One-Dimensional Missing-Data APES via Expectation Maximization - Spectral Analysis of Signals: The Missing Data Case - page 56

TABLE 5.1: RMSEs of the Magnitude Estimates Obtained via the
WFFT, GAPES, and MAPES-EM Spectral Estimators

WFF T GAPES MAPES-EM1 MAPES-EM2

Signal 1 0.420 0.175 0.010 0.011

Signal 2 0.417 0.205 0.010 0.010

Signal 3 0.419 0.169 0.010 0.009

Signal 4 0.205 0.164 0.009 0.011

Next, we increase the number of missing samples to 77 (60% of the original
data). The results of WFFT, WFFT GAPES, MAPES-EM 1, and MAPES-
EM2are shown in Figs. 5.5(a)-5.5(d), respectively. The signal amplitudes in the
WFFT spectrum are low presumably due to the small (40%) amount of avail-
able data samples. The artifacts are so high that we can hardly identify the signal
components. GAPES also performs poorly [see Fig. 5.5(b)], as expected. The
MAPES-EM algorithms provide excellent spectral estimates with relatively minor
artifacts.
In our next experiment, we keep the 40% data missing rate but increase the
noise variance to

2
n

σ = 0 . 1 (10 dB higher than in the previous experiments). The

TABLE 5.2: RMSEs of the Phase (Radian) Estimates Obtained via the
WFFT, GAPES, and MAPES-EM Spectral Estimators

WFF T GAPES MAPES-EM1 MAPES-EM2

Signal 1 0.077 0.042 0.021 0.021

Signal 2 0.059 0.038 0.024 0.025

Signal 3 0.099 0.037 0.012 0.013

Signal 4 0.133 0.029 0.022 0.022