Time–frequency analysis

About: Time–frequency analysis is a research topic. Over the lifetime, 5407 publications have been published within this topic receiving 104346 citations.

Instantaneous Spectral Analysis: Time-Frequency Mapping via Wavelet Matching with Application to Contaminated-Site Characterization by 3D GPR

Abstract: Spectral decomposition, by which a time series is transformed from the 1D time/amplitude domain to the 2D time/spectrum domain, has become a popular and useful tool in seismic exploration for hydrocarbons. The windowed, or short-time Fourier transform (STFT) was one early approach to computing the time-frequency (t-f) distribution. This method relies on the user selecting a fixed time window, then computing the Fourier spectrum within the time window while sliding the window along the length of the trace. The primary limitation of the STFT is the fixed window which prevents either time localization of high frequency components (if a long window is used) or spectral resolution of the low-frequency components (if a short window is used).

Optimal Signal Reconstruction Using the Empirical Mode Decomposition

Abstract: The empirical mode decomposition (EMD) was recently proposed as a new time-frequency analysis tool for nonstationary and nonlinear signals. Although the EMD is able to find the intrinsic modes of a signal and is completely self-adaptive, it does not have any implication on reconstruction optimality. In some situations, when a specified optimality is desired for signal reconstruction, a more flexible scheme is required. We propose a modified method for signal reconstruction based on the EMD that enhances the capability of the EMD to meet a specified optimality criterion. The proposed reconstruction algorithm gives the best estimate of a given signal in the minimum mean square error sense. Two different formulations are proposed. The first formulation utilizes a linear weighting for the intrinsic mode functions (IMF). The second algorithm adopts a bidirectional weighting, namely, it not only uses weighting for IMF modes, but also exploits the correlations between samples in a specific window and carries out filtering of these samples. These two new EMD reconstruction methods enhance the capability of the traditional EMD reconstruction and are well suited for optimal signal recovery. Examples are given to show the applications of the proposed optimal EMD algorithms to simulated and real signals.

Wide-area frequency as a criterion for digital audio recording authentication

Abstract: The Electrical Network Frequency (ENF) criterion is a novel method for digital audio recording authentication in the field of forensic science. Both an accurate frequency estimation method and a reliable frequency reference database are the key requirements for this technique. This paper briefly introduces the Frequency Monitoring Network (FNET) at UTK and analyzes the frequency characteristics of the four North American interconnections. Wide-area frequency measurements in each interconnection conform to the Gaussian distribution, but with slightly varied parameters. Short-time Fourier transform (STFT) is adopted to estimate the power system frequency signal embedded in audio files, and a procedure for using the ENF criterion, ranging from signal preprocessing to frequency estimation and frequency data matching, is proposed and then tested by two cases. Results show that the STFT can be used as an accurate ENF extraction method. Furthermore, factors which influence the accuracy of frequency estimation, such as the signal-to-noise ratio (SNR) and the recording hardware, are also discussed.

Adaptive optimal kernel smooth-windowed wigner-ville distribution for digital communication signal

Abstract: Time-frequency distributions (TFDs) are powerful tools to represent the energy content of time-varying signal in both time and frequency domains simultaneously but they suffer from interference due to cross-terms. Various methods have been described to remove these cross-terms and they are typically signal-dependent. Thus, there is no single TFD with a fixed window or kernel that can produce accurate time-frequency representation (TFR) for all types of signals. In this paper, a globally adaptive optimal kernel smooth-windowed Wigner-Ville distribution (AOK-SWWVD) is designed for digital modulation signals such as ASK, FSK, and M-ary FSK, where its separable kernel is determined automatically from the input signal, without prior knowledge of the signal. This optimum kernel is capable of removing the cross-terms and maintaining accurate time-frequency representation at SNR as low as 0 dB. It is shown that this system is comparable to the system with prior knowledge of the signal.