tailieunhanh - Ebook Digital television technology and standards: Part 2

Part 2 book “Digital television technology and standards” has contents: Frequency analysis and synthesis, closed captioning, subtitling, and teletext, digital television channel coding and modulation, DVB service information and ATSC program and system information protocol, and other contents. | Chapter 8 Frequency Analysis and Synthesis A conversion from time-domain samples to frequency-domain coefficients is the first stage in all of the current standard digital audio compression algorithms. In the MPEG suite of algorithms, this conversion is done using an efficient implementation of a subband filterbank approach, whereas in the Dolby AC-3 algorithm, a cosine transform is used that incorporates time-domain aliasing cancellation. In this chapter, the basic theory behind each of these techniques is explained and the actual implementations used in the standard algorithms are discussed. . THE SAMPLING THEOREM The first stage in digital audio coding is usually the conversion of the analog waveform into a series of digital samples. Probably the most important concept to consider during this conversion is the introduction of aliasing errors. In this section, the mathematical explanation for aliasing, which is more commonly known as the sampling theorem, is introduced. Consider the signal x(t) that has a spectrum X(f) and a bandwidth of B Hz as shown in Figure (a) and (b). If this signal is sampled at a rate of one sample every TS seconds, this is equivalent to multiplying the signal by a unit impulse train with period TS. The sampled signal x(nTS) is given by the following equation: x ( nTS ) x (t ) ∞ ∑ δ (t nT ) S () n ∞ By taking the exponential Fourier series of an impulse train, this equation can be rewritten to give x ( nTS ) 1 TS ∞ ∑ x (t ) e jnω S t () n ∞ Digital Television, by John Arnold, Michael Frater and Mark Pickering. Copyright © 2007 John Wiley & Sons, Inc. 253 254 Chapter 8 Frequency Analysis and Synthesis x(t) 20 10 0 t 0 –10 (a) x(f) 6 4 2 0 –B f 0 B (b) Figure (a) The signal x(t) and (b) its magnitude spectrum |X(f)|. and taking the Fourier transform of x(nTS) gives XS (ω ) 1 TS ∞ ∑ X (ω nω ) S () n ∞ The spectrum of the sampled signal therefore .