ece 3500 signals and systems quiz solutions quiz 2

1
UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL & COMPUTER ENGINIEERING ECE BEOO FUNDAMENTALS OF SIGNALS AND SYSTEMS September 8, 2011 Qlrz ffz L. A(t) is generated from r(t) using a series of transformations as shown in the figure. -9 $(t): o€ -:) < (-rt*> {(t): o(t -:) < eu t-e) ^;- *t_ {_{ _6: What is the mathematical expression that relates the output y(t) of the overall system to its input signal c(t). 3(+N { ,( (+ *}) We wish to implement the same system using a seriEs of three traasformations or less from scaling along the time a>cis, reflection about the y axis and time shifting. How will you do this? (") (b) '."i *-+''{( +-) " t" \ t^-J *r{ b; L / -4r. '/. "x i:1, *9_\ ''"?* *l Compressalong thetime axisby a factorof 2 Expand along the time alds by a factorof 4

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ECE 3500 Signals and Systems Quiz Solutions Quiz 2

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Page 1: ECE 3500 Signals and Systems Quiz Solutions Quiz 2

UNIVERSITY OF UTAHDEPARTMENT OF ELECTRICAL & COMPUTER ENGINIEERING

ECE BEOO FUNDAMENTALS OF SIGNALS AND SYSTEMS September 8, 2011

Qlrz ffz

L. A(t) is generated from r(t) using a series of transformations as shown in the figure.

-9

$(t): o€ -:) < (-rt*>{(t): o(t -:) < eu t-e) ^;- *t_ {_{ _6:What is the mathematical expression that relates the output y(t) of the overall system

to its input signal c(t). 3(+N { ,( (+ *})We wish to implement the same system using a seriEs of three traasformations or less

from scaling along the time a>cis, reflection about the y axis and time shifting. How willyou do this?

(")

(b)

'."i*-+''{( +-) " t"\ t^-J*r{b;L

/ -4r.

'/. "x i:1, *9_\''"?* *l

Compressalongthetime axisby

a factorof 2

Expand along thetime alds by a

factorof 4