By Jacob Benesty, Jingdong Chen
Though noise aid and speech enhancement difficulties were studied for no less than 5 many years, advances in our realizing and the advance of trustworthy algorithms are extra very important than ever, as they help the layout of adapted recommendations for essentially outlined functions. during this paintings, the authors suggest a conceptual framework that may be utilized to the numerous various points of noise aid, providing a uniform strategy
to monaural and binaural noise aid difficulties, within the time area and within the frequency area, and related to a unmarried or a number of microphones. furthermore, the derivation of optimum filters is simplified, as are the functionality measures used for his or her evaluation.
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Extra resources for A Conceptual Framework for Noise Reduction
65) show how the subband NMSEs and the diﬀerent subband MSEs are implicitly related to the subband performance measures. We are only interested in complex ﬁlters for which Ji [iid (k, n)] ≤ Ji [h(k, n)] < Ji [0L×1 (k, n)] , Jq [0L×1 (k, n)] < Jq [h(k, n)] < Jq [iid (k, n)] . 69) h (k, n)Φin (k, n)h(k, n) < 1. 71) 2 hH (k, n)Φin (k, n)h(k, n) , φV (k, n) where μ(k, n) is a positive real number allowing this compromise. 5 Optimal Filters By minimizing Jμ [h(k, n)] [eq. 71)] with respect to h(k, n), we ﬁnd the complex optimal ﬁlter: ho,μ (k, n) = μ(k, n) μ(k, n)ρxX (k, n)ρH xX (k, n) + −1 Φin (k, n) φV (k, n) ρxX (k, n).
7) where x(t) and v(t) are deﬁned in a similar way to y(t). 10) are the correlation matrices of x(t) and v(t), respectively. 2), we deal with complex random variables. A very important statistical characteristic of a complex random variable (CRV) is the so-called circularity property or lack of it (noncircularity) , . A zero-mean CRV, z, is circular if and only if the only nonnull moments and cumulants are the moments and cumulants constructed with the same power in z and z ∗ , . , E |z|2 = 0.
Reduction performance. Comparing Figs. 2, we can see that varying the forgetting factor αv can help optimize the performance even when the noise is stationary. 0 αy (= αv ) Fig. 2 Fullband performance of the MVDR ﬁlter for diﬀerent values of the ﬁlter length, L, as a function of the forgetting factor αy (= αv ) in the white Gaussian noise. The window size is K = 64 (8 ms) with a 75% overlap and the fullband input SNR is 10 dB. optimized separately in an iterative way, which will be left to the reader’s investigation.
A Conceptual Framework for Noise Reduction by Jacob Benesty, Jingdong Chen