Download AKTU B-Tech 3rd Sem 2017-2018 REC303 Signal And System Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 3rd Semester (Third Semester) 2017-2018 REC303 Signal And System Question Paper

Printed pages: 2 Roll No. m Sub Code: REC303
Paper ID: 3 0 0 9
B.TECH
(SEM III) THEORY EXAMINATION 2017-18
SIGNAL AND SYSTEM
T ime: 3 Hours T otal Marks: 70
Note: Attempt all Sections. If require any missing data; then choose suitably.
SECTION - A
Q1. ATTEMPT ALL QUESTIONS IN BRIEF. 2 x 7 = 14
a). Check the periodicity of the signals given below. Determine the fundamental
time period if signal is periodic:-
x(t) = $in(10t ? 1) ? $in(4t ? 1)
b). Find the DTFT 0f the causal sequence x (n) = a"u(n); IaI < 1
c). Check whether the given system are Time Variant and Causal y (t) = tx(t)
(1). State the convolution property for continuous and discrete time domain signal
in z-transform.
e). Determine the Laplace transform & find out ROC for X(t)=e'tu(t)+e'4tu(t)
f). Draw the signal X(t)= u(t)- u(t-Z).
g).Using ?nal value theorem find final value of signal corresponding to Laplace
transform
5 + 1
_ 5(5 + 2)(s + 8)
SECTION-B
X (5)
Q2. ATTEMPT ANY THREE PARTS OF THE FOLLOWING (3*7=21)
a). Find and sketch the autocorrelation unction Rxx(t) forX(t) = e'at u(t), a >0
b). Find the convolution for given sequence
X[n]=l for n=-2,0,l
2 for n=-1
0 else
and h[n]=5[n] ? 5[n-l] + 5[n-2] ? 5[n-3]
c). Find the Fourier transform of the signals given below:-
, A, t < T .. -
1) 9605) = {0? H > T211) X (t)= e at u (t)
Draw the magnitude and phase response of the transformed signal.
55?7
: ? ' ? ? ' ?7
d) If X(S) (5?1) S+Z)W1th 2 < R{S} < 1. F1nd X (t).
e). state and prove sampling theorem and discuss the effect of under sampling.

Q3. ATTEMPT ANY ON E PART OF THE F OLLOWIN G 7*l=7
a). i). What is signal?Give brief classification of signals.
ii). Prove that power of energy signal is zero over infinite time.
b). Plot X(t)=u(t) ?r(t-1)+ 2r(t-2)-r(t-3)+u(t-4)-2u(t-5). Find the even and odd parts of this
signal.
Q4. ATTEMPT ANY ON E PARTS OF THE FOLLOWIN G 7*1=7
a). Determine whether the following continuous time system
y(t)= x(t) cos (100m) is
i) static or dynamic ii) linear or nonlinear iii) shift variant or shift invariant
iV) causal or noncausal V) stable or unstable.
b). Find energy and power of the signal
i). X(t)=cos(t) ii)X(t)=Ae'mu(t), 0L>0
Q5. ATTEMPT ANY ONE PART OF THE F OLLOWIN G 7*l=7
a). An LTI system with impulse response h1 (n)
h1(n)= (1/3) u(n)
is connected in parallel with another causal LTI system with impulse response h2(n). The
resulting parallel interconnection has the frequency response.
. ?12 -1'W
H(e1w)) = + Se
12 ? 7e?jW + e?ziw
find the impulse response h2(n).
b). Find the F ourier transform of the signal X(t) =e'at u(t) and plot is magnitude and phase
spectrum.
Q6. ATTEMPT ANYONEPART OF THE FOLLOWING 7*1=7
a). i)Show that if X3(t)=aX1(t)+bX2(t) thenX3(S)=aX1(S)+bX2(S)
ii) If Laplace transform of x(t) is (s+2)/(SZ+4s+5). Determine Laplace transform of
y(t)=x(2t-1)u(2t-1)
b). A causal LTI system is described by difference equation.
y(n) = y(n-l) +y(n-2) + X(n-l)
Find the system function H(z) for this system. Plot the poles zeros of H(z) and indicate the region
of convergence.
Q7. ATTEMPT ANY ON E PART OF THE F OLLOWIN G 7*l=7
a). Consider the two continuous-time sinusoidal signals
X1(t)=COS(20?Zt) and X2(t)=COS(1007Et)
Which are sampled at a rate fs=40HZ. F ind the corresponding discrete time signals.
b). Explain system bandwidth and rise time for low pass filter and prove that
tr=0.35/B