PI 30

P2 25

P3 115

P4 30

Total 100

EENGINFE 420 Digital Signal Processing

SPRING 2014-2015

QUIZ 1

Na me(full) __________ Date 0604201 5

St Number ________ Duration 50 min

Lecturer Assoc Prof Dr Erhan A ince

Read the following instructions carefully

I) Please put your name on both the question paper and the answer sheet 2) Usejront and back of each page on the anwers booklet to answer each question 3) After the exam submit both the question paper and your solution booklet

Problem 1 Consider an accumulator described by the input-output relationship depicted below and

determine if the system is (a) linear (b) time invariant

Ln

x[l]y[n] = 1=-00

Problem 2 Consider an up-sampler with an input-output relationship as shown below

n = 0 plusmnL plusmn2L

otherwise

Is this system time invariant or time varying Justify your answer by showing work

Problem 3 Explain how a non-causal FIR system can be made causal To justify your answer you may

use an example

Problem 4 Consider an LTI system with inputx[n] and unit impulse response h[n] as given below

x[n] = 2n u[-n]

h[n] = u[1-]

Determine the output y [ n] of the systemmiddot

P(ob~1~

Accu(h u(~WI

alJ Lf

x(eJ

e - 00

~

~t-(nl =- h2 Yl-f~j

Y f

J[1j 4~L] =-- ~ L X[~J -t b L Xl-((1

-e~ ~-o

~

f X(J ~ C z (U -+ I lzf(j --7 ~ [1 2 ctgtlt [lj j~t ttl egt-Jgt

1 1 ~ c L fi [(j +S Z x~[R)

-( -0004 (=~o

i gt

~ sw~ puJ- x CJ ~ x fL -lJ ~r + 1- (viCoJC~ O~V ) [l- eo J a otlgt j CRJ COIrC1f-cL

---e~

~ lt - middotl~J L X l~J k- -ca)

J e ~ [J~ L ~ I [~J =- L X [k -~J

aCc(flltAI~r 5 c

tl~- fvW( ct1 Sj~t-e(l1

VrobefY 2 shy

U f- gtcllrVL

( 0li LI 02l X [1Ij t~(IlLJ

othvLw 5l2

n -=-u il ~ I I

u~u

X (gt-I1J ~ t~ [0deg-10)~ (l= flogt (IplusmnL) ( 170 plusmnzy o

~Se- ~

9

v 0 - ~AscrJL f Il S J sk IV C ot bz rYc ck cauS o-l b j s )S~ ~Ifh- all- ~ppngtr(iC-k1J chC2co(co~~i~ k

5jsklt

~ [d- S(A of 0 - 6 0~ ) bull L

1lN5 s 15k-- lgtr h(l 0- c Ct -cs tLQ

------~--~--------~~ 5 I(-L 11[J =i 0

-I ~( lt0

yrobefY 1Ij

- X[) ~ 02it 1) C-r0 ~ L~ ~ vt lJ hQ) ~ vck)

00 -- 0 0 ----1shy____--+ 1 ~11~11~ k

od (~J ~ L t-[tJ h(tl-8 L- -ob _~ll ~l ~-k~ ~ J ~ 1 ~_~abull

o ~(n-J k

middot - 11111])(1 bull p bull

o

~ [lj IS 22Ao ~ V l gt0

h lJl - kJ S 2flAo ftr ~gtfL

o

L

- 2 ~[Ij - () =

I - ti)

~( ~ 0 JllJ= 2shy

vJhL- Alt-v

Cipound)n ltl -f 00

= ~ jLl=- L L ~ (1shyd(0 L

~

~ -k ~ - - fshy(- - n--=- _0

P(ob~1~

Accu(h u(~WI

alJ Lf

x(eJ

e - 00

~

~t-(nl =- h2 Yl-f~j

Y f

J[1j 4~L] =-- ~ L X[~J -t b L Xl-((1

-e~ ~-o

~

f X(J ~ C z (U -+ I lzf(j --7 ~ [1 2 ctgtlt [lj j~t ttl egt-Jgt

1 1 ~ c L fi [(j +S Z x~[R)

-( -0004 (=~o

i gt

~ sw~ puJ- x CJ ~ x fL -lJ ~r + 1- (viCoJC~ O~V ) [l- eo J a otlgt j CRJ COIrC1f-cL

---e~

~ lt - middotl~J L X l~J k- -ca)

J e ~ [J~ L ~ I [~J =- L X [k -~J

aCc(flltAI~r 5 c

tl~- fvW( ct1 Sj~t-e(l1

VrobefY 2 shy

U f- gtcllrVL

( 0li LI 02l X [1Ij t~(IlLJ

othvLw 5l2

n -=-u il ~ I I

u~u

X (gt-I1J ~ t~ [0deg-10)~ (l= flogt (IplusmnL) ( 170 plusmnzy o

~Se- ~

9

v 0 - ~AscrJL f Il S J sk IV C ot bz rYc ck cauS o-l b j s )S~ ~Ifh- all- ~ppngtr(iC-k1J chC2co(co~~i~ k

5jsklt

~ [d- S(A of 0 - 6 0~ ) bull L

1lN5 s 15k-- lgtr h(l 0- c Ct -cs tLQ

------~--~--------~~ 5 I(-L 11[J =i 0

-I ~( lt0

yrobefY 1Ij

- X[) ~ 02it 1) C-r0 ~ L~ ~ vt lJ hQ) ~ vck)

00 -- 0 0 ----1shy____--+ 1 ~11~11~ k

od (~J ~ L t-[tJ h(tl-8 L- -ob _~ll ~l ~-k~ ~ J ~ 1 ~_~abull

o ~(n-J k

middot - 11111])(1 bull p bull

o

~ [lj IS 22Ao ~ V l gt0

h lJl - kJ S 2flAo ftr ~gtfL

o

L

- 2 ~[Ij - () =

I - ti)

~( ~ 0 JllJ= 2shy

vJhL- Alt-v

Cipound)n ltl -f 00

= ~ jLl=- L L ~ (1shyd(0 L

~

~ -k ~ - - fshy(- - n--=- _0

VrobefY 2 shy

U f- gtcllrVL

( 0li LI 02l X [1Ij t~(IlLJ

othvLw 5l2

n -=-u il ~ I I

u~u

X (gt-I1J ~ t~ [0deg-10)~ (l= flogt (IplusmnL) ( 170 plusmnzy o

~Se- ~

9

v 0 - ~AscrJL f Il S J sk IV C ot bz rYc ck cauS o-l b j s )S~ ~Ifh- all- ~ppngtr(iC-k1J chC2co(co~~i~ k

5jsklt

~ [d- S(A of 0 - 6 0~ ) bull L

1lN5 s 15k-- lgtr h(l 0- c Ct -cs tLQ

------~--~--------~~ 5 I(-L 11[J =i 0

-I ~( lt0

yrobefY 1Ij

- X[) ~ 02it 1) C-r0 ~ L~ ~ vt lJ hQ) ~ vck)

00 -- 0 0 ----1shy____--+ 1 ~11~11~ k

od (~J ~ L t-[tJ h(tl-8 L- -ob _~ll ~l ~-k~ ~ J ~ 1 ~_~abull

o ~(n-J k

middot - 11111])(1 bull p bull

o

~ [lj IS 22Ao ~ V l gt0

h lJl - kJ S 2flAo ftr ~gtfL

o

L

- 2 ~[Ij - () =

I - ti)

~( ~ 0 JllJ= 2shy

vJhL- Alt-v

Cipound)n ltl -f 00

= ~ jLl=- L L ~ (1shyd(0 L

~

~ -k ~ - - fshy(- - n--=- _0

yrobefY 1Ij

- X[) ~ 02it 1) C-r0 ~ L~ ~ vt lJ hQ) ~ vck)

00 -- 0 0 ----1shy____--+ 1 ~11~11~ k

od (~J ~ L t-[tJ h(tl-8 L- -ob _~ll ~l ~-k~ ~ J ~ 1 ~_~abull

o ~(n-J k

middot - 11111])(1 bull p bull

o

~ [lj IS 22Ao ~ V l gt0

h lJl - kJ S 2flAo ftr ~gtfL

o

L

- 2 ~[Ij - () =

I - ti)

~( ~ 0 JllJ= 2shy

vJhL- Alt-v

Cipound)n ltl -f 00

= ~ jLl=- L L ~ (1shyd(0 L

~

~ -k ~ - - fshy(- - n--=- _0