DSP 2m Unit1-Unit 5 With Answer

8/17/2019 DSP 2m Unit1-Unit 5 With Answer

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5.1 SYLLABUS

EC2312 DIGITAL SIGNAL PROCESSING 3 104

1. INTRODUCTION 9

Classification of systems: Continuous, discrete, linear, causal, stable, dynamic, recursive,time variance; classification of signals: continuous and discrete, energy and power;Mathematical representation of signals; spectral density; sampling techniques, quantization,quantization error, Nyquist rate, aliasing effect. Digital signal representation.

2. DISCRETE TIME SYSTEM ANALYSIS 9

!transform and its properties, inverse z!transforms; difference equation " #olution by z!transform, application to discrete systems ! #tability analysis, frequency response " onvolution " $ourier transform of discrete sequence " Discrete $ourier series.

3. DISCRETE FOURIER TRANSFORM & COMPUTATION 9

D$% properties, magnitude and phase representation ! Computation of D$% using $$%algorithm " D&% ' D&$ ! $$% using radi( ) " *utterfly structure.

4. DESIGN OF DIGITAL FILTERS 9

$&+ ' &&+ filter realization " arallel ' cascade forms. $&+ design: -indowing%echniques " Need and choice of windows " inear phase characteristics. &&+ design:/nalog filter design ! *utterworth and Chebyshev appro(imations; digital design usingimpulse invariant and bilinear transformation ! -arping, prewarping ! $requencytransformation.

5. DIGITAL SIGNAL PROCESSORS 9

&ntroduction " /rchitecture " $eatures " /ddressing $ormats " $unctional modes !&ntroduction to Commercial rocessors

TOTAL : 45 PERIODS

TEXT BOOKS

0. 1.2. roa3is and D.2. Manola3is, 4Digital #ignal rocessing rinciples, /lgorithmsand /pplications5, earson 6ducation, New Delhi, )778 9 &.

). #. . Mitra, 4Digital #ignal rocessing " / Computer *ased /pproach5, %ata Mc2rawill, New Delhi, )770.

5.2 SHORT UESTIONS AND ANS!ERS

UNIT"I " SIGNALS & SYSTEMS

1. D#$% # S%' ().

/ #ignal is defined as any physical quantity that varies with time, space or anyother independent variables.


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10. D#$% # S,(,% & D+ (-% *+*,#-*

-hen the output of the system depends only upon the present input sample,then it is called static system, otherwise if the system depends past values of input

then it

is

called

dynamic

system

11. D#$% # (;*() *+*,#-.

-hen the output of the system depends only upon the present and past inputsample, then it is called causal system, otherwise if the system depends on futurevalues of input then it is called non!causal system

12. D#$% # S %$,"I (/%( , *+*,#-.

&f y(*% #)#-# ,* ;*# , *,/; , , # >) ? %('/(- $ %* /#,#,%-# *+*,#-

%he basic elements used to construct the bloc3 diagram of discrete time#ystems are /dder, Constant multiplier '@nit delay element.

16. ! (, %* ROC % @"T/( *$ /-

%he values of z for which z " transform converges is called region of convergence


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18. L%*, ( + $ ;/ / #/,%#* $ @"T/( *$ /-.

inearity %ime #hifting $requency shift or $requency translation %ime reversal

1 . ! (, (/# , # %$$#/# , -#, * $ # ();(,% ' % #/*# ",/( *$ /-

artial fraction e(pansion ower series e(pansion Contour integration


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3. L%*, , # / #/,%#* $ DTFT.1. eriodicity2. inearity3. %ime shift4. $requency shift5. #caling6. Differentiation in frequency domain7. %ime reversal8. Convolution9. Multiplication in time domain10. arseval5s theorem

4. ! (, %* , # DTFT $ ; %, *(- )#

%he D%$% of unit sample is 0 for all values of w.

5. D#$% # DFT.D$% is defined as E


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14. D#$% # ROC.

%he value of for which the transform converged is called region of convergence.

15. F% @ ,/( *$ /- $ < = 1 2 3 4

(E9z8.

16. S,(,# , # );,% / #/,+ $ @ ,/( *$ /-.

%he convolution property states that the convolution of two sequences in time domain isequivalent to multiplication of their transforms.

18. ! (, ,/( *$ /- $ < "-=

*y time shifting propertyA/


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4. L%*, , # / #/,%#* $ DFT.

inearity, eriodicity, Circular symmetry, symmetry, %ime shift, $requency shift, comple(conGugate, convolution, correlation and arseval5s theorem.

5. S,(,# L% #(/%,+ / #/,+ $ DFT.

D$% of linear combination of two or more signals is equal to the sum of linear combinationof D$% of individual signal.

6. ! # ( *# ;# # %* ())# %/ ;)(/)+ # #

%he N point discrete time sequence is circularly even if it is symmetric about the point zeroon the circle.

8. ! (, %* , # %,% $ ( *# ;# # , ># %/ ;)(/)+

/n N point sequence is called circularly odd it if is antisymmetric about point zero on thecircle.

. ! + , # /#*;), $ %/ ;)(/ ( )% #(/ );,% %* , *(-#Circular convolution contains same number of samples as that of (


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sequence h ) >7US.

%he number of comple( multiplications required using $$% is N9) log ) N S>9)log ) S> 0U).

#peed improvement factor >7US90U) )0.88

18. ! (, %* , # -(% ( ( ,('# $ FFT

$$% reduces the computation time required to compute discrete $ourier transform.

1 . C() ;)(,# , # ;->#/ $ -;),% )% (,% * ## # % , # () ;)(,% $ DFT ;*% 'FFT ()' /%, - 7%, ;*% ' FFT ()' /%, - 7%, 32" % , *# ;# #.

$or N!point D$% the number of comple( multiplications needed using $$% algorithm is N9) log ) N.$or N 8), the number of the comple( multiplications is equal to 8)9)log ) 8) 0SFT V7.

19. ! (, %* FFT

%he fast $ourier transforms and )7T for )TS!

point and 07)>!point transforms, respectively.

20. H 7 -( + -;),% )% (,% * ( ( %,% * (/# /# ;%/# , - ;,# N" % , DFT;*% ' /# % "2 FFT

%he number of multiplications and additions required to compute N!point D$% using redi(!) $$% are N log ) N and N9) log ) N respectively.


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21. ! (, %* -#( , >+ /( % "2 FFT%he $$% algorithm is most efficient in calculating N!point D$%. &f the number of output

points N can be e(pressed as a power of ), that is, N ) M, where M is an integer, %hen thisalgorithm is 3nown as radi(!s $$% algorithm.

22. ! (, %* ( # %-(,% "% ",%-# ()' /%, -

Decimation!in!time algorithm is used to calculate the D$% of a N!point #equence. %heidea is to brea3 the N!point sequence into two sequences, the D$%s of which can becombined to give the D$% of the original N!point sequence. &nitially the N!point sequenceis divided into two N9)!point sequences ( e


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UNIT"I " DESIGN OF DEGITAL FILTER

1= D#$% # IIR $%),#/

&&+ filter has &nfinite &mpulse +esponse.

2= ! (, (/# , # (/% ;* -#, * , #*%' IIR $%),#/* /ppro(imation of derivatives &mpulse invariance *ilinear transformation.

3= ! % $ , # -#, * + ; /#$#/ $ / #*%' % ' IIR $%),#/* ! +

*ilinear transformation is best method to design &&+ filter, since there is no aliasing init.

4= ! (, %* , # -(% / >)#- $ >%)% #(/ ,/( *$ /-(,%

$requency warping or nonlinear relationship is the main problem of bilinear transformation.

5= ! (, %* /#7(/ % '

rewarping is the method of introducing nonlinearly in frequency relationship tocompensate warping effect.

6= S,(,# , # $/# ;# + /#)(,% * % % >%)% #(/ ,/( *$ /-(,%

Ω ) tan %)% #(/ ,/( *$ /-(,%

%he GΩ a(is of s!plane is mapped on the unit circle in z!plane in bilinear transformation

= ! #/# )#$, ( *% # ( /%' , ( *% # (/# -( # % " )( # % >%)% #(/,/( *$ /-(,%

eft hand side !! &nside unit circle+ight hand side! outside unit

9= ! (, %* , # $/# ;# + /#* *# $ B;,,#/7 /, $%),#/

*utterworth filter has monotonically reducing frequency response.

10= ! % $%),#/ ( / %-(,% (* /% )#* % %,* /#* *#

Chebyshev appro(imation has ripples in its pass band or stop band.

11= C( IIR $%),#/ ># #*%' # 7%, ;, ( () ' $%),#/*

Kes. &&+ filter can be designed using pole!zero plot without analog filters


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12= ! (, %* , # ( ( ,('# $ #*%' % ' IIR F%),#/* ;*% ' )#" #/ ) ,*

%he frequency response can be located e(actly with the help of poles and zeros.

13= C - (/# , # %'%,() ( ( () ' $%),#/.

Digital flter Analog flter

i) Operates on digitalsamples of the signal.ii) It is governed !linear di"eren#ee$%ation. iii) It #onsistsof adders& m%ltipliersand dela!simplemented in digitallogi#. iv) In digital'lters the 'lter#oe(#ients aredesigned to satisf! the

desired fre$%en#!response.

i) Operates on analogsignals. ii) It isgoverned ! lineardi"eren#e e$%ation. iii)It #onsists of ele#tri#al#omponents li eresistors& #apa#itorsand ind%#tors. iv) Indigital 'lters theappro*imation pro lemis solved to satisf! thedesired fre$%en#!

response.

14= ! (, (/# , # ( ( ,('#* ( %*( ( ,('#* $ %'%,() $%),#/*

A ( ,('#* $ %'%,() $%),#/* igh thermal stability due to absence of resistors, inductors and capacitors. &ncreasing the length of the registers can enhance the performance characteristics li3e

accuracy, dynamic range, stability and tolerance. %he digital filters are programmable. Multiple(ing and adaptive filtering are possible.

D%*( ( ,('#* $ %'%,() $%),#/* %he bandwidth of the discrete signal is limited by the sampling frequency. %he performance of the digital filter depends on the hardware used to implement the

filter.

15= ! (, %* %- ;)*# % (/%( , ,/( *$ /-(,%

%he transformation of analog filter to digital filter without modifying the impulse responseof the filter is called impulse invariant transformation.

16= O>,(% , # %- ;)*# /#* *# $ %'%,() $%),#/ , //#* , ( ( () ' $%),#/ 7%,%- ;)*# /#* *# (


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poles should lie on the left half of s!plane. $or a stable digital filter the poles should lieinside the unit circle in the z!plane.

19= ! + ( %- ;)*# % (/%( , ,/( *$ /-(,% %* , *% #/# , ># #", " #

&n impulse invariant transformation any strip of width )W9% in the s!plane for values of s! plane in the range +* # T+ #"1 $%),#/*.

B ; , , # / 7 2 / , C # > + * # T + 0 # " 1 i . / l l p o l e d e s i g n . i i . % h e p o l e s l i e o n a c i r c l e i n s ! p l a n e . i i i . % h e m a g n i t u d e r e s p o n s e i s

m a ( i m a l l y f l a t a t t h e o r i g i n a n d m o n o t o n i c a l l y d e c r e a s i n g f u n c t i o n o f Ω .

i v . % h e n o r m a l i z e d m a g n i t u d e r e s p o n s e h a s a v a l u e o f 0 9 √ ) a t t h e c u t o f f f r e q u e n c y Ω c . v . ? n l y f e w p a r a m e t e r s h a s t o b e c a l c u l a t e d t o d e t e r m i n e t h e t r a n s f e r f u n c t i o n . i . / l l p o l e d e s i g n . i i . % h e p o l e s l i e o n a e l l i p s e i n s ! p l a n e . i i i . % h e m a g n i t u d e r e s p o n s e i s e q u i r i p p l e

i n p a s s b a n d a n d m o n o t o n i c a l l y d e c r e a s i n g i n t h e s t o p b a n d . i v . % h e n o r m a l i z e d m a g n i t u d e r e s p o n s e )

h a s a v a l u e o f 0 9 √ < 0 B ε = a t t h e c u t o f f f r e q u e n c y Ω c . v . / l a r g e n u m b e r o f p a r a m e t e r s h a s t o b e c a l c u l a t e d t o d e t e r m i n e t h e t r a n s f e r

I I R $ % ) , # / 0 . ) . 8 . > . % h e s e f i l t e r s c a n b e e a s i l y d e s i g n e d t o h a v e p e r f e c t l y l i n e a r p h a s e .

$ & + f i l t e r s c a n b e r e a l i z e d r e c u r s i v e l y a n d n o n ! r e c u r s i v e l y .

2 r e a t e r f l e ( i b i l i t y t o c o n t r o l t h e s h a p e o f t h e i r m a g n i t u d e r e s p o n s e .

6 r r o r s d u e t o r o u n d o f f n o i s e a r e l e s s s e v e r e i n $ & + f i l t e r s , m a i n l y b e c a u s e f e e d b a c 3 i s n o t u s e d . % h e s e f i l t e r s d o n o t h a v e l i n e a r p h a s e . & & + f i l t e r s c a n b e r e a l i z e d r e c u r s i v e l y .

e s s f l e ( i b i l i t y , u s u a l l y l i m i t e d t o 3 i n d o f f i l t e r s . % h e r o u n d o f f n o i s e i n & & + f i l t e r s a r e m o r e .


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22. ! (, %* FIR $%),#/*

%he specifications of the desired filter will be given in terms of ideal frequencyresponse d# (;*() ( *,(>)#.

/ digital filter is causal if its impulse response h)#

$&+ filter is always stable because all its poles are at origin.

29. ! (, (/# , # / #/,%#* $ FIR $%),#/

0. $&+ filter is always stable.

). / realizable filter can always be obtained.8. $&+ filter has a linear phase response.>.30. H 7 (*# %*, /,% ( #)(+ %*, /,% * (/# % ,/ ; #

%he phase distortion is introduced when the phase characteristics of a filter is notlinear within the desired frequency band.

S . N 2 .


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%he delay distortion is introduced when the delay is not constant within the desiredfrequency range.

31. !/%,# , # *,# * % ) # % FIR $%),#/ #*%' .

Choose the desired


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%here are three well!3nown design techniques of linear phase $&+ filters. %hey are $ourier series method and window method $requency sampling method. ?ptimal filter design methods.

39. ! (, %* G%>> * # -# < / G%>> * O* %))(,% =

&n $&+ filter design by $ourier series method the infinite duration impulse response istruncated to finite duration impulse response. %he abrupt truncation of impulse response

introduces oscillations in the passband and stopband. %his effect is 3nown as 2ibb5s phenomenon )# (/( ,#/%*,% * $ , # $/# ;# + /#* *# $ 7% 7$; ,%

%he desirable characteristics of the frequency response of window function are %he width of the mainlobe should be small and it should contain as much of the total

energy as possible. %he sidelobes should decrease in energy rapidly as w tends to W.

42. !/%,# , # / # ;/# $ / #*%' % ' FIR $%),#/ ;*% ' $/# ;# +"*(- )% ' -#, .

Choose the desired W9N. %he ma(imum sidelobe magnitude is "08d*. %he sidelobe magnitude does not decrease significantly with increasing w.

45. L%*, , # $#(,;/#* $ FIR $%),#/ #*%' # ;*% ' /# ,( ';)(/ 7% 7.


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%he width of the transition region is related to the width of the mainlobe of windowspectrum.

2ibb5s oscillations are noticed in the passband and stopband. %he attenuation in the stopband is constant and cannot be varied.

46. ! + G%>> * * %))(,% * (/# # #) # % /# ,( ';)(/ 7% 7 ( 7 %, ( >##)%-% (,# / /# ; #

%he 2ibb5s oscillations in rectangular window are due to the sharp transitions from 0to 7 at the edges of window sequence.

%hese oscillations can be eliminated or reduced by replacing the sharp transition bygradual transition. %his is the motivation for development of triangular and cosinewindows.

48. L%*, , # (/( ,#/%*,% * $ FIR $%),#/* #*%' # ;*% ' 7% 7*.

%he width of the transition band depends on the type of window. %he width of the transition band can be made narrow by increasing the value of N

where N is the length of the window sequence. %he attenuation in the stop band is fi(ed for a given window, e(cept in case of aiser

window where it is variable.

4 . C - (/# , # /# ,( ';)(/ 7% 7 ( ( % ' 7% 7.

49. C - (/# , # /# ,( ';)(/ 7% 7 ( (--% ' 7% 7.

50. !/%,# , # (/( ,#/%*,% $#(,;/#* $ ( % ' 7% 7 * # ,/;-.

%he mainlobe width is equal to VW9N.

R # 4 , ( & ' ; ) ( / 7 % & 3 2 7 H ( - - % & ' ! % & 3 2 7

i = % h e w i d t h o f m a i n l o b e i n w i n d o w s p e c t r u m i s > W 9 N i i = % h e m a ( i m u m s i d e l o b e m a g n i t u d e i n

w i n d o w s p e c t r u m i s " 0 8 d * . i i i = & n w i n d o w s p e c t r u m t h e s i d e l o b e

m a g n i t u d e s l i g h t l y d e c r e a s e s w i t h i n c r e a s i n g w .

i v = & n $ & + f i l t e r d e s i g n e d u s i n g r e c t a n g u l a r w i n d o w t h e m i n i m u m s t o p b a n d a t t e n u a t i o n i s ) ) d * . i = % h e w i d t h o f m a i n l o b e i n w i n d o w s p e c t r u m i s V W 9 N i i = % h e m a ( i m u m s i d e l o b e m a g n i t u d e i n

w i n d o w s p e c t r u m i s " > 0 d * . i i i = & n w i n d o w s p e c t r u m t h e s i d e l o b e

m a g n i t u d e r e m a i n s c o n s t a n t .

i v = & n $ & + f i l t e r d e s i g n e d u s i n g h a m m i n g w i n d o w t h e m i n i m u m s t o p b a n d a t t e n u a t i o n i s > > d * .

R # 4 , ( & ' ; ) ( / 7 % & 3 2 7 H ( & & % & ' ! % & 3 2 7

i = % h e w i d t h o f m a i n l o b e i n w i n d o w s p e c t r u m i s > W 9 N i i = % h e m a ( i m u m s i d e l o b e m a g n i t u d e i n


m a g n i t u d e s l i g h t l y d e c r e a s e s w i t h i n c r e a s i n g w . i v = & n $ & + f i l t e r d e s i g n e d u s i n g r e c t a n g u l a r w i n d o w t h e m i n i m u m s t o p b a n d a t t e n u a t i o n i s ) ) d * . i = % h e w i d t h o f m a i n l o b e i n w i n d o w s p e c t r u m i s V W 9 N i i = % h e m a ( i m u m s i d e l o b e m a g n i t u d e i n


m a g n i t u d e d e c r e a s e s w i t h i n c r e a s i n g w . i v = & n $ & + f i l t e r d e s i g n e d u s i n g h a n n i n g

w i n d o w t h e m i n i m u m s t o p b a n d a t t e n u a t i o n i s > > d * .


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%he ma(imum sidelobe magnitude is ">0d*. %he sidelobe magnitude remains constant for increasing w.

51. ! (, %* , # -(, #-(,% () / >)#- % ) # % , # #*%' $ 7% 7 $; ,%

%he mathematical problem involved in the design of window function)# $#(,;/#* $ K(%*#/ !% 7 * # ,/;-. %he width of the mainlobe and the pea3 sidelobe are variable. %he parameter Y in the aiser -indow function is an independent variable that can be

varied to control the sidelobe levels with respect to mainlobe pea3. %he width of the mainlobe in the window spectrum can be varied by varying the length

N of the window sequence.

53. C - (/# , # (--% ' 7% 7 ( K(%*#/ 7% 7.

UNIT " DIGITAL SIGNAL PROCESSOR

1. !/%,# * /, ,#* '# #/() ;/ *# DSP / #** /*

2eneral!purpose digital signal processors are basically high speed microprocessors withhard ware architecture and instruction set optimized for D# operations. %hese processorsma3e e(tensive use of parallelism, arvard architecture, pipelining and dedicated hardwarewhenever possible to perform time consuming operations.2. !/%,# ,#* * # %() ;/ *# DSP / #** /*.

%here are two types of special; purpose hardware.


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%he principal feature of arvard architecture is that the program and the data memories liein two separate spaces, permitting full overlap of instruction fetch and e(ecution.

%ypically these types of instructions would involve their distinct type.0. &nstruction fetch). &nstruction decode8. &nstruction e(ecute

4. B/%#$)+ # )(% (> ;, -;),% )%#/ ( ;-;)(, /.

%he way to implement the correlation and convolution is array multiplicationMethod.$or getting

down these operations we need the help of adders and multipliers. combination of these accumulator and multiplier is called as multiplier accumulator.

5. ! (, (/# , # ,+ #* $ MAC %* ( (%)(>)#

%here are two types M/C5# available0. Dedicated ' integrated). #eparate multiplier and integrated unit

6. ! (, %* -#( , >+ % #)% # ,# % ;#

%he pipeline technique is used to allow overall instruction e(ecutions to overlap. %hat iswhere all four phases operate in parallel. *y adapting this technique, e(ecution speed isincreased.

8. ! (, (/# $ ;/ (*#* ( (%)(>)# % % #)% # ,# % ;#

%he four phases are


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%he total time delay is 0T7 B 077 B 077 B T 8TT ns#ystem throughput is 098TT ns.

10.!/%,# 7 , # (-# $ , # ( /#**% ' - #*.

Direct addressing.&ndirect addressing.*it!reversed addressing.

&mmediate addressing.

i. #hort immediate addressing.ii. ong immediate addressing.Circular addressing.

11.! (, (/# , # % *,/; ,% * ;*# $ / >) ? ,/( *$#/ % C5X P/ #** /*

%he * DD, * D and * D instructions use the *M/+ to point at the source or destination space of a bloc3 move. %he M/DD and M/D# also use the *M/+ to addressan operand in program memory for a multiply accumulator operation

0). B/%#$)+ # )(% (> ;, , # # % (,# /#'%*,#/ ( /#**% ' - #*.

%he dedicated!registered addressing mode operates li3e the long immediateaddressing modes, e(cept that the address comes from one of two special!purpose memory!mapped registers in the C @: the bloc3 move address register %,"/# #/*# ( /#**% ' - #

&n the bit!reversed addressing mode, &NDE specifies one!half the size of the $$%. %hevalue contained in the current /+ must be equal to )n!0, where n is an integer, and the $$%size is )n. /n au(iliary register points to the physical location of a data value. -hen weadd &NDE t the current /+ using bit reversed addressing, addresses are generated in a bit!reversed fashion. /ssume that the au(iliary registers are eight bits long, that /+)represents the base address of the data in memory ;,

%/ ;)(/

( /#**% '

- #.

Many algorithms such as convolution, correlation, and finite impulse response . C*6+)! Circular buffer ) end register T. C*C+ ! Circular buffer control register.

15. !/%,# , # (-# $ (/% ;* (/, $ C5X (/ 7(/#.

0. Central arithmetic logic unit


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>. Memory!mapped registers.T. rogram controller.


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0S. !/%,# * /, ,#* (> ;, (/%, -#,% ) '% ; %, ( ( ;-;)(, / .

%he 8)!bit general!purpose / @ and /CC implement a wide range of arithmetic andlogical functions, the maGority of which e(ecute in a single cloc3 cycle. ?nce an operationis performed in the / @, the result is transferred to the /CC, where additional operations,such as shifting, can occur. Data that is input to the / @ can be scaled by the prescaler.%he following steps occur in the implementation of a typical / @ instruction:0. Data is fetched from memory on the data bus,

). Data is passed through the prescaler and the / @, where the arithmetic is performed,and8. %he result is moved into the /CC.%he / @ operates on 0S!bit words ta3en from data memory or derived from immediateinstructions. &n addition to the usual arithmetic instructions, the / @ can perform *ooleanoperations, thereby facilitating the bit manipulation ability required of high!speedcontroller. ?ne input to the / @ is always supplied by the /CC. %he other input can betransferred from the +62 of the multiplier, the /CC*, or the output of the prescaler./fter the / @ has performed the arithmetic or logical operation, the result is stored in the/CC.

18. !/%,# * /, ,#* (> ;, (/())#) ) '% ; %,.

%he parallel logic unit < @= can directly set, clear, test, or toggle multiple bits incontrol9status register pr any data memory location. %he @ provides a direct logicoperation path to data memory values without affecting the contents of the /CC or the

+62.

1 . ! (, %* -#( , >+ (; %)%(/+ /#'%*,#/ $%)#

%he au(iliary register file contains eight memory!mapped au(iliary registers

DSP 2m Unit1-Unit 5 With Answer

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