Minimum Variance - Spectral Analysis: Parametric and Non-Parametric Digital Methods - page 193

1
2

2 2 2

() () ()

A f = A f = A f [7.56]

f − f + f

c c c

()

β CNorm c f should be considered as an integration support, which
adapts to the shape of the frequency response around the frequency f c of the filter,
the band ∆ B being the local equivalent band of the lobe containing this frequency.

The quantity

Figure 7.12 illustrates the CAPNORM estimator on the same signal as that used
for Figures 7.5 and 7.11. The peak of the exponential frequency is sharpened. The
amplitude is always underestimated but with a weaker bias. The strong improvement
is especially on the signal wide band. The estimation is of the true spectrum order,
the oscillations being almost non-existent. The amplitude of the wideband spectrum
is around the theoretical value, which is a considerable gain even in relation to the
MV estimator (see Figure 7.13). The factor

()

β CNorm f is weaker and more stable

c

()

than the normalization factor β NMV f . An experimental statistic study of this

c

estimator is presented in [DUR 00].

.

. . .

.

. . . .

.

Figure 7.12. Spectral analysis by the CAPNORM estimator of the same signal as that used
for Figure 7.5. a) Superposition of the true spectrum (in thin line) and of the CAPNORM
estimation at order 12. b) Normalization factor in Hz. Vertical axis: spectra in dB.
Horizontal axes: frequency in Hz