IEEE Signal Processing - March 2018 - 149

Frequency (Hz)

results. Reference [15, Fig. 2(c)] obtained improved results
using the synchrosqueezing transform. Even better results have
been obtained by [20] using CEEMD, improved CEEMD [47],
and VMD [19]. The results in [19, Fig. 8] show that VMD gives
the best results. Reference [19, Fig. 8(c)] is comparable to our
Figure 6(b). The same signal components can be recognized:
VMD has better resolution for the Morlet and Ricker wavelets
while CSTAR has better continuity of the cosine waves.

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Marine seismic data

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We first consider a single trace from a marine seismic as shown
in Figure 7(a) with corresponding STFT (window size L w = 99
time samples) shown in (b). The IAF is shown in red. We compare the performance of the CSTAR [35] time-frequency
analysis technique for different parameter settings. The results
are shown in (c)-(f) with window size L w = 3, 15, 21, 35 time
samples and number of complex coefficients L c = 1, 3, 3, 5,
respectively. The results for L w = 35 and L c = 5 show a stable
low-frequency component followed by two to three components of higher frequency. The other results show much more
variability, in particular L w = 3 and L c = 1 give very local
variations of the most dominant modes in the data.
A marine seismic section for the F3 block, North Sea, from
the OpendTect repository is shown in Figure 8, and the corresponding section displaying the IAF is shown in Figure 9. The

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Figure 6. The CSTAR (Marple) time-frequency analysis of the signal in
Figure 5 with window length L w = 61 time samples and with (a) L c = 2
and (b) L c = 3 complex AR coefficients.

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(d)
Lw = 15, Lc = 3

(e)
Lw = 21, Lc = 3

4.0

(f)
Lw = 35, Lc = 5

Figure 7. Time-frequency analysis of (a) a marine seismic trace showing (b) STFT with window size L w = 99 time samples and CSTAR (Marple) with
window length and number of complex coefficients given by (c) L w = 3 and L c = 1, (d) L w = 15 and L c = 3, (e) L w = 21 and L c = 3, and (f) L w = 35
and L c = 5. The instant average frequency is drawn with a red line.
IEEE Signal Processing Magazine

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March 2018

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149



Table of Contents for the Digital Edition of IEEE Signal Processing - March 2018

Contents
IEEE Signal Processing - March 2018 - Cover1
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