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Compression of media data is a highly developed research area with many successful applications. The prime examples are the development of the various MPEG compression standards for audio and video compression MPEG1 [6 10], MPEG2 [11 19], and MPEG4 [20 35]. These compression standards have since formed an essential component in the development of Video CD, Digital Versatile Disc (DVD), HDTV broadcasting, and so on. In the following, we brie y review the basic concepts in audio and video compression.

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Audio data are typically encoded in PCM at a certain data width and sampling frequency. For example, Figure 2.1 illustrates the audio data sequence for CD audio, which employs a sampling frequency of 44.1 kHz, with each sample represented by a 16 bit word. Thus, a two-channel audio recording will generate data at a rate of 1.4 Mbps, not an insigni cant number even in today s broadband access networks. Thus, researchers have since developed many audio compression algorithms to reduce the audio bit-rate, with the MP3 [36, 37] being the best known and most widely adopted. In addition to the CD audio format, the industry has recently introduced (two actually) new formats for next-generation audio distribution. The rst one, called DVD audio [38], is

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where M represents the inertia of motor, gears, and load, and R > 0 is a motor damping parameter For convenience, torque and R are scaled so that M = 1 The simulation program in Figure 1-8 sets system parameters and models the servomechanism with two defined-variable assignments (1-5) and (1-8) and three state differential equations (1-6) and (1-9) Control-system designers can then exercise the resulting live mathematical model to observe servo input, output, error, and motor torque while they adjust controller parameters and motor characteristics Desirable parameter combinations must, in some sense, produce small servo errors We can use different test inputs u(t) similar to inputs for the intended application, for example, step inputs, ramps, sinusoids (or noise, as in Section 5-8) Simulations must be repeated with different input amplitudes, since the field saturation makes our model nonlinear Such computer-aided experiments provide some intuitive feel for the control problem and may quickly indicate instability or design errors For objective decision-making, though, we must define and compute numerical error measures These are typically functionals determined by the entire time history of the servo error x(t) u(t) for a given input u(t) One can, for instance, record the maximum of the absolute error or the squared error, as in Section 2-16c More commonly used error measures are integrals over the error time history We define such measures as extra state variables with zero initial values, for instance,

a natural extension of the PCM format but with a word length of up to 24 bits and sampling frequency of up to 192 kHz. The medium is also capable of encoding surround sound with up to 6 discrete channels of audio. The resultant data generation rate therefore can reach up to 27 Mbps. Due to the extremely high data rate, the DVD audio standard supports the use of a lossless compression algorithm called Meridian Lossless Packing (MLP) to reduce the data rate by approximately a factor of 2. Apart from the DVD audio standard, another industry group has introduced a second standard targeted to replace the CD format Super Audio CD (SACD) [38]. Unlike CD and DVD audio, SACD employs 1-bit delta sigma modulation at a sampling rate of 2.8 Mhz. Extensive noise shaping is then employed to achieve very high signal-to-noise ratio and wide frequency response performance. Again the standard supports surround sound of up to 6 channels, resulting in a raw data rate of up to 16.9 Mbps. The standard also includes a lossless compression algorithm called Direct Stream Transfer (DST) to reduce the data rate by approximately a factor of 2. It is worth noting that both of the emergent audio formats employ only lossless compression that does not discard any audio information in the compression process. This is clearly done to preserve the highest audio quality, which is one of the major advantages of the new formats. Nevertheless, the resultant data rate even at compressed format is still very substantial, and thus whether lossy compression can be employed to reduce the bit-rate further and yet achieve audio quality superior to the standard CD will be an interesting area of research.

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