A higher order method for concentrating the STFT

D. J. Nelson; D. C. Smith

doi:10.1117/12.618153

A higher order method for concentrating the STFT

D. J. Nelson, D. C. Smith

Research output: Contribution to journal › Conference article › peer-review

4 Scopus citations

Abstract

We present a method for computing the theoretically exact estimate of the instantaneous frequency of a signal from local values of its short time Fourier transform under the assumption that the complex logarithm of the signal is a polynomial in time. We apply the method to the problem of estimating and separating non-stationary components of a multi-component signal. Signal estimation and separation is based on a linear TF model in which the value of the signal at each time is distributed in frequency. This is a significant departure from the conventional nonlinear model in which signal energy is distributed in time and frequency. We further demonstrate by a simple example that IF estimated by the higher order method is significantly better than previously used first order methods.

Original language	English
Article number	59100G
Pages (from-to)	1-8
Number of pages	8
Journal	Proceedings of SPIE - The International Society for Optical Engineering
Volume	5910
DOIs	https://doi.org/10.1117/12.618153
State	Published - 2005
Externally published	Yes
Event	Advanced Signal Processing Algorithms, Architectures, and Implementations XV - San Diego, CA, United States Duration: Aug 2 2005 → Aug 4 2005

Keywords

Adaptive filter
Energy distributions
Interference removal
Linear TF distributions
Linearity
Marginals
Short time fourier transform
Spectrogram
Wigner distribution

Access to Document

10.1117/12.618153

Cite this

@article{a251481a3d84425ba5a779604a2e1e20,

title = "A higher order method for concentrating the STFT",

abstract = "We present a method for computing the theoretically exact estimate of the instantaneous frequency of a signal from local values of its short time Fourier transform under the assumption that the complex logarithm of the signal is a polynomial in time. We apply the method to the problem of estimating and separating non-stationary components of a multi-component signal. Signal estimation and separation is based on a linear TF model in which the value of the signal at each time is distributed in frequency. This is a significant departure from the conventional nonlinear model in which signal energy is distributed in time and frequency. We further demonstrate by a simple example that IF estimated by the higher order method is significantly better than previously used first order methods.",

keywords = "Adaptive filter, Energy distributions, Interference removal, Linear TF distributions, Linearity, Marginals, Short time fourier transform, Spectrogram, Wigner distribution",

author = "Nelson, {D. J.} and Smith, {D. C.}",

year = "2005",

doi = "10.1117/12.618153",

language = "English",

volume = "5910",

pages = "1--8",

journal = "Proceedings of SPIE - The International Society for Optical Engineering",

issn = "0277-786X",

note = "null ; Conference date: 02-08-2005 Through 04-08-2005",

}

TY - JOUR

T1 - A higher order method for concentrating the STFT

AU - Nelson, D. J.

AU - Smith, D. C.

PY - 2005

Y1 - 2005

N2 - We present a method for computing the theoretically exact estimate of the instantaneous frequency of a signal from local values of its short time Fourier transform under the assumption that the complex logarithm of the signal is a polynomial in time. We apply the method to the problem of estimating and separating non-stationary components of a multi-component signal. Signal estimation and separation is based on a linear TF model in which the value of the signal at each time is distributed in frequency. This is a significant departure from the conventional nonlinear model in which signal energy is distributed in time and frequency. We further demonstrate by a simple example that IF estimated by the higher order method is significantly better than previously used first order methods.

AB - We present a method for computing the theoretically exact estimate of the instantaneous frequency of a signal from local values of its short time Fourier transform under the assumption that the complex logarithm of the signal is a polynomial in time. We apply the method to the problem of estimating and separating non-stationary components of a multi-component signal. Signal estimation and separation is based on a linear TF model in which the value of the signal at each time is distributed in frequency. This is a significant departure from the conventional nonlinear model in which signal energy is distributed in time and frequency. We further demonstrate by a simple example that IF estimated by the higher order method is significantly better than previously used first order methods.

KW - Adaptive filter

KW - Energy distributions

KW - Interference removal

KW - Linear TF distributions

KW - Linearity

KW - Marginals

KW - Short time fourier transform

KW - Spectrogram

KW - Wigner distribution

UR - http://www.scopus.com/inward/record.url?scp=30644479084&partnerID=8YFLogxK

U2 - 10.1117/12.618153

DO - 10.1117/12.618153

M3 - Conference article

AN - SCOPUS:30644479084

VL - 5910

SP - 1

EP - 8

JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

SN - 0277-786X

M1 - 59100G

Y2 - 2 August 2005 through 4 August 2005

ER -

A higher order method for concentrating the STFT

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this