Optimality property of the Gaussian window spectrogram

A.J.E.M. Janssen

doi:10.1109/78.80783

Optimality property of the Gaussian window spectrogram

A.J.E.M. Janssen

Control Systems

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

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Abstract

It is shown that for any signal x(t) the minimum of over ¿_-8⁸¿_-8⁸ [(t-t_x)² + (f-f_x)²] S_x^(w)(t, f) dt df over all normalized time-windows w(t) is achieved by the Gaussian window w(t) = 2^1/4 exp (-pt²). Here (t_x, f_x) is the center of gravity of the signal x(t), S_x^(w) (t, f) is the spectrogram of x(t) due to the window w(t), and the double integral is a measure of the spread of S_x^(w) (t, f) around (t_x, f_X) in the time-frequency plane.

Original language	English
Pages (from-to)	202-204
Number of pages	3
Journal	IEEE Transactions on Signal Processing
Volume	39
Issue number	1
DOIs	https://doi.org/10.1109/78.80783
Publication status	Published - 1991

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title = "Optimality property of the Gaussian window spectrogram",

abstract = "It is shown that for any signal x(t) the minimum of over ¿-88¿-88 [(t-tx)2 + (f-fx)2] Sx(w)(t, f) dt df over all normalized time-windows w(t) is achieved by the Gaussian window w(t) = 21/4 exp (-pt2). Here (tx, fx) is the center of gravity of the signal x(t), Sx(w) (t, f) is the spectrogram of x(t) due to the window w(t), and the double integral is a measure of the spread of Sx(w) (t, f) around (tx, fX) in the time-frequency plane.",

author = "A.J.E.M. Janssen",

year = "1991",

doi = "10.1109/78.80783",

language = "English",

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pages = "202--204",

journal = "IEEE Transactions on Signal Processing",

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T1 - Optimality property of the Gaussian window spectrogram

AU - Janssen, A.J.E.M.

PY - 1991

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N2 - It is shown that for any signal x(t) the minimum of over ¿-88¿-88 [(t-tx)2 + (f-fx)2] Sx(w)(t, f) dt df over all normalized time-windows w(t) is achieved by the Gaussian window w(t) = 21/4 exp (-pt2). Here (tx, fx) is the center of gravity of the signal x(t), Sx(w) (t, f) is the spectrogram of x(t) due to the window w(t), and the double integral is a measure of the spread of Sx(w) (t, f) around (tx, fX) in the time-frequency plane.

AB - It is shown that for any signal x(t) the minimum of over ¿-88¿-88 [(t-tx)2 + (f-fx)2] Sx(w)(t, f) dt df over all normalized time-windows w(t) is achieved by the Gaussian window w(t) = 21/4 exp (-pt2). Here (tx, fx) is the center of gravity of the signal x(t), Sx(w) (t, f) is the spectrogram of x(t) due to the window w(t), and the double integral is a measure of the spread of Sx(w) (t, f) around (tx, fX) in the time-frequency plane.

U2 - 10.1109/78.80783

DO - 10.1109/78.80783

M3 - Article

SN - 1053-587X

VL - 39

SP - 202

EP - 204

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 1

ER -

Optimality property of the Gaussian window spectrogram

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