Joint Time-Frequency Analysis), produce equivalent results when the outputs are compared on an “apples to apples” comparison. They further show that the results are stable over extended periods, as shown from the two examples below, taken using 1-minute and 5-minute samples.
In order to produce equivalent results, it is necessary to take into account that the FFT normally produces a “power” measure in “microvolts squared,” and that the JTFA produces a magnitude in “microvolts.” In addition, the windowing used in the FFT epochs is an additional form of attenuation, so that it needs to be compensated for when comparing results. The BrainMaster software is configured so that when we combine the FFT bins (on 1 Hz boundaries) to produce a spectral estimate, it produces a compensated value in “microvolts” that can be compared directly with the JTFA output.