8/12/2019 CCE406APro004 (1)

1/2

American University of Science & Technology

Department of Computer and Communications Engineering

CCE406 - Project 2

Due date: Last week of Januar 20!4

Part A

1) Consider the discrete-time periodic sqare !ave" "#nx having the

fndamental period N#

=otherwise

LnAnx

0

!0"#

$Pay attention, it is a periodic sequence.)

a) %ra! the seqence "#nx sing AT'A( $consider A1* L+ and N1,)

.) Calclate the /orier series coefficients { }kc and the po!er density spectrm2

kc of "#nx

c) Plot* sing AT'A(* the spectrm { }kc of "#nx for A1 and#i) L+0 N,

ii) L+0 N2,

iii) L30 N2,

Compare the 4 graphs and discss

5) Consider the discrete-time aperiodic rectanglar plse "#ny defined .y#

=otherwise

LnAny

0

!0"#

a) Plot "#ny sing AT'A( $consider L+)

.) 6valate the /orier transform or the spectrm $%wX of "#ny

c) Plot* sing AT'A(* the magnitde $%wX and phase spectra$%wX for A1 and L+

d) 6valate the /orier transform at a set of eqally spaced $harmonically

related) freqencies kw * ie evalate

N

kX

2!ith N2,

7erify that kNcN

kX =

2

!here N2, and !here { }kc are the /orier

series coefficients o.tained in part A for the periodic seqence "#nx

8/12/2019 CCE406APro004 (1)

2/2

e) Sho!* for k,* 88*N-1*

N

kX

2on the same graph of $%wX

f) 9ive a .rief analysis of the stdy done on part %

Part (

1) %etermine and s:etch the magnitde and phase response of the follo!ingfilters#

a) [ ]$!%$!%2

!"# ++= nxnxny

.) [ ]$&%$2%&$!%&$%'

!"# +++= nxnxnxnxny

5) ;o :no! that an 'T< system can .e represented in several eqivalent !ays