Block Transform Coding of Presample Filtered Data
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BLOCK TRANSFORM CODING OF PRESAMPLE FILTERED DATA Thomas A. S h u ll Old Dominion U n iv e rs ity , 1984 D ire c to r : Dr. John W. Stoughton This d is s e r ta t io n addresses th e a p p l ic a t io n of non-adap tive t r a n s form coding fo r b i t r a te red u c tio n of presam pled f i l t e r e d d a ta . T rans form coding i s examined as an a l t e r n a t iv e to conven tional pu lse code m odulation (PCM) fo r m u lti-so u rce , f ix ed r a te data a c q u is i t io n system s. T yp ical b and lim iting presample f i l t e r s in tro d u ce redundancy in to th e sequence of d a ta sam ples. L inear tra n sfo rm a tio n of successive N -length blocks of the d a ta sequence and subsequent b inary coding of the r e s u l t in g components is shown to lead to reduced average b i t r a te fo r the same le s s d is to r t io n as PCM. Four B utterw orth f i l t e r s , two corresponding to e ig h t b i t PCM system s, and two corresponding to te n b i t PCM system s, are co n sid ered . The orthonorm al transform s (b ases) examined a re a f i l t e r derived Karhunen-Loueve, a d is c re te co s in e , and a d is c r e te Legendre tran sfo rm . A re fe ren c e fo r th e p rev ious use of the d is c r e te Legendre b a s is fo r tran sfo rm coding i s not known. T ransform ation i s modeled as a bank of b a s is dependent FIR f i l t e r s fo r a n a ly s is . Thus, transform coding i s in te rp re te d in terms of s p e c tr a l energy cap tu re . The magnitude squared t r a n s f e r fu n c tio n of the presample f i l t e r i s assumed to d e fin e the w orst case s p e c tr a l R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. envelope or power s p e c tr a l d en s ity of the sampled f i l t e r o u tp u t. This i s in co rp o ra ted in to th e model to e s ta b l is h an upper bound on th e average component energy fo r the v a rio u s b ases . The bases a re compared a n a ly t ic a l ly using a b i t r a te red u c tio n bound, adapted from Z e lin sk i and N o ll, and energy packing c o n s id e ra tio n s . The a n a ly s is in d ic a te s th a t b i t r a te red u c tio n i s p o ss ib le and th a t la rg e block le n g th s a re not req u ire d . The transfo rm coding s tra te g y fo r N = 16 i s implemented on sim ulated and r e a l d a ta . B it r a te red u c tio n on the o rd er of 25 p e rcen t e s ta b l is h e s m erit fo r the transform coding s tr a te g y . A d d itio n a lly , transform coding i s observed to r e s u l t in le s s d i s to r t io n than PCM fo r s ig n a ls having in te rv a ls of reduced s p e c tr a l a c t iv i t y . R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. DEDICATION This is ded ica ted to my w ife , Sue, and my son, Andy, fo r th e i r and sup p o rt.