By Jacob Benesty, Jingdong Chen
Though noise aid and speech enhancement difficulties were studied for no less than 5 many years, advances in our knowing and the improvement of trustworthy algorithms are extra vital than ever, as they aid the layout of adapted strategies for essentially outlined functions. during this paintings, the authors suggest a conceptual framework that may be utilized to the various various points of noise aid, supplying a uniform procedure
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. in addition, the derivation of optimum filters is simplified, as are the functionality measures used for his or her evaluation.
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Additional info for A Conceptual Framework for Noise Reduction
In this chapter, we approach this problem with the widely linear theory in the time domain, where both the temporal and spatial information is exploited. 1 Signal Model In this study, we consider the signal model in which 2M microphones1 capture a source signal convolved with acoustic impulse responses in some noise ﬁeld. The signal received at the ith microphone is then expressed as yr,i (t) = gi (t) ∗ s(t) + vr,i (t) = xr,i (t) + vr,i (t), i = 1, 2, . . 1) where gi (t) is the acoustic impulse response from the unknown speech source, s(t), location to the ith microphone, ∗ stands for linear convolution, and vr,i (t) is the additive noise at microphone i.
27) is the residual interference. We observe that the estimate of the desired signal at time t is the sum of three terms that are mutually uncorrelated. 31) Φxd = φx1 ρxx1 ρH xx1 is the correlation matrix (whose rank is equal to 1) H of xd (t), and Φxi = E xi (t)xH i (t) , Φx = E x(t)x (t) , and Φv = E v(t)vH (t) are the correlation matrices of xi (t), x(t), and v(t), respectively. 25) that the objective of our noise reduction problem is to ﬁnd optimal ﬁlters that can minimize the eﬀect of xri (t) + vrn (t) while preserving the desired signal, x1 (t).
Therefore, we deﬁne the subband and fullband speech quality indices as 38 4 Single-Channel Noise Reduction in the STFT Domain φVrn (k, n) φV (k, n) hH (k, n)Φv (k, n)h(k, n) , k = 0, 1, . . 48) and υq [h(:, n)] = = = K−1 k=0 φVrn (k, n) K−1 k=0 φV (k, n) K−1 H k=0 h (k, n)Φv (k, n)h(k, n) K−1 k=0 φV (k, n) K−1 k=0 φV (k, n)υq [h(k, n)] . 49) The speech quality indices are also expected to be upper bounded by 1 for optimal ﬁlters. Low values of the speech quality indices imply a good signal quality.