Aggregate spectrum

4.9 Aggregate spectrum

Figure 14

shows the two-sided power spectrum of two-way fractional Doppler frequency, S_y2(f), computed from data taken at DSS 25 during the 2001 – 2002 solar opposition (from [19

]). It is derived after using the multi-link plasma corrections and the AMC tropospheric calibrations. The intrinsic frequency resolution of the spectrum is about 3 $×$ 10^–7 Hz. The spectrum in Figure 14

is smoothed to a resolution bandwidth of 3 $×$ 10^–6 Hz to reduce estimation error. Approximate 95% confidence limits for the logarithm of an individual smoothed spectral estimate are indicated [67

, 84

Figure 14:

Power spectrum of the two-way fractional frequency fluctuations (calibrated for plasma and troposphere) for 2001–2002 Cassini solar opposition observations (adapted from [19

]). The spectrum has been smoothed from the intrinsic resolution of the observations to a bandwidth of $≃$ 3 $μ$ Hz to reduce estimation error. Representative 95% confidence limits are indicated.

The low-frequency part of the spectrum in Figure 14 consists of a continuum plus spectral lines between $≃$ 10^–5 – 10^–4 Hz. The lines in the unsmoothed spectrum are near the resolution limit of the 40 day observation; their apparent width in Figure 14 is due to the spectral smoothing used to reduced estimation error. The lowest frequency line is near one cycle/day; the other lines are near harmonics of one cycle/day. Because of the multi-link plasma correction, all random processes contributing to this spectrum are non-dispersive. At frequencies greater than about 1/T₂ there is clear, approximately cosinusoidal, modulation. This is characteristic of positive correlation in the time series at lag $τ$ = T₂, i.e. either antenna mechanical noise or residual tropospheric noise. The level is too large to be dominated by residual tropospheric scintillation, however, and so is interpreted as mechanical noise. Many minima of the mechanical noise transfer function – at odd multiples of 1/(2 T₂) – are easily visible in Figure 14 . The spectrum appears to continue to be dominated by mechanical noise up to $≃$ 0.01 Hz, with the signature of the transfer function being, however, difficult to see on this log plot (and also blurred at high frequencies since T₂ changed with time by about 3% over the course of the 40 day observation.)