Millisecond and binary pulsars as nature's frequency standards - III. Fourier analysis and spectral sensitivity of timing observations to low-frequency noise
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Millisecond and binary pulsars are the most stable natural frequency standards which allow the introduction of modified versions of universal and ephemeris time scales based on the intrinsic rotation of pulsar and on its orbital motion around the barycentre of a binary system. The measured stability of these time scales depends on numerous physical phenomena which affect the rotational and orbital motion of the pulsar and observer on the Earth, perturb the propagation of electromagnetic pulses from the pulsar to the observer, and bring about random fluctuations in the rate of time measured by an atomic clock used as a primary time reference in timing observations. Over long time intervals the main reason for the instability of the pulsar time scales is the presence of correlated, low-frequency timing noise in residuals of times of arrivals (TOA) of electromagnetic signals from the pulsar which has both astrophysical and geophysical origins. Hence, the timing noise can carry important physical information about the interstellar medium, the interior structure of the pulsar, stochastic gravitational waves coming from the early universe and/or binary stars, etc. Each specific type of low-frequency noise can be described in a framework of the power law spectrum model. Although data processing of pulsar timing observations in the time domain seems to be the most imformative, it is also important to know to which spectral bands single and binary pulsars, considered as detectors of the low-frequency noise signal, are the most sensitive. A solution to this problem may be reached only if the parallel processing of timing data in the frequency domain is fulfilled. This requires a development of the Fourier analysis technique for an adequate interpretation of data contaminated by the correlated noise with the noise spectrum which is divergent at low frequencies. The given problem is examined in the present article.