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The design of high-resolution and cross-term (CT) free time-frequency distributions (TFDs) has been an open problem. Classical kernel based methods are limited by the trade-off between resolution and CT suppression, even under optimally derived parameters. To break the current limitation, we propose a data-driven model directly based on Wigner-Ville distribution (WVD). The proposed data-driven high-resolution TFD (DH-TFD) includes several stacked multi-channel convolutional kernels. Specifically, convolutional layers with skipping operators are utilized to learn coarse features, while a weighted block is employed to refine these features independently in both channel and spatial dimensions. By doing so, CTs can be effectively eliminated while maintaining a high resolution. Numerical experiments on both synthetic and real-world data confirm the superiority of the proposed DH-TFD in simultaneously extracting and representing a target signal over state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Time-frequency representation (TFR) plays a significant role in interpreting and analyzing nonstationary multi-mode signals. However, currently, it is still challenging to handle multi-mode signals with closely-spaced or spectrally-overlapped instantaneous frequencies (IFs), especially under low signal-to-noise ratio (SNR) conditions. To address this issue, we propose an enhanced TFR and mode decomposition (ETFR-MD) method, which is especially suitable to represent and decompose multi-mode signals with such complex IFs. The proposed ETFR-MD method exploits both the IFs and instantaneous amplitudes (IAs) of the signal under investigation. First, we design an initial IF estimation method to deal with overlapped IFs. Then, a low-complexity mode enhancement scheme is proposed so that the enhanced IFs could better fit the underlying IF laws. After that, three alternatives, i.e., short-time Fourier transform (STFT) coefficients, de-chirping, and intrinsic chirp component decomposition (ICCD), are considered for IA recovery. Finally, the extracted IAs are combined with the enhanced IFs to reconstruct each signal mode, respectively. To gain more insights, we quantitatively analyze the interference during mode decomposition and derive the optimal window length for mode separation. Experimental results implemented on both simulated and real-world data confirm the superior performance of the ETFR-MD compared with the state-of-the-art solutions. [ABSTRACT FROM AUTHOR]

The detection of the electric network frequency (ENF) in digital recordings is an essential step before the subsequent ENF extraction and forensic analysis. In this letter, we extend the state-of-the-art single-tone time-frequency (TF) domain ENF detector to the multi-tone scenario and propose a multi-harmonic combining (MHC) method, exploiting ENF harmonic components for improved detection performance. To exclude the corrupted components interfering rather than contributing to ENF detection, the proposed detector first performs a pre-screening based on the estimated average subband signal-to-noise ratios (SNRs) to exclude interfering components. Then, with the selected harmonic candidates, a second screening process is applied based on the TF test statistics (TSs), i.e., the variances of observed subband traces. After that, the multi-harmonic components are combined to form the final TS, whose sign determines the final decision. The advantages of the proposed method are illustrated via both synthetic analysis and real-world experimental results using the ENF-WHU dataset. [ABSTRACT FROM AUTHOR]

The electric network frequency (ENF) is an important and extensively researched forensic criterion to authenticate digital recordings, but currently it is still challenging to extract reliable ENF traces from recordings in uncontrollable environments. In this paper, we present a framework for robust ENF extraction from real-world audio recordings, featuring multi-tone harmonic ENF enhancement and graph-based harmonic selection. We first extend the recently developed single-tone robust filtering algorithm (RFA) to the multi-tone scenario and propose a harmonic robust filtering algorithm (HRFA). It can enhance each harmonic component without cross-component interference, thus alleviating the effects of unwanted noise and audio content. In addition, considering the fact that some harmonic components could still be severely corrupted after the HRFA, interfering rather than facilitating ENF estimation, we propose a graph-based harmonic selection algorithm (GHSA), which finds a subset of harmonic components having the overall highest mutual cross-correlation. Noticeably, the harmonic selection problem is found to be equivalent to the maximum weight clique problem in graph theory, and the Bron-Kerbosch algorithm is adopted in the GHSA. With the enhanced and carefully selected harmonic components, both the existing maximum likelihood estimator (MLE) and weighted MLE are incorporated to yield the final ENF estimation results. The proposed framework is evaluated using both synthetic signals and the ENF-WHU dataset consisting of 130 real-world audio recordings, demonstrating its advantages over both the existing single- and multi-tone competitors. This work further improves the applicability of the ENF as a forensic criterion in real-world situations. [ABSTRACT FROM AUTHOR]

In electric network frequency (ENF) based audio forensics, the ENF signal captured in a questioned audio recording is estimated and analyzed for authentication purposes. However, the captured ENF signal is usually contaminated by very strong noise and interference. In this paper, we propose a robust filtering algorithm (RFA) for ENF signal enhancement in audio recordings, which could effectively suppress the additive noise and facilitate subsequent ENF estimation, especially in practical low signal-to-noise ratio (SNR) situations. The proposed algorithm encodes the time domain expression of the preprocessed audio signal (ENF signal plus noise) as the instantaneous frequencies (IFs) of an analytical sinusoidal frequency modulated (SFM) signal. Then, a kernel function is utilized to generate a sinusoidal time-frequency distribution (STFD) whose peaks correspond to the IFs of the analytical signal, i.e., the denoised ENF signal. It is then proven that finding the STFD peaks is equivalent to finding the averaged phases of the kernel function if the additive noise is a zero mean wide sense stationary (WSS) process. The RFA serves as a noise reduction mechanism yielding improved SNR at the filter output. Combined with generic frequency estimation methods, ENF extraction accuracy could be substantially improved with the use of the proposed RFA than without using it. Both synthetic and experimental results are provided to illustrate the effectiveness of our proposal. Reliable ENF extraction could be achieved under noise level down to −20 dB SNR, and the RFA is suitable for a wide range of ENF-based forensic applications. [ABSTRACT FROM AUTHOR]

This paper considers the problem of estimating multiple frequency hopping signals with unknown hopping pattern. By segmenting the received signals into overlapped measurements and leveraging the property that frequency content at each time instant is intrinsically parsimonious, a sparsity-inspired high-resolution time-frequency representation (TFR) is developed to achieve robust estimation. Inspired by the sparse Bayesian learning algorithm, the problem is formulated hierarchically to induce sparsity. In addition to the sparsity, the hopping pattern is exploited via temporal-aware clustering by exerting a dependent Dirichlet process prior over the latent parametric space. The estimation accuracy of the parameters can be greatly improved by this particular information-sharing scheme and sharp boundary of the hopping time estimation is manifested. Moreover, the proposed algorithm is further extended to multi-channel cases, where task-relation is utilized to obtain robust clustering of the latent parameters for better estimation performance. Since the problem is formulated in a full Bayesian framework, labor-intensive parameter tuning process can be avoided. Another superiority of the approach is that high-resolution instantaneous frequency estimation can be directly obtained without further refinement of the TFR. Results of numerical experiments show that the proposed algorithm can achieve superior performance particularly in low signal-to-noise ratio scenarios compared with other recently reported ones. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of estimating the instantaneous frequency (IF) of multicomponent radar signals, which are assumed to be frequency-modulated (FM). The difficulties lie in that different FM components which overlap in time-frequency (TF) domain have different time-supports, and their spectral contents may present continuous and stepped IF laws. We propose an IF estimation algorithm by exploiting the combination of TF distributions (TFDs) and image processing techniques. Numerical results are provided to demonstrate desirable capabilities of the proposed algorithm. [ABSTRACT FROM AUTHOR]