Minimum Variance - Spectral Analysis: Parametric and Non-Parametric Digital Methods - page 177

diminution with the order for a sinusoid at a high signal to noise ratio of 20 dB. This
figure clearly shows that for a high order relative to the signal size (order of 70 for
128 samples), the variance is of the same magnitude order as that of the
periodogram. In Figure 7.2, where we present the analysis of a real signal with a
high order (order of 300), the variance is still weak in relation to that of the
periodogram because the signal size is of 50,000 samples. The effects of the
estimation of the signal autocorrelation matrix are thus sensitive when the ratio of
the order to the signal sample number is of the order of or more than 1/2.

For a complete asymptotic statistic study, the reader will be able to refer to the
works of Liu and Sherman [LIU 98a] and to those of Ioannidis [IOA 94].

MV power

. . . . .

Periodogram
rectangular
1 segment

. . . . .

Figure 7.7. Variance and resolution of the MV estimator for the analysis of a signal made up
of a noisy sinusoid (0.25 Hz, sampling frequency 1 Hz, signal to noise ratio of 20 dB, time
support 128 samples). Top: superposition of spectra estimated by the MV method at the
orders 3, 10, 20, and 70. Bottom: simple non-weighted periodogram. Horizontal axes:
frequency. Vertical axes: spectrum in dB