Synchro-Transient-Extracting Transform for the Analysis of Signals with Both Harmonic and Impulsive Components

Time-frequency analysis (TFA) techniques play an increasingly important role in the field of machine fault diagnosis attributing to their superiority in dealing with nonstationary signals. Synchroextracting transform (SET) and transient-extracting transform (TET) are two newly emerging techniques that can produce energy concentrated representation for nonstationary signals. However, SET and TET are only suitable for processing harmonic signals and impulsive signals, respectively. This poses a challenge for each of these two techniques when a signal contains both harmonic and impulsive components. In this paper, we propose a new TFA technique to solve this problem. The technique aims to combine the advantages of SET and TET to generate energy concentrated representations for both harmonic and impulsive components of the signal. Furthermore, we theoretically demonstrate that the proposed technique retains the signal reconstruction capability. The effectiveness of the proposed technique is verified using numerical and real-world signals

High clarity speech separation using synchro extracting transform

Degenerate unmixing estimation technique (DUET) is the most ideal blind source separation (BSS) method for underdetermined conditions with number of sources exceeds number of mixtures. Estimation of mixing parameters which is the most critical step in the DUET algorithm, is developed based on the characteristic feature of sparseness of speech signals in time frequency (TF) domain. Hence, DUET relies on the clarity of time frequency representation (TFR) and even the slightest interference in the TF plane will be detrimental to the unmixing performance. In conventional DUET algorithm, short time Fourier transform (STFT) is utilized for extracting the TFR of speech signals. However, STFT can provide on limited sharpness to the TFR due to its inherent conceptual limitations, which worsens under noise contamination. This paper presents the application of post-processing techniques like synchro squeezed transform (SST) and synchro extracting transform (SET) to the DUET algorithm, to improve the TF resolution. The performance enhancement is evaluated both qualitatively and quantitatively by visual inspection, Renyi entropy of TFR and objective measures of speech signals. The results show enhancement in TF resolution and high clarity signal reconstruction. The method also provides adequate robustness to noise contamination

An adaptive synchroextracting transform for the analysis of noise contaminated multi-component non-stationary signals

The Synchro-Extracting Transform technique (SET) can capture the changing dynamic in a non-stationary signal which can be applied for fault diagnosis of rotating machinery operating under vary-ing speed or/and load conditions. However, the time frequency representation (TFR) of a signal pro-duced by SET can be affected by noise contained in the signal, which can largely reduce the accuracy of fault diagnosis. This paper addresses this drawback and presents a new extraction operator to im-prove the energy concentration of the TFR of a noise contaminated multi-component signal by using an adaptive ridge curve identification process together with SET. The adaptive ridge curve extraction is deployed to extract the signal components of a multi-component signal via an iterative approach. The effectiveness of the algorithm is verified using one set of simulated noise-added signals and two sets of experimental bearing and gearbox defect signals. The result shows that the proposed technique can accurately identify the fault components from noise contaminated multi-component non-stationary machine defect signals

Drude conductivity of a granular metal

We present a complete derivation of the granular analogue to Drude conductivity using diagrammatic methods. The convergence issues arising when changing the order of momentum and frequency summation are more severe than in the homogeneous case. This is because there are now two momentum sums rather than one, due to the intragrain momentum scrambling in tunnelling events. By careful analytic continuation of the frequency sum, and use of integration by parts, we prove that the system is in the normal (non-superconducting) state, and derive the formula for the granular Drude conductivity expected from Einstein's relation and Fermi's golden rule. We also show that naively performing the momentum sums first gives the correct result, provided that we interpret a divergent frequency sum by analytic continuation using the Hurwitz zeta function.Comment: 18 pages, 5 figure

Multi-Component LFM Signal Parameter Estimation for Symbiotic Chirp-UWB Radio Systems

Symbiotic chirp-ultra wide bandwidth (UWB) radio system (SCURS) is a UWB radio system with the symbiosis of linear frequency modulation (LFM) and orthogonal frequency division multiplexing (OFDM) signals. It has a high data rate and can transmit data on two channels simultaneously. Moreover, multi-component LFM (MCLFM) parameter estimation plays an important role in the demodulation of SCURS. Furthermore, the complex electromagnetic environment also brings impulsive noise. In this paper, a novel parameter estimation method for MCLFM signals based on the fractional Fourier transform-bald eagle search algorithm (FRFT-BES) and synchroextracting short-time fractional Fourier transform-Hough (SSFT-Hough) with alpha-stable noise is proposed. First, we use a nonlinear transformation to eliminate the negative effect of alpha-stable noise on parameter estimation. Second, we combine the improved BES with FRFT to propose FRFT-BES and use it to estimate the frequency modulation rate. Finally, we propose a new time-frequency (TF) transform method with high TF resolution as SSFT, and we combine it with Hough transform (HT) to propose SSFT-Hough to estimate the initial frequency. Frequency modulation rate and initial frequency are widely used in MCLFM signals separation. Simulation results demonstrate that the proposed method performs well in low mixed signal-to-noise ratio (MSNR), and it is superior to existing methods

The W transform with a chirp-modulated window

A high-resolution time-frequency spectrum is desirable for processing and interpreting seismic data. The standard W transform is a method that effectively preserves the resolution in the low-frequency region of the time-frequency spectrum of non-stationary seismic signals. To further increase the energy concentration of the time-frequency spectrum estimated with the standard W transform, we propose to combine the W transform with a chirp-modulated window. The chirp rate in the chirp-modulated window can control the rotation of the window in the time-frequency plane to achieve a better match with the time-frequency spectrum. Unlike the general linear chirplet transform, the chirp rate in the proposed algorithm can be directly determined with the estimated instantaneous frequency. It has been shown that the W transform with a chirp-modulated window maintains the resolution of the time-frequency spectrum and improves the energy concentration around the dominant frequency against noise. To speed up the computational process of the W transform with a chirp-modulated window, we formulate the transform as a matrix-vector multiplication, which can be accelerated by using GPU computations. The application of the proposed algorithm to synthetic and field data shows that the frequency anomalies can be easily identified with the proposed algorithm