Time-Frequency Analysis

Novel time-frequency analysis techniques are proposed
for deterministic signals. We show that among all
linear time-frequency representations only the
short-time Fourier transformation (STFT) family
satisfies both the shift-invariance and
rotation-invariance properties in time,
frequency and all fractional Fourier domains. The
time-frequency domain localization by STFT is
characterized by introducing a novel generalized
time-bandwidth product (GTBP) definition, which is an
extension of the time-bandwidth product on the
fractional Fourier domains. GTBP provides a
rotation-independent measure of compactness for
mono-component signals. The GTBP optimal STFT is a
well-localized and high resolution time-frequency
representation providing optimal results for
chirp-like signals that are encountered
in a variety of application areas including radar,
sonar, seismic, and biological signal processing. An
improved GTBP optimal STFT analysis is obtained for
signals with non-convex time-frequency support and
its computationally efficient form is presented.
Finally, we extend these ideas from time-frequency
distributions to joint fractional Fourier domain
representations.

Autorentext

Lutfiye Durak, PhD: Studied EE at Bilkent University, Turkey. Shehas been at KAIST in Korea and at University of Pittsburgh in USA. Assistant professor in the ECE Dept of Yildiz Technical University, Istanbul. Research interests are in time-frequency signal processing, adaptive and statistical signal processing, and communications theory.

Klappentext

Novel time-frequency analysis techniques are proposedfor deterministic signals. We show that among alllinear time-frequency representations only theshort-time Fourier transformation (STFT) family satisfies both the shift-invariance androtation-invariance properties in time,frequency and all fractional Fourier domains. Thetime-frequency domain localization by STFT ischaracterized by introducing a novel generalizedtime-bandwidth product (GTBP) definition, which is anextension of the time-bandwidth product on thefractional Fourier domains. GTBP provides arotation-independent measure of compactness formono-component signals. The GTBP optimal STFT is awell-localized and high resolution time-frequencyrepresentation providing optimal results forchirp-like signals that are encounteredin a variety of application areas including radar,sonar, seismic, and biological signal processing. Animproved GTBP optimal STFT analysis is obtained forsignals with non-convex time-frequency support andits computationally efficient form is presented.Finally, we extend these ideas from time-frequencydistributions to joint fractional Fourier domainrepresentations.