Reconstruction of Gapped Missing Samples Based on Instantaneous Frequency and Instantaneous Amplitude Estimation

2021 ◽  
pp. 108429
Author(s):  
Nabeel Ali Khan ◽  
Sadiq Ali
Keyword(s):  
Instantaneous Frequency ◽  
Instantaneous Amplitude ◽  
Amplitude Estimation

Theory of 2-D complex seismic trace analysis

Geophysics ◽  
1996 ◽  
Vol 61 (1) ◽  
pp. 264-272 ◽  
Author(s):  
Arthur E. Barnes
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Hilbert Transform ◽  
Instantaneous Frequency ◽  
Trace Analysis ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Instantaneous Amplitude ◽  
Dip Angle

The ideas of 1-D complex seismic trace analysis extend readily to two dimensions. Two‐dimensional instantaneous amplitude and phase are scalars, and 2-D instantaneous frequency and bandwidth are vectors perpendicular to local wavefronts, each defined by a magnitude and a dip angle. The two independent measures of instantaneous dip correspond to instantaneous apparent phase velocity and group velocity. Instantaneous phase dips are aliased for steep reflection dips following the same rule that governs the aliasing of 2-D sinusoids in f-k space. Two‐dimensional frequency and bandwidth are appropriate for migrated data, whereas 1-D frequency and bandwidth are appropriate for unmigrated data. The 2-D Hilbert transform and 2-D complex trace attributes can be efficiently computed with little more effort than their 1-D counterparts. In three dimensions, amplitude and phase remain scalars, but frequency and bandwidth are 3-D vectors with magnitude, dip angle, and azimuth.

Instantaneous spectral bandwidth and dominant frequency with applications to seismic reflection data

Geophysics ◽  
1993 ◽  
Vol 58 (3) ◽  
pp. 419-428 ◽  
Author(s):  
Arthur E. Barnes
Keyword(s):  
Instantaneous Frequency ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Power Spectra ◽  
Dominant Frequency ◽  
Center Frequency ◽  
Spectral Bandwidth ◽  
Instantaneous Amplitude ◽  
Seismic Reflection Data ◽  
Reflection Data

Fourier power spectra are often usefully characterized by average measures. In reflection seismology, the important average measures are center frequency, spectral bandwidth, and dominant frequency. These quantities have definitions familiar from probability theory: center frequency is the spectral mean, spectral bandwidth is the standard deviation about that mean, and dominant frequency is the square root of the second moment, which serves as an estimate of the zero‐crossing frequency. These measures suggest counterparts defined with instantaneous power spectra in place of Fourier power spectra, so that they are instantaneous in time though they represent averages in frequency. Intuitively reasonable requirements yield specific forms for these instantaneous quantities that can be computed with familiar complex seismic trace attributes. Instantaneous center frequency is just instantaneous frequency. Instantaneous bandwidth is the absolute value of the derivative of the instantaneous amplitude divided by the instantaneous amplitude. Instantaneous dominant frequency is the square root of the sum of the squares of the instantaneous frequency and instantaneous bandwidth. Instantaneous bandwidth and dominant frequency find employment as additional complex seismic trace attributes in the detailed study of seismic data. Instantaneous bandwidth is observed to be nearly always less than instantaneous frequency; the points where it is larger may mark the onset of distinct wavelets. These attributes, together with instantaneous frequency, are perhaps, of greater use in revealing the time‐varying spectral properties of seismic data. They can help in the search for low frequency shadows or in the analysis of frequency change due to effects of data processing. Instantaneous bandwidth and dominant frequency complement instantaneous frequency and should find wide application in the analysis of seismic reflection data.

Research on the Parameter Measurement Methods of Digital Channelized Reconnaissance Receiver

2011 ◽  
Vol 346 ◽  
pp. 578-583
Author(s):  
Hai Qing Jiang ◽  
Mei Guo Gao ◽  
Guo Hong Sun ◽  
Pu Zhao Tang
Keyword(s):  
Instantaneous Frequency ◽  
Pulse Width ◽  
Measurement Method ◽  
Direction Of Arrival ◽  
Measurement Methods ◽  
Parameter Measurement ◽  
Instantaneous Amplitude

The pulse description word (PDW) measurement method of digital channelized reconnaissance receiver was investigated. The parameter measurement flow of digital channelized reconnaissance receiver was introduced. The measurement methods of the instantaneous amplitude, the instantaneous frequency, the pulse width of wideband frequency modulated signal and the direction of arrival (DOA) were discussed in detail, which have been applied to reconnaissance receiver in ESM system successfully.

THE UNIQUENESS OF THE INSTANTANEOUS FREQUENCY BASED ON INTRINSIC MODE FUNCTION

2013 ◽  
Vol 05 (03) ◽  
pp. 1350011 ◽  
Author(s):  
NORDEN E. HUANG ◽  
VINCENT YOUNG ◽  
MENTZUNG LO ◽  
YUNG HUNG WANG ◽  
C. K. PENG ◽  
...  
Keyword(s):  
Instantaneous Frequency ◽  
Phase Function ◽  
Intrinsic Mode Function ◽  
Constructive Method ◽  
Instantaneous Amplitude ◽  
Amplitude Function ◽  
Physical Sense ◽  
Mode Function

It has been claimed that any expression of a(t) cos θ(t) with a(t) as the instantaneous amplitude and cos θ(t) as the carrier varying along with the phase θ(t) could not be uniquely defined. However, based on the fact that a(t) cos θ(t) with all its variational forms have the same numerical value at any given time, we propose the existence of a unique true intrinsic amplitude function ai(t) and phase function θi(t) that ai(t) cos θi(t) satisfying the envelope–carrier relationship is the only expression making physical sense. A constructive method is also presented to find such amplitude-phase pair uniquely from any Intrinsic Mode Function (IMF). As a result, we can treat any IMF in the form of ai(t) cos θi(t) as the unique defined amplitude-phase pair, from which the instantaneous frequency (IF) can also be determined.

GENERALIZED INSTANTANEOUS AMPLITUDE AND FREQUENCY FUNCTIONS AND THEIR APPLICATION FOR PITCH FREQUENCY DETERMINATION

1995 ◽  
Vol 05 (02) ◽  
pp. 145-165 ◽  
Author(s):  
RUDOLF FÖLDVÁRI
Keyword(s):  
Instantaneous Frequency ◽  
Signal To Noise Ratio ◽  
Frequency Function ◽  
Instantaneous Amplitude ◽  
Time Frequency ◽  
Frequency Representation ◽  
Pitch Frequency ◽  
True Time ◽  
Human Hearing ◽  
Frequency Detector

By defining an instantaneous frequency function it could be shown that if a signal is analytic, instantaneous frequency is analytic, too. A generalized instantaneous amplitude function could then be introduced which is also analytic in character. These functions — apart from an arbitrary constant phase — uniquely define the analytic time function. It could be proved that the transformation gives a true time-frequency representation which fulfills all the necessary requirements. Moreover, the application of instantaneous parameters in connection with a Zwicker's filter bank makes it possible even to model human hearing. By applying a simplified hearing model, an efficient pitch-frequency detector able to decide between voiced-unvoiced signals with the same reliability as visual detection even at a 0 dB signal-to-noise ratio could be developed.

HHT-Based Selection of Optimal Time-Frequency Patterns for Motor Imagery

2013 ◽  
Vol 380-384 ◽  
pp. 3522-3525 ◽  
Author(s):  
Ping Gong ◽  
Min You Chen ◽  
Li Zhang ◽  
Wen Juan Jian
Keyword(s):  
Motor Imagery ◽  
Instantaneous Frequency ◽  
Optimal Time ◽  
Instantaneous Amplitude ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Frequency Components ◽  
Novel Method ◽  
Selection Of

In this paper, a novel method based on Hilbert-Huang transform (HHT) is presented to select optimal timefrequency patterns for single-trial motor imagery electroencephalograph (EEG). The method comprises three progressive steps: 1) employ Empirical Mode Decomposition (EMD) method to decompose EEG signal into a superposition of components or functions called IMFs, and then apply Hilbert transform to the IMFs to calculate the instantaneous frequency and instantaneous amplitude; 2) select the IMFs including the most useful frequency components 3) the optimal timefrequency patterns can be selected according to the instantaneous frequency and instantaneous amplitude of the selected IMFs. After selecting the optimal timefrequency patterns, the features extracted by different methods are classified by Fisher linear discriminator. The results showed that the proposed method could improve the classification accuracy.

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