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

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