The discrete-time phase derivative as a definition of discrete instantaneous frequency and its relation to discrete time-frequency distributions

1995 ◽  
Vol 43 (1) ◽  
pp. 341-344 ◽  
Author(s):  
Jechang Jeong ◽  
G.S. Cunningham ◽  
W.J. Williams
Keyword(s):  
Discrete Time ◽  
Instantaneous Frequency ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Phase Derivative ◽  
Definition Of

TRANSIENT TIME-FREQUENCY DISTRIBUTION BASED ON MONO-COMPONENT DECOMPOSITIONS

2013 ◽  
Vol 11 (03) ◽  
pp. 1350022 ◽  
Author(s):  
PEI DANG ◽  
TAO QIAN ◽  
YUAN YUAN GUO
Keyword(s):  
Frequency Distribution ◽  
Instantaneous Frequency ◽  
Characteristic Property ◽  
Transient Time ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Fourier Frequency ◽  
New Type ◽  
Negative Time ◽  
Time Frequency Distribution

In this paper we propose a new type of non-negative time-frequency distribution associated with mono-components in both the non-periodic and periodic cases, called transient time-frequency distribution (TTFD), and study its properties. The TTFD of a mono-component signal can be obtained directly through its analytic instantaneous frequency. The characteristic property of TTFD is its complete concentration along the analytic instantaneous frequency graph. For multi-components there are induced time-frequency distributions called composing transient time-frequency distribution (CTTFD). Each CTTFD is defined as the superposition of the TTFDs of the composing intrinsic mono-components in a suitable mono-components decomposition of the targeted multi-component. In studying the properties of TTFD and CTTFD the relations between the Fourier frequency and analytic instantaneous frequency are examined.

scholarly journals The Wigner-Ville Distribution Based on the Linear Canonical Transform and Its Applications for QFM Signal Parameters Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yu-E Song ◽  
Xiao-Yan Zhang ◽  
Chun-Heng Shang ◽  
Hong-Xia Bu ◽  
Xiao-Yan Wang
Keyword(s):  
Signal To Noise Ratio ◽  
Parameters Estimation ◽  
Accurate Estimation ◽  
Linear Canonical Transform ◽  
Estimation Of Parameters ◽  
Position Information ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Definition Of ◽  
Short Time

The Wigner-Ville distribution (WVD) based on the linear canonical transform (LCT) (WDL) not only has the advantages of the LCT but also has the good properties of WVD. In this paper, some new and important properties of the WDL are derived, and the relationships between WDL and some other time-frequency distributions are discussed, such as the ambiguity function based on LCT (LCTAF), the short-time Fourier transform (STFT), and the wavelet transform (WT). The WDLs of some signals are also deduced. A novel definition of the WVD based on the LCT and generalized instantaneous autocorrelation function (GWDL) is proposed and its applications in the estimation of parameters for QFM signals are also discussed. The GWDL of the QFM signal generates an impulse and the third-order phase coefficient of QFM signal can be estimated in accordance with the position information of such impulse. The proposed algorithm is fast because it only requires 1-dimensional maximization. Also the new algorithm only has fourth-order nonlinearity thus it has accurate estimation and low signal-to-noise ratio (SNR) threshold. The simulation results are provided to support the theoretical results.

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