Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis

Chen Yun Lin; Li Su; Hau Tieng Wu

doi:10.1007/s00041-017-9523-0

Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis

Chen Yun Lin, Li Su, Hau Tieng Wu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We propose to combine cepstrum and nonlinear time–frequency (TF) analysis to study multiple component oscillatory signals with time-varying frequency and amplitude and with time-varying non-sinusoidal oscillatory pattern. The concept of cepstrum is applied to eliminate the wave-shape function influence on the TF analysis, and we propose a new algorithm, named de-shape synchrosqueezing transform (de-shape SST). The mathematical model, adaptive non-harmonic model, is introduced and the de-shape SST algorithm is theoretically analyzed. In addition to simulated signals, several different physiological, musical and biological signals are analyzed to illustrate the proposed algorithm.

Original language	English (US)
Pages (from-to)	451-505
Number of pages	55
Journal	Journal of Fourier Analysis and Applications
Volume	24
Issue number	2
DOIs	https://doi.org/10.1007/s00041-017-9523-0
State	Published - Apr 1 2018

Keywords

Adaptive non-harmonic model
Cepstrum
De-shape SST
De-shape STFT
Instantaneous frequency
Short-time cepstral transform
Synchrosqueezing transform

ASJC Scopus subject areas

Analysis
General Mathematics
Applied Mathematics

Access to Document

10.1007/s00041-017-9523-0

Cite this

@article{2e9e677987a8441d9c0ba7ea45a963d7,

title = "Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis",

abstract = "We propose to combine cepstrum and nonlinear time–frequency (TF) analysis to study multiple component oscillatory signals with time-varying frequency and amplitude and with time-varying non-sinusoidal oscillatory pattern. The concept of cepstrum is applied to eliminate the wave-shape function influence on the TF analysis, and we propose a new algorithm, named de-shape synchrosqueezing transform (de-shape SST). The mathematical model, adaptive non-harmonic model, is introduced and the de-shape SST algorithm is theoretically analyzed. In addition to simulated signals, several different physiological, musical and biological signals are analyzed to illustrate the proposed algorithm.",

keywords = "Adaptive non-harmonic model, Cepstrum, De-shape SST, De-shape STFT, Instantaneous frequency, Short-time cepstral transform, Synchrosqueezing transform",

author = "Lin, {Chen Yun} and Li Su and Wu, {Hau Tieng}",

note = "Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media New York.",

year = "2018",

month = apr,

day = "1",

doi = "10.1007/s00041-017-9523-0",

language = "English (US)",

volume = "24",

pages = "451--505",

journal = "Journal of Fourier Analysis and Applications",

issn = "1069-5869",

publisher = "Birkhauser Boston",

number = "2",

}

TY - JOUR

T1 - Wave-Shape Function Analysis

T2 - When Cepstrum Meets Time–Frequency Analysis

AU - Lin, Chen Yun

AU - Su, Li

AU - Wu, Hau Tieng

PY - 2018/4/1

Y1 - 2018/4/1

N2 - We propose to combine cepstrum and nonlinear time–frequency (TF) analysis to study multiple component oscillatory signals with time-varying frequency and amplitude and with time-varying non-sinusoidal oscillatory pattern. The concept of cepstrum is applied to eliminate the wave-shape function influence on the TF analysis, and we propose a new algorithm, named de-shape synchrosqueezing transform (de-shape SST). The mathematical model, adaptive non-harmonic model, is introduced and the de-shape SST algorithm is theoretically analyzed. In addition to simulated signals, several different physiological, musical and biological signals are analyzed to illustrate the proposed algorithm.

AB - We propose to combine cepstrum and nonlinear time–frequency (TF) analysis to study multiple component oscillatory signals with time-varying frequency and amplitude and with time-varying non-sinusoidal oscillatory pattern. The concept of cepstrum is applied to eliminate the wave-shape function influence on the TF analysis, and we propose a new algorithm, named de-shape synchrosqueezing transform (de-shape SST). The mathematical model, adaptive non-harmonic model, is introduced and the de-shape SST algorithm is theoretically analyzed. In addition to simulated signals, several different physiological, musical and biological signals are analyzed to illustrate the proposed algorithm.

KW - Adaptive non-harmonic model

KW - Cepstrum

KW - De-shape SST

KW - De-shape STFT

KW - Instantaneous frequency

KW - Short-time cepstral transform

KW - Synchrosqueezing transform

UR - http://www.scopus.com/inward/record.url?scp=85013073055&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85013073055&partnerID=8YFLogxK

U2 - 10.1007/s00041-017-9523-0

DO - 10.1007/s00041-017-9523-0

M3 - Article

AN - SCOPUS:85013073055

SN - 1069-5869

VL - 24

SP - 451

EP - 505

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 2

ER -

Wave-Shape Function Analysis: When Cepstrum Meets Time–Frequency Analysis

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this