Spectra of data sampled at frequency-modulated rates in application to cardiovascular signals: Part 2. Evaluation of Fourier transform algorithms.

For three direct Fourier transform algorithms we quantified the influence of pulse frequency modulation (PFM) on the spectral estimation of pulse amplitude modulation (PAM). The simulation study is based on sinusoid functions sampled according to a pulse sequence which is the output of an integral pulse frequency modulator (IPFM). One algorithm exactly reproduces the theoretical spectrum derived in Part 1. The other two, including the classical FFT, scale all PFM-induced components in a different way, and in addition, generate higher modulating frequency harmonics. For a PFM depth below 30%, the sum of spurious PFM components is almost linearly dependent on this modulation depth, for all three algorithms. Dividing the effect of PFM in a 'harmonic' and 'aliasing' distortion, we found that the FFT has a relatively high harmonic distortion, compared to an algorithm that takes into account the non-uniform character of the data. In the cardiovascular (worst) case of 30% modulation in heart rate (PFM) at a frequency of 0.1 Hz, the FFT spectrum of beat-to-beat systolic blood pressure variations contains approximately 20% of spurious components caused solely by the modulation in time occurrences of the blood pressure samples. The 'non-uniform' algorithm performs twice as well in this case.