On the local frequency, group shift, and cross-terms in some multidimensional time-frequency distributions: a method for multidimensional time-frequency analysis

Stanković, Srdjan; Stanković, Ljubiša; Uskokovic, Zdravko

doi:10.1109/78.398736

Cited by 37 publications

(24 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The presence of cross-terms, often as twice strength as auto-terms, has limited the use of WD in some practical applications. Several efforts has been done to remove the presence of cross-terms such as low-pass filtering [12], the use of analytic images [10], modified distributions [13], oversampling or assuming certain signal restrictions [14,15]. These techniques however often remove important auto-component data at the same time, which can be self-defeating.…”

Section: Wd Implementationmentioning

confidence: 97%

A 2D Wigner Distribution-based multisize windows technique for image fusion

Redondo¹,

Fischer²,

Šroubek

et al. 2008

Journal of Visual Communication and Image Representation

View full text Add to dashboard Cite

Section: Wd Implementationmentioning

confidence: 97%

A 2D Wigner Distribution-based multisize windows technique for image fusion

Redondo¹,

Fischer²,

Šroubek

et al. 2008

Journal of Visual Communication and Image Representation

View full text Add to dashboard Cite

“…4͑c͔͒ than the other phase-space distributions. Nevertheless, it is very difficult to interpret the PWVD because of some interference terms 14 and negative values. 22 Islands are concentrated on the radiation circle, while interferences are centered between the corresponding islands.…”

Section: Phase Space Of Four Variablesmentioning

confidence: 99%

Phase-space analysis of acoustics fields and its application to waveguide

Teyssandier

Pagneux

Simon

et al. 2005

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

A description of two-dimensional acoustic fields by means of a joint "space-wave number" representation is discussed. A function defined in the phase-space domain (x,y,k(x),k(y)) is associated with a signal which is a function of spatial coordinates (x,y). This paper presents two methods to realize it. The first is to associate with each point (x,y) of the wave field a two-dimensional wave number spectrum (k(x),k(y)), called local spectrum. The second is to process by other coordinates the wave field along an arbitrary direction, introduced in quantum mechanics for the study of classical billiards, and provided by the Birkhoff variables (s,cos phi). Phase-space diagrams are given by quadratic phase-space distributions. Simulations are presented for wave fields in a 2D planar waveguide for a pedagogical point of view with Gaussian beam or point-source excitation, and nonuniform waveguides as a sudden area expansion chamber and an open billiard with a single incoming mode at the entrance of each of them. In these problems, local spectrum and Birkhoff analysis are used in order to identify the structures hidden in the field. The result is the contribution of different wave vectors which contribute to the field value at the analysis point or at a certain section of the boundary, and show complicated structure of the acoustic field like whispering gallery or diffracted waves.

show abstract

“…However, to preserve each auto-term separately, it should correspond to the widest signal component. This can be inappropriate for most S/SF points and can negatively influence the cross-terms reduction [4]. New method for S/SF signal representation: To reduce 2-D WD crossterms (or to completely eliminate them in the case of a non-overlapping signal components), the 2-D convolution in (3) must be terminated outside the 2-D STFT auto-terms' domains, corresponding to regions of support D i ðñ;kÞ; i ¼ 1; .…”

mentioning

confidence: 98%

“…Reduced interference S/SFDs suppress this problem with preservation of marginal properties, but in a computationally very intensive way, even in the 1-D case [3]. The 2-D S-method (2-D SM) [4,5] reduces cross-terms with preservation of the 2-D WD autoterms. However, to preserve each auto-term separately, it should correspond to the widest signal component.…”

mentioning

confidence: 99%

“…1: 2-D WD (2) calculated using FFT routines; 2: 2-D SM using recursive 2-D STFT calculation (that includes two complex summations and one complex multiplication [4]); 3: proposed method with 2-D STFT calculation based on FFT routines; 4: proposed method using recursive 2-D STFT calculation. L 1 , L 2 and L 2 denote L 1 ðñ;kÞ; L 2 ðñ;k; 0Þ; L 2 ðñ;kÞ ¼ sum i1 ¼1;...;L1ðñ;kÞ ðL 2 ðñ;k; þi 1 Þ þ L 2 ðñ;k; Ài 1 ÞÞ=2, respectively.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Signal adaptive method for improved space/spatial-frequency representation

Ivanovic

Jovanovski

2009

Electron. Lett.

View full text Add to dashboard Cite

A signal adaptive method for space/spatial-frequency (S/SF) analysis is proposed. Based on a variable number of operations (only the necessary ones regarding optimal auto-terms presentation) in different S/SF points, it produces auto-terms presentation of the 2-D Wigner distribution, without the cross-terms presence, and optimises calculation complexity (critical performance of the S/SF distributions (S/SFDs)).Introduction: The 2-D short-time Fourier transform (2-D STFT), its energetic version (2-D SPEC) and the 2-D WD are conventional S/ SFDs, defined, in a vector notation, as [1, 2]:

show abstract

On the local frequency, group shift, and cross-terms in some multidimensional time-frequency distributions: a method for multidimensional time-frequency analysis

Cited by 37 publications

References 15 publications

A 2D Wigner Distribution-based multisize windows technique for image fusion

A 2D Wigner Distribution-based multisize windows technique for image fusion

Phase-space analysis of acoustics fields and its application to waveguide

Signal adaptive method for improved space/spatial-frequency representation

Contact Info

Product

Resources

About