Digital Signal Processing Reference
In-Depth Information
at
and
()
φ
()
t
are the instantaneous range and instantaneous phase of the real
xt
. The IF is defined as the derivative of instantaneous phase to time t, the
formula is
()
signal
ˆ
()
dd
x t
φ
ω
( )
t
==
arctan
(11)
dt
dt
x t
()
Reference [7] points that in order to make the IF meaningful in practice, the signal
should satisfy the following conditions: (1) Narrowband signal. (2) The average value
of the signal should be 0; (3) the signal should be symmetrical locally. It's found that,
every IMF of the signals satisfies the three conditions above; therefore, by formula
(11), we can calculate the IF of every IMF, and then estimate the Hilbert spectrum of
entire signal.
4
Target Number Recognition Based on HHT
Since the radar echo signal of target could be regarded as linear combination of
several LFM signals which has similar frequencies and same range, we could see a
couple of parallel lines with slope in the Hilbert spectrum of the signal. The number
of the lines in the spectrum is the number of the targets. Fighters are taken as an
example to illustrate the algorithm in this paper.
Without the interference of noise, through the discrete equidistance sampling, the
formula can be written as
2
1
sn
()
=
a
exp [2 (
j
π
fnT
+
μ
(
nT
))
2
+
ϕ
],
n
=
0,1, ,
⋅⋅⋅
N
−
1
(12)
i
0
i
i
i
2
i
=
1
Where
T
is sample interval
N
is the number of the samples. In the relevant
processing time, suppose the signal amplitude
a
of the two fighters is a constant 1,
ϕ
the initial phase
is 0, the coefficients of linear-frequency modulation of two LFM
signals is the same, and the change of the normalization frequency of them are
0.05~0.2 and 0.2~0.35 respectively, N is 512. As in Fig.1, (a) and (b) are the waves
of the two LFM signals above, (c) is the linear combination of (a) and (b).
i
1) Signal decomposition
Use the EMD of the HHT to decompose the echo signals of the formation target, and
get a set of IMF, as in Fig.2. Fig.2 shows that the EMD decompose the signal from
high frequency to low frequency. While, imf1 and imf2 are the LFM signals
contained in the formation target, and imf3~imf8 are the component generated by the
errors caused by EMD.
