Differential Encoding

Transcription

1 Dfferetal Ecog C.M. Lu Perceptual Sgal Processg Lab College of Computer Scece Natoal Chao-Tug Uversty Offce: EC538 (03)

2 Iea eucg the yamc rage/varace of coe sequece by ecog sample ffereces

3 Eample Image Hstogram 3 99% [-3, 3] 5 bts/pel (or less)

4 Basc Algorthm 4 Coser sequece: Dffereces: Lossless ecog Smply cog the fferece s suffcet to recover orgal Lossy ecog Quatzer: Quatze sequece: Lossless recostructo: QE: Observato: QE seems to grow over tme s t a cocece?

5 Basc Algorthm () 5 Coser: { } a - q Q ] [ 0 0, 0 ] [ q Q q q ] [ q Q q q q q k k q

6 Basc Algorthm (3) 6 Alteratve cog: 0 ] [ q Q q q ] [ q Q q q q

7 7 Basc Algorthm: Eample

8 8 Dfferetal Ecog Scheme

9 Dfferetal Pulse Coe Moulato (DPCM) 9 p f (,, K, ) 0

10 Precto DPCM 0 σ [( p ) ] E Choce of f ( ) affects σ, however q Depeeces: f ( ) σ f ( ) where q epes o the varace of Fe Quatzato Assumpto: Graularty s fe eough so that Thus, p f (,, K ), 0

11 Lear Prector N s caller orer of the prector N a p ( ) N a E σ F {a }: mmze ( ) [ ] ( ) [ ] 0 0 N N N N a E a a E a σ σ M

12 Lear Prector () N N N a a a ( ( ( ) M ) N ) () () ( N ) where s the autocorrelato fucto: ( k) E[ ] k

13 Lear Prector (3) 3 (0) ) ( ) ( ) ( (0) () ) ( () (0) N N N N L M O M M L L ) ( ) ( ) ( () k k N P a a A M M P. A P A

14 4 Lear Prector Eample: Speech

15 Lear Prector Eample () 5 M k ( ) M k k N a 0.66 N a 0.596, a N 3 a 0.577, a -0.05, a k

16 Lear Prector Eample: Laplaca Quatzato 6 Uform Step szes 4-level: st orer: 0.75, orer: 0.59, 3 r orer: level: st orer: 0.3, orer: 0.4, 3 r orer: 0.5 SN(B) SPE(B) Precto Error M ( ) M M M ( p )

17 Lear Prector Eample: Performace 7 SN creases a lot for orer to orer.

18 Lear Prector Eample: ecostructo 8 Although the recostructe sequece looks lke the orgal, otce that there s sgfcat storto areas where the source output values are small. Orgal ecostructo: 8-level quatzer Laplaca pf 3 r -orer prector

19 Aaptve DPCM 9 Motvato Eve after DPCM, a lot of structure remas the sgal Structure more compresso s possble esuals for 3 r -orer prector

20 Approaches Aaptve DPCM 0 Aaptato ca be apple to Quatzato Precto Observato Quatzato aaptato s epeet of precto Precto aaptato quatzato aaptato Goo precto epes o goo quatzato

21 Aaptve Quatzato DPCM Forwar aaptato Parameters are estmate for each block Trasmtte to recever Overall, ths s coveet DPCM as parameters are ot eplctly avalable (ue to feeback loop) Backwar aaptato Essetally, a verso of the Jayat quatzer Eample: 8-level quatzer, 3 r -orer prector M 0 0.9, M 0.9, M.5, M 3.75

22 Eample: Aaptve Jayat DPCM Orgal Jayat No-aaptve

23 Forwar Aaptve Precto: DPCM-APF 3 Speech cog 8000 sample/sec, 8 samples/block (6ms) Image cog 88 blocks Autocorrelato coeffcets Assumg samples are zero outse block. l meas the l th block. ( l ) ( l ) ( l ) ( k) ( k) ( k) M k M k ( l ) ( k) lm k ( l) M lm ( l) M k, for k > 0 k (k) ca be effcetly ecoe usg partal correlato (parcor) for k < 0 coeffcets

24 Backwar Aaptve Precto: DPCM-APB 4 st -orer prector Aapts wth sample eplacg by to have the cosstet result wth ecoer ) ( ) ( ) ( a a a a α α N th -orer prector j j j j a a X A A ) ( ) ( ) ( ) ( α α A.k.a. Least Mea Square (LMS) ) ( ) ( a a α

25 Delta Moulato (DM) 5 DM DPCM w/ -bt quatzer Samplg frequecy At least twce the hghest frequecy sgal compoet Usually, much hgher

26 6 Lear DM ecostructo

27 Costat Factor Aaptve DM (CFDM) 7 < > 0 f 0 f s Δ Δ Δ f f s s M s s M < < M M M

28 Seco-Orer CFDM 8 Eamples for samples precto

29 Speech Cog 9 Autocorrelato fucto for speech sample Icates a pero of 47 samples Ptch pero Nee a separate compoet to take avatage of t

30 DPCM wth Ptch Prector 30 P : b, τ p τ ptch pero Also: Nose Feeback Cog (NFC) Shapg of QE such that most falls hgh-ampltue peros

31 DPCM wth Ptch Prector Performace 3 DPCM esuals DPCM w/ Ptch Prector esuals

32 G.76 3 ITU recommeato for staar ADPCM Supersees G.7 & G.73 ates: 40/3/4/6 kbts/sec Compresso w.r.t. 8-bt PCM:.6:, :,.67:, 4: Quatzer levels: b - mtrea quatzer Backwar aaptve quatzato A verso of the Jayat quatzer Descrbe terms of a scale factor α k Q[ k /α k ] * α k

33 33 G.76 4kb Quatzer I/O Map

34 G.76: Quatzer Aaptato 34 Base o y(k) log α k Two factors: y u ulocke to hale large fluctuatos (e.g. speech) y l locke for small oes lke ata trasmsso. ( a ( k) ) y ( ) y( k) a ( k) yu( k ) l k a epe o put varace: for speech t s close to y u ( k) 5 [ I ], where W [] log M [], ( ε ) y( k ) εw ε k y l ( k) ( γ ) y ( k ) γ y ( k), γ l u 6

35 G.76: Prector 35 Backwar aaptable base o last recostructe values last 6 quatze ffereces p k ( 6 k) ( k) a k b k Smplfe LMS:

36 Dfferetal Image Cog 36 Coser the prector combato wth -bt uform quatzer & AC bt/pel ecog compare to JPEG at the same rate Dff coe: SNB, PSN3B JPEG: SN33B, PSN4B

37 Dfferetal Image Cog () 37 Improve scheme ecursvely ee quatzer Improve prector Dff coe: SN9B, PSN38B JPEG: SN33B, PSN4B

38 emarks 38 Precto DPCM Aaptve DPCM Delta Moulato Speech Cog Image Cog

39 Homeworks 39 P. 35 3, 4, 6