SPECTRA OF DATA SAMPLED AT FREQUENCY-MODULATED RATES IN APPLICATION TO CARDIOVASCULAR SIGNALS .1. ANALYTICAL DERIVATION OF THE SPECTRA

Beat-to-beat cardiovascular signals, e.g a series of systolic pressure values, can be considered as time series which are pulse amplitude mo dulated (PAM) and pulse frequency modulated (PFM). The latter process, due to variations in heart rate, causes the series to become non-unif ormly spaced in time. If PAM is to be quantified by spectral analysis, the influence of PFM must be known. An analytical expression is there fore derived for the spectrum of sinusoids which are sampled according to the output event series of a linear integral pulse frequency modul ator (IPFM). We conclude that two spectral components arise at the dif ference and sum of PFM and PAM frequencies, f(p) +/- f(x,) with amplit udes proportional to the PFM modulation depth. These components appear as a DC component and as a first harmonic if both modulating frequenc ies are equal. In addition, a cluster of spectral components appears a round the mean pulse frequency f(o) (i.e. mean heart rate), at frequen cies f(o)-nf(p) +/- f(x,) which may leak into the signal band. From th ese theoretical considerations, we conclude that the amplitude spectru m of a sinusoidally varying systolic blood pressure series can contain up to 20-30% spurious components, owing to the heart rate modulation process.