By Bernd Iser
Bandwidth Extension of Speech signs presents dialogue on diverse techniques for effective and strong bandwidth extension of speech indications whereas acknowledging the impression of noise corrupted real-world indications. The booklet describes the idea and strategies for caliber enhancement of fresh speech indications and distorted speech indications equivalent to those who have gone through a band difficulty, for example, in a mobile community. difficulties and the respective recommendations are mentioned with regard to various ways. different ways are evaluated and robustness concerns for a real-time implementation are coated in addition. The publication comprises subject matters regarding speech coding, development- / speech reputation, speech enhancement, data and electronic sign processing in general.
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59) leads to the formulation ∞ ci e−jΩi = ln S(ejΩ ) . 59) the cepstral coeﬃcients used in this book are so-called linear predictive cepstral coeﬃcients. As indicated by the name these coeﬃcients are computed on the basis of linear predictive coeﬃcients. 66) z=ejΩ = ln σ − ln (A(z)) z=ejΩ . 69) k=0 P ln 1 − uk z −1 . 70) P P ak z −k = − ln (A(z)) = ln k=0 k=0 ∞ ∞ unk −n z n n=1 P =− n=1 k=0 unk −n z . 65) we observe that the two sums do not have equal limits. This means that the ci are equal to zero for i < 0.
DLR (a, ˆ a) = a ˆ aT Rss ˆ − 1. 125) Within this work this distance measure has been used for codebooks that have been trained on predictor coeﬃcients directly as will be explained in Sect. 1. Since only the index i corresponding to the codebook entry producing the minimum of all distances (and not the minimum distance itself) is needed within a codebook search, it is suﬃcient to evaluate d˜LR (n, i) = ˆ aTi Rss (n)ˆ ai . 126) can be computed very eﬃciently since the autocorrelation matrix Rss (n) has Toeplitz structure.
Rss,n (P ) rss,n ⎤⎡ a1 . . rss,n (P − 1) ⎢ a2 . . rss,n (P − 2) ⎥ ⎥⎢ ⎥ ⎢ .. ⎦⎣ . aP rss,n (P − 1) rss,n (P − 2) . . rss,n (0) Rss,n a ⎤ ⎥ ⎥ ⎥ . 1 Linear Predictive Analysis 23 Solving this equation for the optimal predictor coeﬃcients ai leads to a = R−1 ss,n rss,n . 30) This equation is only solvable for Rss,n being positive deﬁnite and therefore invertible. Since the matrix Rss,n is symmetric and has Toeplitz structure, there exist very eﬃcient algorithms to solve this set of equations [Rabiner 93].
Bandwidth Extension of Speech Signals by Bernd Iser