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the early 1980s brought all of the advantages of digital audio representation, including high fidelity, dynamic range, and robustness These advantages, however, came at the expense of high data rates Conventional CD and digital audio tape (DAT) systems are typically sampled at either 441 or 48 kHz using PCM with a 16-bit sample resolution This results in uncompressed data rates of 7056/768 Kbps for a monaural channel or 141/154 Mbps for a stereo pair at 441/48 kHz, respectively19 Compression techniques other than PCM are now also being sought for high-fidelity music Uniform Quantization In a basic PCM system, input to the quantizer hardware comes in the form of an analog voltage provided by the sampler circuit The simplest approach would be to use a uniform quantization method Here, the range of input voltages is divided into 2n segments, and a unique codeword of n bits is associated with each segment The width of each segment is known as the step size The range, R, of an n-bit quantizer with step size s is R (s)(2n) This implies that if the input voltage were to exceed R, clipping would result To address this issue, logarithmic quantization is used Logarithmic Quantization The goal of logarithmic quantization is to maintain a reasonably constant SNR over a wide range of analog amplitudes Using this technique, the SNR will not vary with incoming signal amplitude To accomplish this, quantize the log value of the signal instead of the incoming signal; for example, for analog values, w, the equation y h k log(w) with h and k constants provides such a logarithmic function21 Logarithmic quantization is a compression process: It reduces the dynamic range of a signal according to a logarithmic function After compression, a reverse process called exponentiation is required to recover a facsimile of the original; the entire cycle is often referred to as companding (for compressing/expanding)22 In North America, a specific logarithmic scheme called m-law is used; in Europe, a similar but not identical approach called A-law is used Both methods employ 8-bit logarithmic quantization with 16 regions and 16 steps per region Adaptive Quantization Speech signals contain a significant amount of redundant information By making use of this fact and by removing some of these redundancies through processing, you can produce data parameters describing the waveform with a lower data rate than otherwise possible and still be able to make a reasonably faithful reconstruction of the original Speech samples generated at the Nyquist rate are correlated from sample to sample (Actually, they remain moderately correlated over a number of consecutive samples) This implies that values of adjacent samples
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Technologies for Packet-Based Voice Applications
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e( j) y( j)
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do not differ significantly Consequently, given some number of past samples, it is possible to predict the value of the next sample with a degree of accuracy You can achieve further reductions in voice bit rate in a waveform-coding environment by employing analysis algorithms that make use of the technique of dynamically adapting the quantizer step size in response to variations in the input signal amplitude The goal is to maintain a quantizer range that is matched to the input signal s dynamic range This discussion has mainly historical value since VoP systems have generally not utilized encoding other than PCM (for example, VoATM) or vocoding (discussed in the next section)23 PCM techniques that adapt step size are referred to as adaptive PCM (APCM) The technique can be applied to both uniform and logarithmic (nonuniform) quantizers There are several adaptation algorithms, but all aim at estimating the slowly varying amplitude of the input signal while balancing the need to increase step size to attain the appropriate range against the worsening SNR that results from larger step sizes For syllabic companding techniques, the quantization characteristics change at about the same rate as syllables occur in speech Other methods use instantaneous companding Yet other methods calculate signal amplitude statistics over a relatively short group of samples and adjust the step size accordingly (for example, feedforward adaptive PCM and feedback adaptive PCM) Some of these adaptive techniques are discussed next In the differential coding technique (also called linear prediction),24 rather than coding the input waveform directly, you can code the difference between that waveform and the one generated from the linear predictions of past quantized samples At sample time j, this encoder codes e( j), the prediction errors at time j, where
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