**THIS QUESTIONS ARE IMPORTANT QUESTIONS ONLY THIS MAY OR MAY NOT COME FOR EXAMS . WHO NEED GOOD GRADE PLEASE HAVE A LOOK OF ALL QUESTIONS
Unit 1
1. (a) For the systems represented by the following
functions. Determine whether
every system is (1) stable (2) Causal (3) linear (4) Shift
invariant (4)
(i) T[x(n)]= ex(n)
(ii) T[x(n)]=ax(n)+6
2. Determine whether the following systems are static or
Dynamic, Linear or Nonlinear,Shift variant or Invarient, Causal or Non-causal,
Stable or unstable. (4)
(i) y(t) = x(t+10) + x2(t)
(ii) dy(t)/dt + 10 y(t) = x(t)
3. Explain about the properties of continuous time fourier
series. (8)
4. Find the fourier coefficients of the given signal. (4)
x(t) = 1+ sin 2_ot + 2 cos 2_ot + cos (3_ot + _/3)
5. Determine the Fourier series coefficient of exponential
representation of x(t)
x(t) = 1, ItI (8)
0, T1< ItI < T/
2
6. Find the exponential series of the following signal.
(8)
7. Find which of the following signal are energy or power
signals. (8)
a) x(t)=e-3t u(t) b) x(t) = ej(2t+_/4) c) x(n)= cos(_/4n)
8. Explain the properties of Discrete time fourier serier
(8)
9. Find the cosine fourier series of an half wave rectified
sine function. (8)
10. Explain the classification of signals with examples. (8)
Unit 2
1. State and prove
properties of Fourier
transform.
(16)
2.a. State the properties of Fourier
Series.
(8)
b. Use the Fourier series analysis equation to calculate the coefficients ak for the
b. Use the Fourier series analysis equation to calculate the coefficients ak for the
continuous-time periodic
signal
(8)
1.5, 0 ≤ t 1;<
x (t ) <
−
1.5, 1 ≤ t 2<
with fundamental frequency ω0= It.
3. a.
State and prove Parseval’s power theorem and Rayleigh’s energy
theorem. (8)
b. Find the cosine Fourier series of an half wave rectified sine
function.
(8)
4. A
system is described by the differential equation,
d2y(t)/dt2+3dy(t)/dt+2y(t)= dx(t)/dt if y(0) =2;dy(0)/dt = 1 and
x(t)=e-t u(t)
Determine the response of the system to a unit step input applied
at t=0. (16)
5. Find the Fourier transform of
triangular pulse x (t) = _(t/m) ={1-2|t|/m |t|
0
otherwise
(16)
6. Determine
the Fourier series coefficient of exponential representation of x(t) x(t) = 1,
ItI
0, T1< ItI < T/
2
(16)
UNIT III
1. a. Give the
properties of convolution
Integral
(8)
b. Determine the state Equations and Matrix
representation of
systems
(8)
2. a. Describe the
properties of impulse
response
(8)
b. Determine y(t) by convolution integral if
x(t)=e at u(t) and
h(t)=u(t)
(8)
3. a. Find whether
the system is causal or not?
h(t)=e-2t u(t-1)
(8)
b. Give the summary of elementary blocks used to represent continuous time
b. Give the summary of elementary blocks used to represent continuous time
Systems
(8)
4. Find
the natural and forced response of an LTI system given
by
(16)
10dy (t)/dt+2y(t)=x(t)
10dy (t)/dt+2y(t)=x(t)
Univt 4
1. State and prove
properties of
DTFT.
(16)
2. a. Find the DTFT
of
x(n)={1,1,1,1,1,1,0,0}.
(8)
b. Find the convolution of x1(n)={1,2,0,1} ,
x2(n)={2,2,1,1}
(8)
3. a. State and prove
the sampling
theorem.
(8)
b Derive the Lowpass sampling
theorem.
(8)
4. Find the
z-transform of x(n)= an u(n) and for unit impulse
signal
(16)
5. a. Give the
relationship between z-transform and Fourier
transform.
(8)
b. Determine the inverse z transform of the
following
function
(8)
x(z)=1/(1+z-1) (1-z-1 )2 ROC : |Z>1|
Unit 5
1. a. State and prove
the properties of convolution
sum.
(8)
b. Determine the convolution of x(n)={1,1,2}
h(n)=u(n)-u(n-6)
graphically
(8)
2. Determine the
parallel form realization of the discrete time system
y(n) -1/4y(n-1) -1/8 y(n-2) = x(n)
+3x(n-1)+2x(n-2)
(16)
3. a. Determine the
transposed structure for the system given by difference equation
y(n)=(1/2)y(n-1)-(1/4)y(n-2)+x(n)+x(n-1)
(8)
b. Realize H(s)=s(s+2)/(s+1)(s+3)(s+4) in
cascade
form
(8)
4. a. Determine the recursive and
nonrecursive
system
(8)
b. Determine the parallel form realization of the discrete time
system is
y (n) -1/4y(n-1) -1/8 y (n-2) = x(n)
+3x(n-1)+2x(n-2)
(8)
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