Digital Signal Processing Reference
In-Depth Information
Fig. 1.
The waves of the two LFM signals and the wave after they added together
2) Calculating the Hilbert spectrum of the signal
Conduct Hilbert Transform on the IMFs, and get the Hilbert spectrum of the signal, as
shown in Fig.3. As shown in Fig.3, the two diagonals are the IF curves of imf1 and
imf2, due to the range of IF of imf3~imf8 are very low that it's not clear in this figure.
Because there are errors and end effect, jitter appears at the end of the IF curves of
imf1 and imf2; the problem can be solved by smoothing filter with appropriate
bandwidth. The Fig.4 shows the Hilbert spectrum after smooth processing.
Consider
the
noises,
the
observed
signal
could
be
expressed
rn sn wn
()
=+
()
()
wn
is an additive white Gaussian noise with
()
as
,where
sn
.
Fig.5 shows Hilbert spectrum of the signal when signal-to-noise ratio (SNR) is
10dB. It can be seen that the jitter of the IF curves of imf1 and imf2 is enhanced
because of the interference of noise, even some outlier value. In order to eliminate the
effect of noise, 1/3 values of the IF should be selected to fit a straight line, if some
value of the IF exceed the corresponding value of the line by 1.5 times, it should be
regarded as a outlier value.
Then the fitted value is taken as the estimated value. At
last smooth processing is taken on the correcting value of the IF and the result is as
shown in Fig.6.
σ
2
and zero mean, which is independent of the signal
()
variance
3)Target number estimation
Conduct Hough Transform on the Hilbert spectrum of Fig.6 to transform the lines into
corresponding peaks as shown in Fig.7., and get the number of peaks by setting a
specific threshold value. The number of the peaks is the estimator of the target
number.
