Instantaneous Frequency Estimation of Discrete Time Signals

The classical concept of instantaneous frequency, obtained by differentiating the instantaneous phase is one of the most used approaches. Nonlinear signals usually have nonlinear and nonstationary behavior. Revealing hidden properties of time discrete signals could be important in understanding specific phenomena or processes. This paper uses simulated signals to prove the utility of instantaneous frequency estimation in dedicated signal processing. The procedure is based on empirical mode decomposition of the signal into monocomponents. The Hilbert transform of these monocomponents reveals they instantaneous frequencies. There are certain mathematical requirements and limitations for signals that the proposed procedure could perform proper instantaneous frequency estimation. The used signals are artificial and the procedure is carried out in MATLAB

Adaptive time-frequency distribution for accurate representation of radar signals

Electronic Support is one of the key elements in electronic warfare where the main interest is to detect and classify emitted radar signals. Quadratic time-frequency distribution (TFD) is often used to represent this type of signal due to its high resolution representation in time and frequency. However, it is greatly affected by the cross-terms which cause inaccurate signal interpretation. The purpose of this study is to design a cross-term suppression technique for a non-cooperative environment where the exact signal characteristics are unknown. A new adaptive directional ambiguity function Wigner-Ville distribution (ADAF-WVD) is developed to adaptively estimate the kernel parameters based on the ambiguity properties of a signal. Two adaptive procedures, which are the Doppler-lag block searching and the ambiguity domain energy concentration estimation are developed to separate the auto-term from the cross-term in the ambiguity domain. ADAF-WVD measures the energy level of the signal in the ambiguity domain to distinguish between the auto-terms and cross-terms. Four radar signal types are used to verify the accuracy of the time-frequency representation (TFR): simple pulse, Costas coded, pulsed linear frequency modulation and continuous wave linear frequency modulation. Accurate TFRs are produced for most of the signal as low as at signal-to-noise ratio (SNR) of -1 dB. The performance of instantaneous frequency estimation is verified using Monte Carlo simulation. Both approaches are proven to be efficient estimators as they meet the requirements of the Cramer-Rao Lower Bound at SNR > 6 dB. The computational complexity of ADAFWVD is four times lower than the adaptive smooth window cross Wigner-Ville distribution. Thus, it has been demonstrated that the developed TFD is an efficient solution for the analysis of radar signals