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The multitaper reassigned spectrogram for oscillating transients with Gaussian envelopes

Reinhold, Isabella LU and Sandsten, Maria LU (2022) In Signal Processing 198.
Abstract

Joint time-frequency representations are important tools when estimating the instantaneous frequency. The widely used spectrogram is known to have poor energy localisation, which the reassignment method improves. However, the reassignment method is sensitive to noise. In this paper we present a multitaper reassigned spectrogram (MTRS) that is robust to noise and tailored to short duration transient signals. The MTRS is designed for oscillating transients with Gaussian envelopes and uses the Hermite functions as windows. The novel reassignment coordinates needed for the MTRS are derived in this paper. The MTRS localises energy at the instantaneous frequencies of transients, while white Gaussian noise is made flatter by the use of... (More)

Joint time-frequency representations are important tools when estimating the instantaneous frequency. The widely used spectrogram is known to have poor energy localisation, which the reassignment method improves. However, the reassignment method is sensitive to noise. In this paper we present a multitaper reassigned spectrogram (MTRS) that is robust to noise and tailored to short duration transient signals. The MTRS is designed for oscillating transients with Gaussian envelopes and uses the Hermite functions as windows. The novel reassignment coordinates needed for the MTRS are derived in this paper. The MTRS localises energy at the instantaneous frequencies of transients, while white Gaussian noise is made flatter by the use of multiple windows. It is shown that the MTRS is more noise robust compared to reassignment with just one window, and that it improves on the energy localisation of the spectrogram. Thus, our MTRS is sparse, easy to interpret, and well suited for instantaneous frequency estimation, even for signals with overlapping transients and low signal-to-noise ratios.

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organization
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type
Contribution to journal
publication status
published
subject
keywords
Instantaneous frequency, Reassignment method, Robust estimation, Signal detection, Time-frequency analysis
in
Signal Processing
volume
198
article number
108570
publisher
Elsevier
external identifiers
  • scopus:85127736728
ISSN
0165-1684
DOI
10.1016/j.sigpro.2022.108570
language
English
LU publication?
yes
id
e4bdc32c-8567-4453-8824-e5869b604121
date added to LUP
2022-06-14 12:09:49
date last changed
2022-06-14 12:09:49
@article{e4bdc32c-8567-4453-8824-e5869b604121,
  abstract     = {{<p>Joint time-frequency representations are important tools when estimating the instantaneous frequency. The widely used spectrogram is known to have poor energy localisation, which the reassignment method improves. However, the reassignment method is sensitive to noise. In this paper we present a multitaper reassigned spectrogram (MTRS) that is robust to noise and tailored to short duration transient signals. The MTRS is designed for oscillating transients with Gaussian envelopes and uses the Hermite functions as windows. The novel reassignment coordinates needed for the MTRS are derived in this paper. The MTRS localises energy at the instantaneous frequencies of transients, while white Gaussian noise is made flatter by the use of multiple windows. It is shown that the MTRS is more noise robust compared to reassignment with just one window, and that it improves on the energy localisation of the spectrogram. Thus, our MTRS is sparse, easy to interpret, and well suited for instantaneous frequency estimation, even for signals with overlapping transients and low signal-to-noise ratios.</p>}},
  author       = {{Reinhold, Isabella and Sandsten, Maria}},
  issn         = {{0165-1684}},
  keywords     = {{Instantaneous frequency; Reassignment method; Robust estimation; Signal detection; Time-frequency analysis}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Signal Processing}},
  title        = {{The multitaper reassigned spectrogram for oscillating transients with Gaussian envelopes}},
  url          = {{http://dx.doi.org/10.1016/j.sigpro.2022.108570}},
  doi          = {{10.1016/j.sigpro.2022.108570}},
  volume       = {{198}},
  year         = {{2022}},
}