Heart rate variability (HRV) is commonly intended as the variation in the heart rate (HR) and it is evaluated in the time and frequency domains with various well known methods. In the present paper, we first consider an abstract model in which the HR is the instantaneous frequency of an otherwise periodic signal such as the electrocardiogram (ECG). Thus the ECG is assumed as a frequency modulated signal, or carrier signal, where HRV or HRVt is a supposed time-domain signal which is frequency modulating the carrier ECG signal around its average frequency. Hence we describe an algorithm able to frequency demodulate the ECG signal to extract a continuous signal HRVt with possibly enough time resolution to analyse fast time-domain variations in the instantaneous HR. After exhaustive testing of the method on simulated frequency modulated sinusoidal signals, we have applied the procedure on actual ECG tracings. The purpose of the work is to eventually use the heart as a kind of biological sensor of the fast activity of the autonomous nervous system (ANS) to study the ANS ultra-short-term event-evoked responses. A few preliminary, not clinical, real examples are also given.