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Redundancy, measurable and quantifiable, can be removed in the coder and replaced in the decoder; this process often is referred to as statistical compression. Irrelevancy, on the other hand, referred to as perceptual coding, once removed from the signal cannot be replaced and is lost, irretrievably. This is entirely a subjective process, with each proprietary algorithm using a different psychoacoustic model. Critically perceived signals, such as pure tones, are high in redundancy and low in irrelevancy. They compress quite easily; almost totally a statistical compression process. Conversely, noncritically perceived signals, such as complex audio or noisy signals, are low in redundancy and high in irrelevancy. These compress easily in the perceptual coder, but with the total loss of all the irrelevancy content. Human Auditory System (Psychoacoustics). The sensitivity of the human ear is biased toward the lower end of the audible frequency spectrum, around 3 kHz [16]. At 50 Hz, the bottom end of the spectrum and 17 kHz at the top end, the sensitivity of the ear is down by approximately 50 dB relative to its sensitivity at 3 kHz (Figure E.13). Additionally, very few audio signals music- or speech-based carry fundamental frequencies above 4 kHz. The designers of the predictive range of compression algorithms take advantage of these characteristics of the ear, the structure of audible sounds and the redundancy content of the PCM signal to reduce bit rate. Another well-known feature of the hearing process is that loud sounds mask out quieter sounds at a similar or nearby frequency. This compares with the action of an automatic gain control, turning the gain
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Figure E.13 Generalized frequency response of the human ear. Note how the PCM process captures signals that the ear cannot distinguish. (From [16]. Used with permission.)
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down when subjected to loud sounds, thus making quieter sounds less likely to be heard. For example, as illustrated in Figure E.14, if we assume a 1 kHz tone at a level of 70 dBu, levels of greater than 40 dBu at 750 Hz and 2 kHz would be required for those frequencies to be heard. The ear also exercises a degree of temporal masking, being exceptionally tolerant of sharp transient sounds. It is by mimicking these additional psychoacoustic features of the human ear and identifying the irrelevancy content of the input signal that the transform range of low bit rate algorithms operate, adopting the principle that if the ear is unable to hear the sound then there is no point in transmitting it in the first place.
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Figure E.14 Example of the masking effect of a high-level sound. (From [16]. Used with permission.)
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Quantization. Quantization is the process of converting an analog signal to its representative digital format or, as in the case with compression, the requantizing of an already converted signal [16]. This process is the limiting of a finite level measurement of a signal sample to a specific present integer value. This means that the actual level of the sample may be greater or smaller than the preset reference level it is being compared with. The difference between these two levels, called the quantization error, is compounded in the decoded signal as quantization noise. Quantization noise, therefore, will be injected into the audio signal after each A/D and D/A conversion, the level of that noise being governed by the bit allocation associated with the coding process (i.e., the number of bits allocated to represent the level of each sample taken of
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the analog signal). For linear PCM, the bit allocation is commonly 16. The level of each audio sample, therefore, will be compared with one of 216 or 65,536 discrete levels or steps. Compression or bit rate reduction of the PCM signal leads to the requantizing of an already quantized signal, which will unavoidably inject further quantization noise. It always has been good operating practice to restrict the number of A/D and D/A conversions in an audio chain. Nothing has changed in this regard and now the number of compression stages also should be kept to a minimum. Additionally, the bit rates of these stages should be set as high as practical; put another way, the compression ratio should be as low as possible. Sooner or later, after a finite number of A/D, D/A conversions and passes of compression coding, of whatever type the accumulation of quantization noise and other unpredictable signal degradations eventually will break through the noise/signal threshold, be interpreted as part of the audio signal, be processed as such, and be heard by the listener. Sampling Frequency and Bit Rate. is defined by:
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