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Unformatted text preview: On VSB Modulation Philliph Schniter February 24, 1998 VSB modulation still has wide applications in analog communication, but not much any more for data communication. —Gitlin, Hayes, and Weinstein , 1992 . 1 Introduction The ATSC’s recent adoption of the VSB modulation method for digital cable television trans mission [2] motivates the importance of a good VSBtransmission model. An understanding of the model should provide answers to the following questions: • What is meant by the equivalence between SQAM and VSB? • Does there exist a valid system model with transmitted sequence of the form { Re , Im , Re , Im , ···} ? 2 What is VSB? Vestigial sideband modulation (VSB) is a modulation method which attempts to eliminate the spectral redundancy of pulse amplitude modulated (PAM) signals. It is well known that modulating a real data sequence by a cosine carrier results in a symmetric doublesided passband spectrum. The symmetry implies that one of the sidebands is redundant, and thus removing one sideband with an ideal brickwall filter should preserve the ability for perfect demodulation. As brickwall filters with zero transition bands cannot be physically realized, the filtering actually implemented in attempting such a scheme leaves a vestige of the redundant sideband, hence the name “VSB”. In understanding VSB, consider the use of a Nyquist filter, i.e., a filter which satisfies the Nyquist criterion. Such filters satisfy the time and frequency domain properties g ( t ) : braceleftBigg g ( t ) = 1 t = 0 , g ( t ) = 0 t = nT, n ∈ Z \ (1) 1 = ∞ summationdisplay n =∞ G parenleftbigg j ( ω 2 π T n ) parenrightbigg . (2) The raisedcosine filters, a common family of Nyquist filters, have real positive frequency re sponses locally symmetric about ω = π T and are easy to visualize. For PAM using data sequence { a n } , the following use of the pulse shape: s ( t ) = ∑ n a n g ( t nT ), guarantees no intersymbol interference when sampling the transmitted sequence s ( t ) at 1 the proper instants: s ( nT ) = a n . Here T denotes the baud interval. In the frequency do main, implementing the Nyquist filtering with a raised cosine filter results in a doublesideband spectrum with lowpass cutoff at  ω  = π T ....
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 Spring '11
 TU

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