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)=10e2tu(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)=x2tt0+2
11) x(t)= cos (10πt).u(2t)
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)=e2tcost
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(t1)+2r(t2)r(t3)+u(t4)2u(t5)
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(2tπ4)
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)=e2t
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[2n]
20) xt=e5tu(t)
21) x(t)=cos(√2t)+cos(t)
22) Determine the fundamental period of the signal g(t)=4 cos(20t+1)2 sin(8t1).
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...