By Lajos Hanzo, F. Clare Somerville, Dr Jason Woodard(auth.)
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Extra resources for Voice and Audio Compression for Wireless Communications, Second Edition
41) for its partial derivatives to become zero. However, if the PDF p(s) is logconcave, that is the second derivative of its logarithm is negative, then the minimum found is a global one. For the frequently encountered uniform (U), Gaussian (G) and Laplacian (L) PDFs the log-concave condition is satisfied but, for example, for Gamma (Γ) PDFs is not. 4. 41) with respect to a specific rn to zero, there is only one term in the sum which depends on the rn value considered, hence we arrive at ∂σq2 =2 ∂rn which leads to tn+1 (s − rn ) · p(s) ds = 0, n = 1, .
The waveform codecs can be further subdivided into time-domain waveform codecs and frequency-domain waveform codecs. 1 Time-domain Waveform Coding The most well-known representative of signal independent time-domain waveform coding is the so-called A-law companded pulse code modulation (PCM) scheme, which has been standardised by the CCITT – now known as the International Telecommunications Union (ITU) – at 64 kbps, using nonlinear companding characteristics to result in near-constant signal-to-noise ratio (SNR) over the total input dynamic range.
Hence, here only a rudimentary interpretation is offered. 6: Speech quality versus bitrate classification of speech codecs. 3. 1 Waveform Coding  Waveform codecs have been comprehensively characterised by Jayant and Noll  and hence the spirit of virtually all treatises on the subject follows their approach. Our discourse in this section is no exception. In general, waveform codecs are designed to be signal independent. They are designed to map the input waveform of the encoder into a facsimile-like replica of it at the output of the decoder.