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ASSIGNMENT| February 10
2011
|
SIGNALS AND SYSTEMS ASSIGNMENT SUBMITTED BY ALL THE STUDENTS OF ELECTRONICS AND TELECOMMUNICATION| |

EVEN AND ODD SIGNAL QUESTIONS

Sketch the following signals and determine and sketch their even and odd componenets: 1) x(t)=0.8t;0≤t≤40;otherwise

2) x(t)=1;0≤n≤40;otherwise

3) x(t)=10e-2tu(t)

4) x(t)=n for 1≤n≤30;otherwise

5) x(t)=sint+2sint+2sin2tcost

6) x(t)=cost + sin t + cost sin t

7) x(t)=4ejt+3π4u(t)

8) y(t)=x(t)sin100πt

9) y(t)=10x(t)+5

10) y(t)=x2t-t0+2

11) x(t)= cos (10πt).u(2-t)

12) x(t)=ejt

13) x(t)=sin(w0t+π4)

14) x(t)=(1+t3)cos310t

15) x(t)=1+t+3t2+5t3+9t4

16) x(n)=sin(5n) cos (7n)

17) x(t)=e-2tcost

18) Let x(t) be an arbitrary signal with even and odd parts denoted by xet and x0t, respectively. show that

-∞∞x2tdt = -∞∞xe2tdt+-∞∞x02tdt

Let x[n] be an arbitrary sequence with even and odd parts denoted by xe[n] and x0[n], respectively. Show that n=-∞∞x2n= n=-∞∞xe2n+n=-∞∞x02[n]
19) x(t)=u(t)-r(t-1)+2r(t-2)-r(t-3)+u(t-4)-2u(t-5)

20) Show that if x1n is an odd signal and x2n is an even signal, then x1n.x2n is an odd signal.

21) Find the even and odd components of x(n)={3,2,1,4,5}. 22) Find even and odd components of the given signal

23) Find even and odd components of the signal
24) Find even and odd components of the given signal

25) Find even and odd components of the signal
26) Draw the even and odd representations of the signal

27) Decompose the signal shown into its odd and even parts?

28) If x(n) is odd signal , show that n=-∞∞xn=0

29) Show that
If x(t) and x(n) are even, then
-aaxtdt=20axtdt

n=-kkxn=x0+2n=1kx[n]

30) Find the even and odd components of the signal

31) Find the even and odd components of x(t)=ejt

32) Show that the product of two even signals or two odd signals is an even signal and that the product of ans even and an odd signal is an odd signal.

33) Find the even and odd components of the signal

34) Show that

If x(t) and x(n) are even, then
x(0)=0 and x[0]=0

-aaxtdt=0 and n=-kkxn=0

35) Consider a signal

sinπtT;-T≤t≤T0;otherwise

Is the signal x(t) an even or odd function of time t?

36) Find even and odd component part of signal

PERIODIC AND APERIODIC SIGNAL QUESTIONS
1) Verify whether the following continuous time signal is periodic. If periodic, find the fundamental period
x(t)=cos2(2t-π4)
Find whether the following signal are periodic or not. If so, find the fundamental period:
2) x(t)=sin(15πt)

3) x(t)=Aejwt+∅

4) x(t)=e-2t

5) x(t)=2cos(10πt+π6)

6) x(t)=sin2t

7) x(t)=cosπ3t+sinπ3t

8) x(t)=cost+sin√2

9) x[n]=cos14n

10) zn=4sin8πn3+7π8

11) x(n)=1+ej4πn7 - ej2πn5
12) x(n)=ejπn4

13) x(t)=cos√2 πt

14) x(t)=ej2πt

15) x(t)=3sin(19πt- π3)

16) x(t)=sin 0.1t

17) x(t)=cos2t+cos5t

18) x(t)=4ejt+3π4u(t)

19) x[n]=u[n]+u[2-n]

20) xt=e-5tu(t)

21) x(t)=cos(√2t)+cos(t)

22) Determine the fundamental period of the signal g(t)=4 cos(20t+1)-2 sin(8t-1).

23) Consider the sinusoidal signal x(t)=cos 10t

a) Find the value of sampling interval Ts such that x[n]=x(nTs) is a periodic sequence. b) Find the fundamental period...
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