AMIETE – ET/CS/IT (NEW SCHEME)
– Code:
AE57/AC57/AT57
Subject: SIGNALS AND SYSTEMS
Time: 3 Hours
Max. Marks: 100
NOTE: There are 9 Questions in all.
· Question 1 is
compulsory and carries 20 marks. Answer to Q. 1 must be written in the space
provided for it in the answer book supplied and nowhere else.
· Out of the
remaining EIGHT Questions, answer any FIVE Questions. Each question carries 16
marks.
· Any required data
not explicitly given, may be suitably assumed and stated.
Q.1 Choose the correct or the best alternative in the following: (2
10)
a. Signal
x (t) = cos t if t < 0; and x (t) = sin t if t > 0 is _________.
(A) periodic (B) non-periodic
(C) limitedly
periodic (D) can’t define
b. System y (n) = [2x (n) – x 2(n)] 2 is __________.
(A) with
memory (B) memory less
(C) requires
additional data (D) can’t defined
c. u(n)
=
is correct ___________.
(A) all
time (B) sometime
(C) never (D) requires additional data
d. For
h (n) = an u (n); H (e 
)
equals __________.
(A) 1 /
(1 – a e
) (B) 1 / (1 + a e )
(C) 1 / (1
+ a e
) (D) 1 / (1 – a e )
e. Fourier
transform of x (t) =1 is ________.
(A) 2π δ (
) (B) π δ ()
(C) π/2 δ () (D) 2π δ (2)
f. In filter, the width of the ‘Transition Band’ is Characteristics
of ________.
(A) Fourier
series (B) Fourier Transform
(C) Frequency
domain (D) Time domain
g. Any signal x (t) can be represented as ____________.
(A) xe(t)
(B) xe(t) – xo(t)
(C) 
(D) xe(t) xo(t)
where xe(t) and xo(t) are even and odd parts
of the signal x(t).
h. x
( 0 + ) = 
defines __________.
(A)
initial value Theorem (B) final value theorem
(C) both
(A) & (B) (D)
None.
i. The ROC does not
contain any pole in Z-transform. This statement is _________.
(A) false (B) true
(C) requires
Additional data (D) can’t
define
j. All ergodic
processes are ___________ processes.
(A) non -
stationary (B) marginally - stationary
(C) stationary (D) semi - stationary
Answer any FIVE
Questions out of EIGHT Questions.
Each question
carries 16 marks.
Q.2 a. Consider
the system y (n) = 2 x (n) + 3. Determine whether the system is linear or non–linear.
Calculate the Zero-Input Response of the system. Draw the structure of the
above system. (8)
b. For an LTI system with input x (n) and unit
impulse response h(n) specified as follows:
x (n) = 2 n u (–n) & h (n) =
u(n) ;
determine
and plot output signal y(n). (8)
Q.3 a. Consider
the periodic impulse train 
and defined by 
. Determine the complex exponential Fourier series of .
(8)
b. Plot magnitude and phase of
the Fourier coefficients for the signal
x (t) = 1 + sin t + 2cos t + cos (2 t + π /4);
where ω is the
fundamental frequency of the signal. (8)
Q.4 a. Let
; a > 0. Plot signal x (t).
Also, obtain and plot Fourier Transform of signal x (t). (8)
b.
Consider a stable LTI system
characterized by the differential equation
d 2 y (t) / dt 2 + 4 dy(t)
/ dt + 3y(t) = d x(t) / d(t) + 2x(t).
Obtain h (t). (8)
Q.5 a. For
the periodic signal x (n) =cos on ; Obtain & plot Discrete Time
Fourier Transform
of x (n), where o is the fundamental frequency of
the signal. (8)
b. Consider a causal LTI system characterized
by the difference equation
y(n) – ( 3 / 4) y ( n–1) + ( 1 / 8) y ( n – 2)
= 2 x(n) ; Obtain frequency. (8)
Q.6 a. Explain
the following with suitable example: (8)
(i) Linear and non-linear phase
(ii) Group delay
b. Define
NYQUIST RATE and ALIASING. Determine the Nyquist rate corresponding to each of
the following signals: (8)
(i) x (t) = 1+ cos( 2000 π t)+ sin (4000
π t)
(ii) x (t) = sin
(4000 π t) / π t
(iii) x (t) = { sin (4000
π t) / π t }2
Q.7 a. Obtain
the
x(t) = e – 2t u(t) + e – t (cos3t) u(t). (8)
b. The output y (t) of a continuous-time LTI
system is found to be 
when the input x (t)
is u (t). Find the impulse response h (t)
of the system. using Laplace Transform. (8)
Q.8 a. A wide sense stationary noise process has an
autocorrelation function
Rnn ( τ ) = K e –3
| τ | where K is a constant.
Find its power spectral density. (8)
b. Write a short note on: (8)
(i) Power Spectral Density.
(ii) Gaussian Processes.
Q.9 a. y(n) – (1 /2) y (n–1) = x (n) + (1/3) x (n–1);
Obtain impulse response of the system using Z-transform only for ROC | z|
>1. (8)
b. For the signal x (n) = an, 0 ≤ n
≤ N–1; a > 0 and x (n) = 0, otherwise. Calculate the Z-Transform of x (n). Plot pole-zero
pattern for N =16. (8)