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8/14/2019 adsp qb.doc

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PRIST UNIVERSITY (Estd. u/s 3 of UGC Act, 1956)

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2/8

12271H12 A2VANCE2 2IGITA SIGNA PRCESSING TPC 31*

UNIT I 2ISCRETE RAN2+ SIGNA PRCESSING

Discrete Random Processes-, Autocorrelation and Auto covariance matrices. Parseval's

Theorem, Wiener - hintchine Relation- Po!er "#ectral Densit$-Periodo%ram -,Parameter estimation& ias and consistenc$.

UNIT II SPECTRU+ ESTI+ATIN

(on-Parametric )ethods-*orrelation )ethod, Periodo%ram +stimator, PerormanceAnal$sis o +stimators n/iased *onsistent +stimators-0 artlett, lacman Tue$

method.

Parametric )ethods - AR, )A, and AR)A model /ased s#ectral estimation.

UNIT III INEAR ESTI+ATIN AN2 PRE2ICTIN

inear #rediction- 3or!ard and /ac!ard #redictions, - evinson-Dur/in al%orithms.

east mean s4uared error criterion -Wiener ilter or ilterin% and #rediction, 35RWiener ilter and Wiener 55R ilters, Discrete alman ilter

UNIT IV A2APTIVE ITERS

35R ada#tive ilters -ada#tive ilter /ased on stee#est descent method-Widro!-Ho

)" ada#tive al%orithm Ada#tive recursive ilters 655R. R" ada#tive ilters-+8#onentiall$ !ei%hted R"-slidin% !indo! R".

UNIT V +UTIRATE 2IGITA SIGNA PRCESSING

)athematical descri#tion o chan%e o sam#lin% rate - 5nter#olation and Decimation,Decimation /$ an inte%er actor - 5nter#olation /$ an inte%er actor, 3ilter

im#lementation or sam#lin% rate conversion- A##lication to su/ /and codin% and3ilter /an im#lementation o !avelet e8#ansion o si%nals.

REERENCES

1. )onson H.Ha$es, "tatistical Di%ital "i%nal Processin% and )odelin%, 9ohn

Wile$ and "ons, 5nc., "in%a#ore, 2::2.

2. 9ohn ;. Proais, Dimitris ;.)anolais, Di%ital "i%nal Processin% Pearson+ducation, 2::2.

. Dimitris ;.)anolais et.al.,="tatistical and ada#tive si%nal Processin%=,

)c;ra! Hill, (e!$or,2:::.


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UNIT I

PART - A

1. "tate Wiener-hintchine relationshi#.

2. *alculate the P"D o ?ero mean ;aussian !hite noise.

. ist out the conditions or a random #rocess to /e !ide sense stationar$.

@. "tate Parseval=s Theorem.

. What is the condition or a #eriod%ram is as$m#toticall$ un/iasedB

7. Deine the term #eriodo%ram

C. What is autocorrelation unctionB

PART - 0

1. "tate and #rove !iener hintechine relation.

2. *om#ute the #o!er s#ectral densit$ o the se4uence R6n 61,


4/8

UNIT II

PART - A

1. Write the /ias e4uation o modiied Periodo%ram.

2. *om#are AR, )A and AR)A models !ith res#ect to com#le8it$.

. Determine the re4uenc$ resolution o the artlett method o #o!er s#ectrum.

@. Write do!n the /ias e4uation o modiied #eriodo%ram.

. *om#are the #ro#erties o #eriodo%ram and modiied #eriodo%ram

7. Deine the term D3T in s#ectral estimation.

C. What are the limitation o non #arametric methods or #o!er s#ectrum

+stimation.

PART - 0

1. Derive the mean and variance o #o!er s#ectral estimation usin% the arlett method.

2. ;ive the e8#ression or #o!er s#ectral estimatiom o Auto re%ressive #rocess

. ;ive the e8#ression or #o!er s#ectral estimatiom o )ovin% avera%e #rocess.

@. +8#lain the mean and variance o #eriodo%ram /$ derivin% necessar$ e4uation

. +8#lain the Auto re%ressive movin% avera%e #rocess !ith #ro#er e4uation

7. ;ive the various ste#s involved in the #arameter estimation #rocess


5/8

+ P

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C. Write the e8#ression or #o!er s#ectral estimation o modiied avera%e #erido%ram

UNIT III

PART - A

1. Ho! Wiener ilter can /e modiied as linear #redictorB

2. ;ive the order u#date e4uation.

. What are the t!o al%orithms or solvin% the normal e4uationB

@. Deine mathematicall$ or!ard #rediction error ilter.

. Distin%uish /et!een 55R and 55R Wiener ilter.

7. What is the need or ada#tivit$B

C. ;ive some e8am#les o a##lication !here ada#tive ilterin% is used


6/8

PART -0

1. Derive Wiener-Ho# e4uation and ))"+ or the %eneral 35R Wiener ilter2. +8#lain the a##lication o Wiener ilter or noise cancellation !ith suita/le dia%ram

. se eveinson-Dur/in al%orithm to solve the normal e4uation recursivel$ or the m-

ste# or!ard and /ac!ard #redictors.

@. Derive ))"W and s$stem unction or 55R !iener ilter.

. +8#lain ho! the Jule-Waler e4uations can /e solved usin% evinson-Dur/in

al%orithm

7. With suita/le model and assum#tion, esta/lish that Weiner ilters are desi%ned /ased

on the criterion o minimi?in% the mean s4uare error

C. sin% ))"+ criterion derive the e8#ression or o#timal ilter co-eicient


7/8

UNIT IV

PART - A

1. Wh$ )" is normall$ #reerred over R"B

2. What is the relationshi# /et!een the orders o the ilter !ith the ste# si?e in )"

ada#tive ilterB

. What are the t$#es o R" al%orithmB

@. *om#are )" and R)" al%orithm

. What are the ste#s involved in )" al%orithm

7. What are the advanta%es and disadvanta%es o )" al%orithmB

C. What are the ste#s involved in !ei%hted R" al%orithmB

K. What is the e8#ression or minimum error in ))"+ criterion

PART -0

1. +8#lain in detail the )" al%orithm or direct 35R ilter

2. ;ive com#lete discussion on ho! )" al%orithm is conver%in% !ith necessar$e4uations and dia%rams

. +8#lain ada#tive ilterin% usin% stee#est descent method

@. +8#lain the need or ada#tive channel e4uali?ation in di%ital communication

. "ummari?e the ste#s involved in stee#est descent al%orithm

7. +8#lain the ollo!in%&

6i Ada#tive e4uali?ation 6ii +cho cancellation

C. Derive the mean s4uare error in R" al%orithm !ith o#timi?ation


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UNIT V

PART - A

1. What is inter#olationB2. What is the need or multi rate si%nal #rocessin%B

. What is the #rinci#le o su/ /and codin%B

@. Wh$ #ol$ #hase ilters are named soB

. Dra! an$ one o the no/le identit$ o an inter#olator

7. What is su/-/and codin%B ;ive a##lications

C. Dra! the direct orm reali?ation o 35R ilter in inter#olation /$ a actor 5

PART -0

1. +8#lain the inter#olation #rocess !ith an e8am#le

2. +8#lain a/out su/-/and codin% !ith necessar$ dia%rams

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