Minimum Variance - Spectral Analysis: Parametric and Non-Parametric Digital Methods - page 165

relatively short duration on which the theoretical results established in an asymptotic
context are not applicable.

MV power
order 80

, , ,

Periodogram
Hanning 43 ms
1 segment

,

, ,

Figure 7.3. Spectral analysis of an acoustics real signal (duration 43 ms, 128 samples,
sampling frequency 3,000 Hz) by the MV method (top figure) and by the periodogram method
(bottom figure). Horizontal axes: frequency in Hz. Vertical axes: spectrum in decibels

Initiated by M.A. Lagunas, modifications were proposed and led to estimators
called normalized MV. All these modifications are presented in section 7.5. More
recently, the study of the properties of the MV filters led to a new estimator more
adapted to the analysis of the mixed signals. This estimator, called CAPNORM, is
described in section 7.6.

7.1. Principle of the MV method

Let x ( k ) be a discrete, random, stationary signal sampled at frequency f s = 1/ T s
and of power spectral density S x ( f ). The concept of the MV method, schematized in
Figure 7.4, is based on the construction of a FIR filter at a frequency f c , applied to
the signal x ( k ) according to the following two constraints:
- at frequency f c , the filter transfers the input signal without modification;
- the filter output power of other frequencies than the frequency f c is minimized.